diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 9fa26644..1d324ecb 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -11,11 +11,11 @@ jobs:
       fail-fast: false
       matrix:
         include:
+          - elixir: "1.15.6"
+            otp: "26.1"
+            lint: true
           - elixir: "1.14.5"
-            otp: "24.3"
-          - elixir: "1.15.4"
             otp: "25.3"
-            lint: true
     steps:
       - uses: actions/checkout@v2
 
diff --git a/README.md b/README.md
index 0533a518..b07e9ab4 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,11 @@
-<h1><img src="./images/scholar.png" alt="Scholar" width="400"></h1>
+<p align="center">
+  <img src="https://github.com/elixir-nx/scholar/raw/main/images/scholar.png" alt="Scholar" width="400">
+  <br />
+  <a href="https://hexdocs.pm/scholar"><img src="http://img.shields.io/badge/hex.pm-docs-green.svg?style=flat" title="Documentation" /></a>
+  <a href="https://hex.pm/packages/scholar"><img src="https://img.shields.io/hexpm/v/scholar.svg" title="Package" /></a>
+</p>
 
-[![Documentation](http://img.shields.io/badge/hex.pm-docs-green.svg?style=flat)](https://hexdocs.pm/scholar)
-[![Package](https://img.shields.io/hexpm/v/scholar.svg)](https://hex.pm/packages/scholar)
+<br />
 
 Traditional machine learning tools built on top of Nx. Scholar implements
 several algorithms for classification, regression, clustering, dimensionality
@@ -45,6 +49,15 @@ config :nx, :default_backend, EXLA.Backend
 config :nx, :default_defn_options, [compiler: EXLA, client: :host]
 ```
 
+> #### JIT required! {: .warning}
+>
+> It is important you set the `default_defn_options` as shown in the snippet above,
+> as many algorithms in Scholar use loops which are much more memory efficient when
+> JIT compiled.
+>
+> If for some reason you cannot set a default `defn` compiler, you can explicitly
+> JIT any function, for example: `EXLA.jit(&Scholar.Cluster.AffinityPropagation.fit/1)`.
+
 ### Notebooks
 
 To use Scholar inside code notebooks, run:
@@ -60,6 +73,15 @@ Nx.global_default_backend(EXLA.Backend)
 Nx.Defn.global_default_options(compiler: EXLA, client: :host)
 ```
 
+> #### JIT required! {: .warning}
+>
+> It is important you set the `Nx.Defn.global_default_options/1` as shown in the snippet
+> above, as many algorithms in Scholar use loops which are much more memory efficient
+> when JIT compiled.
+>
+> If for some reason you cannot set a default `defn` compiler, you can explicitly
+> JIT any function, for example: `EXLA.jit(&Scholar.Cluster.AffinityPropagation.fit/1)`.
+
 ## License
 
 Copyright (c) 2022 The Machine Learning Working Group of the Erlang Ecosystem Foundation
diff --git a/benchmarks/kd_tree.exs b/benchmarks/kd_tree.exs
new file mode 100644
index 00000000..18dda797
--- /dev/null
+++ b/benchmarks/kd_tree.exs
@@ -0,0 +1,15 @@
+# mix run benchmarks/kd_tree.exs
+Nx.global_default_backend(EXLA.Backend)
+Nx.Defn.global_default_options(compiler: EXLA)
+
+key = Nx.Random.key(System.os_time())
+{uniform, _new_key} = Nx.Random.uniform(key, shape: {1000, 3})
+
+Benchee.run(
+  %{
+    "unbounded" => fn -> Scholar.Neighbors.KDTree.unbounded(uniform) end,
+    "bounded" => fn -> Scholar.Neighbors.KDTree.bounded(uniform, 2) end
+  },
+  time: 10,
+  memory_time: 2
+)
diff --git a/lib/scholar.ex b/lib/scholar.ex
deleted file mode 100644
index abf64ad8..00000000
--- a/lib/scholar.ex
+++ /dev/null
@@ -1,11 +0,0 @@
-defmodule Scholar do
-  @moduledoc """
-  Traditional machine learning tools built on top of Nx. Scholar implements
-  several algorithms for classification, regression, clustering, dimensionality
-  reduction, metrics, and preprocessing.
-
-  For deep learning, see [Axon](https://github.com/elixir-nx/axon).
-
-  Click on the "Guides" tab for some example notebooks.
-  """
-end
diff --git a/lib/scholar/cluster/affinity_propagation.ex b/lib/scholar/cluster/affinity_propagation.ex
index b2523829..028710d2 100644
--- a/lib/scholar/cluster/affinity_propagation.ex
+++ b/lib/scholar/cluster/affinity_propagation.ex
@@ -4,6 +4,10 @@ defmodule Scholar.Cluster.AffinityPropagation do
   of `:clusters_centers` is set to the number of samples in the dataset.
   The artificial centers are filled with `:infinity` values. To fillter
   them out use `prune` function.
+
+  The algorithm has a time complexity of the order $O(N^2T)$, where $N$ is
+  the number of samples and $T$ is the number of iterations until convergence.
+  Further, the memory complexity is of the order $O(N^2)$.
   """
 
   import Nx.Defn
@@ -13,16 +17,16 @@ defmodule Scholar.Cluster.AffinityPropagation do
            containers: [
              :labels,
              :cluster_centers_indices,
-             :affinity_matrix,
              :cluster_centers,
-             :num_clusters
+             :num_clusters,
+             :iterations
            ]}
   defstruct [
     :labels,
     :cluster_centers_indices,
-    :affinity_matrix,
     :cluster_centers,
-    :num_clusters
+    :num_clusters,
+    :iterations
   ]
 
   @opts_schema [
@@ -39,9 +43,18 @@ defmodule Scholar.Cluster.AffinityPropagation do
       current value is maintained relative to incoming values (weighted 1 - damping).
       """
     ],
-    self_preference: [
-      type: {:or, [:float, :boolean, :integer]},
-      doc: "Self preference."
+    preference: [
+      type: {:or, [:float, :atom]},
+      default: :reduce_min,
+      doc: """
+      How to compute the preferences for each point - points with larger values
+      of preferences are more likely to be chosen as exemplars. The number of clusters is
+      influenced by this option.
+
+      The preferences is either an atom, each is a `Nx` reduction function to
+      apply on the input similarities (such as `:reduce_min`, `:median`, `:mean`,
+      etc) or a float.
+      """
     ],
     key: [
       type: {:custom, Scholar.Options, :key, []},
@@ -56,6 +69,14 @@ defmodule Scholar.Cluster.AffinityPropagation do
       doc: ~S"""
       If `true`, the learning loop is unrolled.
       """
+    ],
+    converge_after: [
+      type: :pos_integer,
+      default: 15,
+      doc: ~S"""
+      Number of iterations with no change in the number of estimated clusters
+      that stops the convergence.
+      """
     ]
   ]
 
@@ -70,8 +91,6 @@ defmodule Scholar.Cluster.AffinityPropagation do
 
   The function returns a struct with the following parameters:
 
-    * `:affinity_matrix` - Affinity matrix. It is a negated squared euclidean distance of each pair of points.
-
     * `:clusters_centers` - Cluster centers from the initial data.
 
     * `:cluster_centers_indices` - Indices of cluster centers.
@@ -81,32 +100,25 @@ defmodule Scholar.Cluster.AffinityPropagation do
   ## Examples
 
       iex> key = Nx.Random.key(42)
-      iex> x = Nx.tensor([[12,5,78,2], [1,-5,7,32], [-1,3,6,1], [1,-2,5,2]])
+      iex> x = Nx.tensor([[12,5,78,2], [9,3,81,-2], [-1,3,6,1], [1,-2,5,2]])
       iex> Scholar.Cluster.AffinityPropagation.fit(x, key: key)
       %Scholar.Cluster.AffinityPropagation{
-        labels: Nx.tensor([0, 3, 3, 3]),
-        cluster_centers_indices: Nx.tensor([0, -1, -1, 3]),
-        affinity_matrix: Nx.tensor(
-          [
-            [-0.0, -6162.0, -5358.0, -5499.0],
-            [-6162.0, -0.0, -1030.0, -913.0],
-            [-5358.0, -1030.0, -0.0, -31.0],
-            [-5499.0, -913.0, -31.0, -0.0]
-          ]),
+        labels: Nx.tensor([0, 0, 2, 2]),
+        cluster_centers_indices: Nx.tensor([0, -1, 2, -1]),
         cluster_centers: Nx.tensor(
           [
             [12.0, 5.0, 78.0, 2.0],
             [:infinity, :infinity, :infinity, :infinity],
-            [:infinity, :infinity, :infinity, :infinity],
-            [1.0, -2.0, 5.0, 2.0]
+            [-1.0, 3.0, 6.0, 1.0],
+            [:infinity, :infinity, :infinity, :infinity]
           ]
         ),
-        num_clusters: Nx.tensor(2, type: :u64)
+        num_clusters: Nx.tensor(2, type: :u64),
+        iterations: Nx.tensor(22, type: :s64)
       }
   """
   deftransform fit(data, opts \\ []) do
     opts = NimbleOptions.validate!(opts, @opts_schema)
-    opts = Keyword.update(opts, :self_preference, false, fn x -> x end)
     key = Keyword.get_lazy(opts, :key, fn -> Nx.Random.key(System.system_time()) end)
     fit_n(data, key, NimbleOptions.validate!(opts, @opts_schema))
   end
@@ -115,13 +127,11 @@ defmodule Scholar.Cluster.AffinityPropagation do
     data = to_float(data)
     iterations = opts[:iterations]
     damping_factor = opts[:damping_factor]
-    self_preference = opts[:self_preference]
-    data = to_float(data)
-
-    {initial_a, initial_r, s, affinity_matrix} =
-      initialize_matrices(data, self_preference: self_preference)
+    converge_after = opts[:converge_after]
+    n = Nx.axis_size(data, 0)
+    s = initialize_similarity(data, opts)
 
-    {n, _} = Nx.shape(initial_a)
+    zero_n = Nx.tensor(0, type: Nx.type(s)) |> Nx.broadcast({n, n})
     {normal, _new_key} = Nx.Random.normal(key, 0, 1, shape: {n, n}, type: Nx.type(s))
 
     s =
@@ -132,9 +142,12 @@ defmodule Scholar.Cluster.AffinityPropagation do
 
     range = Nx.iota({n})
 
-    {{a, r}, _} =
-      while {{a = initial_a, r = initial_r}, {s, range, i = 0}},
-            i < iterations do
+    e = Nx.broadcast(Nx.s64(0), {n, converge_after})
+    stop = Nx.u8(0)
+
+    {{a, r, it}, _} =
+      while {{a = zero_n, r = zero_n, i = 0}, {s, range, stop, e}},
+            i < iterations and not stop do
         temp = a + s
         indices = Nx.argmax(temp, axis: 1)
         y = Nx.reduce_max(temp, axes: [1])
@@ -160,7 +173,24 @@ defmodule Scholar.Cluster.AffinityPropagation do
         temp = temp * (1 - damping_factor)
         a = a * damping_factor - temp
 
-        {{a, r}, {s, range, i + 1}}
+        curr_e = Nx.take_diagonal(a) + Nx.take_diagonal(r) > 0
+        curr_e_slice = Nx.reshape(curr_e, {:auto, 1})
+        e = Nx.put_slice(e, [0, Nx.remainder(i, converge_after)], curr_e_slice)
+        k = Nx.sum(curr_e, axes: [0])
+
+        stop =
+          if i >= converge_after do
+            se = Nx.sum(e, axes: [1])
+            unconverged = Nx.sum((se == 0) + (se == converge_after)) != n
+
+            if (not unconverged and k > 0) or i == iterations do
+              Nx.u8(1)
+            else
+              stop
+            end
+          end
+
+        {{a, r, i + 1}, {s, range, stop, e}}
       end
 
     diagonals = Nx.take_diagonal(a) + Nx.take_diagonal(r) > 0
@@ -198,14 +228,28 @@ defmodule Scholar.Cluster.AffinityPropagation do
       end
 
     %__MODULE__{
-      affinity_matrix: affinity_matrix,
       cluster_centers_indices: cluster_centers_indices,
       cluster_centers: cluster_centers,
       labels: labels,
-      num_clusters: k
+      num_clusters: k,
+      iterations: it
     }
   end
 
+  defnp initialize_similarity(data, opts \\ []) do
+    n = Nx.axis_size(data, 0)
+    dist = -Scholar.Metrics.Distance.pairwise_squared_euclidean(data)
+    preference = initialize_preference(dist, opts[:preference])
+    Nx.put_diagonal(dist, Nx.broadcast(preference, {n}))
+  end
+
+  deftransformp initialize_preference(dist, preference) do
+    cond do
+      is_atom(preference) -> apply(Nx, preference, [dist])
+      is_float(preference) -> preference
+    end
+  end
+
   @doc """
   Optionally prune clusters, indices, and labels to only valid entries.
 
@@ -214,26 +258,20 @@ defmodule Scholar.Cluster.AffinityPropagation do
   ## Examples
 
       iex> key = Nx.Random.key(42)
-      iex> x = Nx.tensor([[12,5,78,2], [1,-5,7,32], [-1,3,6,1], [1,-2,5,2]])
+      iex> x = Nx.tensor([[12,5,78,2], [9,3,81,-2], [-1,3,6,1], [1,-2,5,2]])
       iex> model = Scholar.Cluster.AffinityPropagation.fit(x, key: key)
       iex> Scholar.Cluster.AffinityPropagation.prune(model)
       %Scholar.Cluster.AffinityPropagation{
-        labels: Nx.tensor([0, 1, 1, 1]),
-        cluster_centers_indices: Nx.tensor([0, 3]),
-        affinity_matrix: Nx.tensor(
-          [
-            [-0.0, -6162.0, -5358.0, -5499.0],
-            [-6162.0, -0.0, -1030.0, -913.0],
-            [-5358.0, -1030.0, -0.0, -31.0],
-            [-5499.0, -913.0, -31.0, -0.0]
-          ]),
+        labels: Nx.tensor([0, 0, 1, 1]),
+        cluster_centers_indices: Nx.tensor([0, 2]),
         cluster_centers: Nx.tensor(
           [
             [12.0, 5.0, 78.0, 2.0],
-            [1.0, -2.0, 5.0, 2.0]
+            [-1.0, 3.0, 6.0, 1.0]
           ]
         ),
-        num_clusters: Nx.tensor(2, type: :u64)
+        num_clusters: Nx.tensor(2, type: :u64),
+        iterations: Nx.tensor(22, type: :s64)
       }
   """
   def prune(
@@ -271,64 +309,19 @@ defmodule Scholar.Cluster.AffinityPropagation do
   ## Examples
 
       iex> key = Nx.Random.key(42)
-      iex> x = Nx.tensor([[12,5,78,2], [1,5,7,32], [1,3,6,1], [1,2,5,2]])
+      iex> x = Nx.tensor([[12,5,78,2], [9,3,81,-2], [-1,3,6,1], [1,-2,5,2]])
       iex> model = Scholar.Cluster.AffinityPropagation.fit(x, key: key)
       iex> model = Scholar.Cluster.AffinityPropagation.prune(model)
-      iex> Scholar.Cluster.AffinityPropagation.predict(model, Nx.tensor([[1,6,2,6], [8,3,8,2]]))
+      iex> Scholar.Cluster.AffinityPropagation.predict(model, Nx.tensor([[10,3,50,6], [8,3,8,2]]))
       #Nx.Tensor<
         s64[2]
-        [1, 1]
+        [0, 1]
       >
   """
   defn predict(%__MODULE__{cluster_centers: cluster_centers} = _model, x) do
-    {num_clusters, num_features} = Nx.shape(cluster_centers)
-    {num_samples, _} = Nx.shape(x)
-    broadcast_shape = {num_samples, num_clusters, num_features}
-
-    Scholar.Metrics.Distance.euclidean(
-      Nx.new_axis(x, 1) |> Nx.broadcast(broadcast_shape),
-      Nx.new_axis(cluster_centers, 0) |> Nx.broadcast(broadcast_shape),
-      axes: [-1]
-    )
-
     dist = Scholar.Metrics.Distance.pairwise_euclidean(x, cluster_centers)
 
     Nx.select(Nx.is_nan(dist), Nx.Constants.infinity(Nx.type(dist)), dist)
     |> Nx.argmin(axis: 1)
   end
-
-  defnp initialize_matrices(data, opts \\ []) do
-    {n, _} = Nx.shape(data)
-    self_preference = opts[:self_preference]
-
-    {similarity_matrix, affinity_matrix} =
-      initialize_similarities(data, self_preference: self_preference)
-
-    zero = Nx.tensor(0, type: Nx.type(similarity_matrix))
-    availability_matrix = Nx.broadcast(zero, {n, n})
-    responsibility_matrix = Nx.broadcast(zero, {n, n})
-
-    {availability_matrix, responsibility_matrix, similarity_matrix, affinity_matrix}
-  end
-
-  defnp initialize_similarities(data, opts \\ []) do
-    n = Nx.axis_size(data, 0)
-    self_preference = opts[:self_preference]
-
-    dist = -Scholar.Metrics.Distance.pairwise_squared_euclidean(data)
-
-    fill_in =
-      cond do
-        self_preference == false ->
-          Nx.broadcast(Nx.median(dist), {n})
-
-        true ->
-          if Nx.size(self_preference) == 1,
-            do: Nx.broadcast(self_preference, {n}),
-            else: self_preference
-      end
-
-    s_modified = dist |> Nx.put_diagonal(fill_in)
-    {s_modified, dist}
-  end
 end
diff --git a/lib/scholar/cluster/dbscan.ex b/lib/scholar/cluster/dbscan.ex
index 4ec5516d..dcd637c1 100644
--- a/lib/scholar/cluster/dbscan.ex
+++ b/lib/scholar/cluster/dbscan.ex
@@ -5,6 +5,9 @@ defmodule Scholar.Cluster.DBSCAN do
   DBSCAN - Density-Based Spatial Clustering of Applications with Noise.
   Finds core samples of high density and expands clusters from them.
   Good for data which contains clusters of similar density.
+
+  The time complexity is $O(N^2)$ for $N$ samples.
+  The space complexity is $O(N^2)$.
   """
   import Nx.Defn
   import Scholar.Shared
diff --git a/lib/scholar/cluster/gmm.ex b/lib/scholar/cluster/gmm.ex
index f0d08e78..3f95149c 100644
--- a/lib/scholar/cluster/gmm.ex
+++ b/lib/scholar/cluster/gmm.ex
@@ -12,6 +12,8 @@ defmodule Scholar.Cluster.GaussianMixture do
   the parameters. Thus the procedure consists of repeating the algorithm several times
   and taking the best obtained result.
 
+  Time complexity is $O(NKD^3)$ for $N$ data points, $K$ Gaussian components and $D$ dimensions
+
   References:
 
   * [1] - Mixtures of Gaussians and the EM algorithm https://cs229.stanford.edu/notes2020spring/cs229-notes7b.pdf
diff --git a/lib/scholar/cluster/k_means.ex b/lib/scholar/cluster/k_means.ex
index 20f42827..2443bac0 100644
--- a/lib/scholar/cluster/k_means.ex
+++ b/lib/scholar/cluster/k_means.ex
@@ -11,6 +11,10 @@ defmodule Scholar.Cluster.KMeans do
   converges. Since some initializations are unfortunate and converge to sub-optimal results
   we need repeat the whole procedure a few times and take the best result.
 
+  Average time complexity is $O(CKNI)$, where $C$ is the number of clusters, $N$ is the number of samples,
+  $I$ is the number of iterations until convergence, and $K$ is the number of features. Space
+  complexity is $O(K*(N+C))$.
+
   Reference:
 
   * [1] - [K-Means Algorithm](https://cs.nyu.edu/~roweis/csc2515-2006/readings/lloyd57.pdf)
diff --git a/lib/scholar/decomposition/pca.ex b/lib/scholar/decomposition/pca.ex
index 67e09a86..40624b54 100644
--- a/lib/scholar/decomposition/pca.ex
+++ b/lib/scholar/decomposition/pca.ex
@@ -6,6 +6,8 @@ defmodule Scholar.Decomposition.PCA do
   of data set [1]. The sample data is decomposed using linear combination of
   vectors that lie on the directions of those components.
 
+  The time complexity is $O(NP^2 + P^3)$ where $N$ is the number of samples and $P$ is the number of features.
+  Space complexity is $O(P * (P+N))$.
   Reference:
 
   * [1] - [Principal Component Analysis](https://en.wikipedia.org/wiki/Principal_component_analysis)
diff --git a/lib/scholar/interpolation/bezier_spline.ex b/lib/scholar/interpolation/bezier_spline.ex
index 94311f81..c039de25 100644
--- a/lib/scholar/interpolation/bezier_spline.ex
+++ b/lib/scholar/interpolation/bezier_spline.ex
@@ -15,6 +15,8 @@ defmodule Scholar.Interpolation.BezierSpline do
   or `Scholar.Interpolation.Linear` algorithms, will only affect
   the segments right next to it, instead of affecting the curve as a whole.
 
+  Computing Bezier curve is $O(N^2)$ where $N$ is the number of points.
+
   Reference:
 
     * [1] - [Bezier theory](https://en.wikipedia.org/wiki/B%C3%A9zier_curve)
diff --git a/lib/scholar/interpolation/cubic_spline.ex b/lib/scholar/interpolation/cubic_spline.ex
index 925fbe78..00901f00 100644
--- a/lib/scholar/interpolation/cubic_spline.ex
+++ b/lib/scholar/interpolation/cubic_spline.ex
@@ -10,6 +10,8 @@ defmodule Scholar.Interpolation.CubicSpline do
   could appear if a single n-th degree polynomial were to be
   fitted over all of the points.
 
+  Cubic spline interpolation is $O(N)$ where $N$ is the number of points.
+
   Reference:
 
     * [1] - [Cubic Spline Interpolation theory](https://en.wikiversity.org/wiki/Cubic_Spline_Interpolation)
@@ -50,8 +52,8 @@ defmodule Scholar.Interpolation.CubicSpline do
       %Scholar.Interpolation.CubicSpline{
         coefficients: Nx.tensor(
           [
-            [0.0, 1.500000238418579, -3.500000238418579, 2.0],
-            [0.0, 1.5, -0.4999999403953552, 0.0]
+            [0.0, 1.5, -3.5, 2.0],
+            [0.0, 1.5, -0.5, 0.0]
           ]
         ),
         x: Nx.tensor(
@@ -108,7 +110,7 @@ defmodule Scholar.Interpolation.CubicSpline do
 
           b = Nx.stack([2 * slope[0], 3 * (dx[0] * slope[1] + dx[1] * slope[0]), 2 * slope[1]])
 
-          Nx.LinAlg.solve(a, b)
+          tridiagonal_solve(a, b)
 
         {_, :not_a_knot} ->
           up_diag =
@@ -149,7 +151,7 @@ defmodule Scholar.Interpolation.CubicSpline do
               Nx.new_axis(b_n, 0)
             ])
 
-          Nx.LinAlg.solve(a, b)
+          tridiagonal_solve(a, b)
 
         _ ->
           up_diag =
@@ -188,7 +190,7 @@ defmodule Scholar.Interpolation.CubicSpline do
               Nx.new_axis(b_n, 0)
             ])
 
-          Nx.LinAlg.solve(a, b)
+          tridiagonal_solve(a, b)
       end
 
     t = (s[0..-2//1] + s[1..-1//1] - 2 * slope) / dx
@@ -289,4 +291,46 @@ defmodule Scholar.Interpolation.CubicSpline do
 
     Nx.reshape(result, original_shape)
   end
+
+  defnp tridiagonal_solve(a, b) do
+    n = Nx.size(b)
+    w = Nx.broadcast(0, {n - 1})
+    p = g = Nx.broadcast(0, {n})
+    i = Nx.take_diagonal(a, offset: -1)
+    j = Nx.take_diagonal(a)
+    k = Nx.take_diagonal(a, offset: 1)
+
+    w_0 = k[0] / j[0]
+    g_0 = b[0] / j[0]
+    w = Nx.indexed_put(w, Nx.new_axis(0, 0), w_0)
+    g = Nx.indexed_put(g, Nx.new_axis(0, 0), g_0)
+
+    {{w, g}, _} =
+      while {{w, g}, {index = 1, i, j, k, b}}, index < n do
+        w =
+          if index < n - 1 do
+            w_i = k[index] / (j[index] - i[index - 1] * w[index - 1])
+            Nx.indexed_put(w, Nx.new_axis(index, 0), w_i)
+          else
+            w
+          end
+
+        g_i = (b[index] - i[index - 1] * g[index - 1]) / (j[index] - i[index - 1] * w[index - 1])
+        g = Nx.indexed_put(g, Nx.new_axis(index, 0), g_i)
+
+        {{w, g}, {index + 1, i, j, k, b}}
+      end
+
+    p = Nx.indexed_put(p, Nx.new_axis(n - 1, 0), g[n - 1])
+
+    {p, _} =
+      while {p, {index = n - 1, g, w}}, index > 0 do
+        p_i = g[index - 1] - w[index - 1] * p[index]
+        p = Nx.indexed_put(p, Nx.new_axis(index - 1, 0), p_i)
+
+        {p, {index - 1, g, w}}
+      end
+
+    p
+  end
 end
diff --git a/lib/scholar/interpolation/linear.ex b/lib/scholar/interpolation/linear.ex
index 9f65152a..d981eeb8 100644
--- a/lib/scholar/interpolation/linear.ex
+++ b/lib/scholar/interpolation/linear.ex
@@ -14,12 +14,31 @@ defmodule Scholar.Interpolation.Linear do
   b = y_1 - ax_1 = y_0 - ax_0
   \end{cases}
   $$
+
+  Linear interpolation has $O(N)$ time and space complexity where $N$ is the number of points.
   """
   import Nx.Defn
+  import Scholar.Shared
 
   @derive {Nx.Container, containers: [:coefficients, :x]}
   defstruct [:coefficients, :x]
 
+  @type t :: %Scholar.Interpolation.Linear{}
+
+  opts_schema = [
+    left: [
+      type: {:or, [:float, :integer]},
+      doc:
+        "Value to return for values in `target_x` smaller that the smallest value in training set"
+    ],
+    right: [
+      type: {:or, [:float, :integer]},
+      doc:
+        "Value to return for values in `target_x` greater that the greatest value in training set"
+    ]
+  ]
+
+  @opts_schema NimbleOptions.new!(opts_schema)
   @doc """
   Fits a linear interpolation of the given `(x, y)` points
 
@@ -39,7 +58,7 @@ defmodule Scholar.Interpolation.Linear do
           ]
         ),
         x: Nx.tensor(
-          [0, 1]
+          [0, 1, 2]
         )
       }
   """
@@ -77,7 +96,7 @@ defmodule Scholar.Interpolation.Linear do
 
     coefficients = Nx.stack([a, b], axis: 1)
 
-    %__MODULE__{coefficients: coefficients, x: x0}
+    %__MODULE__{coefficients: coefficients, x: x}
   end
 
   @doc """
@@ -95,24 +114,120 @@ defmodule Scholar.Interpolation.Linear do
           [2.0, 6.0]
         ]
       )
+
+      iex> x = Nx.iota({5})
+      iex> y = Nx.tensor([2.0, 0.0, 1.0, 3.0, 4.0])
+      iex> model = Scholar.Interpolation.Linear.fit(x, y)
+      iex> target_x = Nx.tensor([-2, -1, 1.25, 3, 3.25, 5.0])
+      iex> Scholar.Interpolation.Linear.predict(model, target_x, left: 0.0, right: 10.0)
+      #Nx.Tensor<
+        f32[6]
+        [0.0, 0.0, 0.25, 3.0, 3.25, 10.0]
+      >
   """
-  defn predict(%__MODULE__{x: x, coefficients: coefficients} = _model, target_x) do
-    original_shape = Nx.shape(target_x)
+  deftransform predict(model, target_x, opts \\ []) do
+    predict_n(model, target_x, NimbleOptions.validate!(opts, @opts_schema))
+  end
+
+  defnp predict_n(%__MODULE__{x: x, coefficients: coefficients} = _model, target_x, opts) do
+    shape = Nx.shape(target_x)
 
     target_x = Nx.flatten(target_x)
 
-    idx_selector = Nx.new_axis(target_x, 1) >= x
+    indices = Nx.argsort(target_x)
+
+    left_bound = x[0]
+    right_bound = x[-1]
+
+    target_x = Nx.sort(target_x)
+    res = Nx.broadcast(Nx.tensor(0, type: to_float_type(target_x)), {Nx.axis_size(target_x, 0)})
+
+    # while with smaller than left_bound
+    {{res, i}, _} =
+      while {{res, i = 0}, {x, coefficients, left_bound, target_x}},
+            check_cond_left(target_x, i, left_bound) do
+        val =
+          case opts[:left] do
+            nil ->
+              coefficients[0][0] * Nx.take(target_x, i) + coefficients[0][1]
+
+            _ ->
+              opts[:left]
+          end
+
+        res = Nx.indexed_put(res, Nx.new_axis(i, -1), val)
+        {{res, i + 1}, {x, coefficients, left_bound, target_x}}
+      end
+
+    {{res, i}, _} =
+      while {{res, i}, {x, right_bound, coefficients, target_x, j = 0}},
+            check_cond_right(target_x, i, right_bound) do
+        {j, _} =
+          while {j, {i, x, target_x}},
+                j < Nx.axis_size(x, 0) and Nx.take(x, j) < Nx.take(target_x, i) do
+            {j + 1, {i, x, target_x}}
+          end
+
+        res =
+          Nx.indexed_put(
+            res,
+            Nx.new_axis(i, -1),
+            coefficients[Nx.max(j - 1, 0)][0] * Nx.take(target_x, i) +
+              coefficients[Nx.max(j - 1, 0)][1]
+          )
+
+        i = i + 1
+
+        {{res, i}, {x, right_bound, coefficients, target_x, j}}
+      end
+
+    {res, i}
+
+    # while with bigger than right_bound
+
+    {res, _} =
+      while {res, {x, coefficients, target_x, i}},
+            i < Nx.axis_size(target_x, 0) do
+        val =
+          case opts[:right] do
+            nil ->
+              coefficients[-1][0] * Nx.take(target_x, i) + coefficients[-1][1]
+
+            _ ->
+              opts[:right]
+          end
+
+        res = Nx.indexed_put(res, Nx.new_axis(i, -1), val)
+        {res, {x, coefficients, target_x, i + 1}}
+      end
+
+    res = Nx.take(res, indices)
+    Nx.reshape(res, shape)
+  end
 
-    idx_poly = Nx.argmax(idx_selector, axis: 1, tie_break: :high)
+  defnp check_cond_left(target_x, i, left_bound) do
+    cond do
+      i >= Nx.axis_size(target_x, 0) ->
+        Nx.u8(0)
 
-    idx_poly = Nx.select(Nx.all(idx_selector == 0, axes: [1]), 0, idx_poly)
+      Nx.take(target_x, i) >= left_bound ->
+        Nx.u8(0)
 
-    coef_poly = Nx.take(coefficients, idx_poly)
+      true ->
+        Nx.u8(1)
+    end
+  end
 
-    x_poly = Nx.stack([target_x, Nx.broadcast(1, target_x)], axis: 1)
+  defnp check_cond_right(target_x, i, right_bound) do
+    cond do
+      i >= Nx.axis_size(target_x, 0) ->
+        Nx.u8(0)
 
-    result = Nx.dot(x_poly, [1], [0], coef_poly, [1], [0])
+      Nx.take(target_x, i) > right_bound ->
+        Nx.u8(0)
 
-    Nx.reshape(result, original_shape)
+      true ->
+        Nx.u8(1)
+    end
   end
 end
diff --git a/lib/scholar/linear/linear_regression.ex b/lib/scholar/linear/linear_regression.ex
index ddf0b7cd..c0033fc1 100644
--- a/lib/scholar/linear/linear_regression.ex
+++ b/lib/scholar/linear/linear_regression.ex
@@ -1,6 +1,9 @@
 defmodule Scholar.Linear.LinearRegression do
   @moduledoc """
   Ordinary least squares linear regression.
+
+  Time complexity of linear regression is $O((K^2) * (K+N))$ where $N$ is the number of samples
+  and $K$ is the number of features.
   """
   require Nx
   import Nx.Defn
diff --git a/lib/scholar/linear/logistic_regression.ex b/lib/scholar/linear/logistic_regression.ex
index c7dea72c..3c62c9fa 100644
--- a/lib/scholar/linear/logistic_regression.ex
+++ b/lib/scholar/linear/logistic_regression.ex
@@ -1,6 +1,8 @@
 defmodule Scholar.Linear.LogisticRegression do
   @moduledoc """
   Logistic regression in both binary and multinomial variants.
+
+  Time complexity is $O(N * K * I)$ where $N$ is the number of samples, $K$ is the number of features, and $I$ is the number of iterations.
   """
   import Nx.Defn
   import Scholar.Shared
diff --git a/lib/scholar/linear/polynomial_regression.ex b/lib/scholar/linear/polynomial_regression.ex
index 1a500d68..241d1a9f 100644
--- a/lib/scholar/linear/polynomial_regression.ex
+++ b/lib/scholar/linear/polynomial_regression.ex
@@ -1,6 +1,8 @@
 defmodule Scholar.Linear.PolynomialRegression do
   @moduledoc """
   Least squares polynomial regression.
+
+  Time complexity of polynomial regression is $O((K^2) * (K+N))$ where $N$ is the number of samples and $K$ is the number of features.
   """
 
   import Nx.Defn
diff --git a/lib/scholar/linear/ridge_regression.ex b/lib/scholar/linear/ridge_regression.ex
index ea00d5c1..c702b81d 100644
--- a/lib/scholar/linear/ridge_regression.ex
+++ b/lib/scholar/linear/ridge_regression.ex
@@ -15,6 +15,9 @@ defmodule Scholar.Linear.RidgeRegression do
   * $w$ is the model weights matrix
 
   * $\alpha$ is the parameter that controls level of regularization
+
+  Time complexity is $O(N^2)$ for `:cholesky` solver and $O((N^2) * (K + N))$ for `:svd` solver,
+  where $N$ is the number of observations and $K$ is the number of features.
   """
   require Nx
   import Nx.Defn
diff --git a/lib/scholar/linear/svm.ex b/lib/scholar/linear/svm.ex
index ad9ebd85..688c034b 100644
--- a/lib/scholar/linear/svm.ex
+++ b/lib/scholar/linear/svm.ex
@@ -1,13 +1,17 @@
 defmodule Scholar.Linear.SVM do
   @moduledoc """
-  SVM classifier
+  Support Vector Machine linear classifier.
 
-  It uses the OvR strategy to handle both binary and multinomial classification.
+  It uses the One-vs-Rest strategy to handle both binary and multinomial classification.
   This implementation uses stochastic gradient descent from default or any other optimizer
   available in `Polaris`. This makes it similar to a sklearn SGDClassifier [1].
-  It means that on average it will work slower than algorithms that use QP and kernel trick (LIBSVM [2]) or
-  Coordinate Descent Algorithm (LIBLINEAR [3]). It also cannot use different kernels like in LIBSVM,
-  but you can use any type of optimizer available in `Polaris`.
+
+  On average it is slower than algorithms that use QP and kernel trick (LIBSVM [2]) or
+  Coordinate Descent Algorithm (LIBLINEAR [3]). It also cannot use different kernels
+  like in LIBSVM, but you can use any type of optimizer available in `Polaris`.
+
+  Time complexity is $O(N * K * I * C)$ where $N$ is the number of samples, $K$ is the
+  number of features $I$ is the number of iterations and $C$ is the number of classes.
 
   [1] - https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDClassifier.html
   [2] - https://www.csie.ntu.edu.tw/~cjlin/libsvm/
diff --git a/lib/scholar/manifold/tsne.ex b/lib/scholar/manifold/tsne.ex
index 50245689..fbebf650 100644
--- a/lib/scholar/manifold/tsne.ex
+++ b/lib/scholar/manifold/tsne.ex
@@ -1,6 +1,8 @@
 defmodule Scholar.Manifold.TSNE do
   @moduledoc """
-  TSNE (t-Distributed Stochastic Neighbor Embedding) is a nonlinear dimensionality reduction technique.
+  t-SNE (t-Distributed Stochastic Neighbor Embedding) is a nonlinear dimensionality reduction technique.
+
+  This is an exact implementation of t-SNE and therefore it has time complexity is $O(N^2)$ for $N$ samples.
 
   ## Reference
 
diff --git a/lib/scholar/metrics/classification.ex b/lib/scholar/metrics/classification.ex
index b2054757..a1e1d124 100644
--- a/lib/scholar/metrics/classification.ex
+++ b/lib/scholar/metrics/classification.ex
@@ -13,6 +13,7 @@ defmodule Scholar.Metrics.Classification do
 
   import Nx.Defn, except: [assert_shape: 2, assert_shape_pattern: 2]
   import Scholar.Shared
+  import Scholar.Preprocessing
   alias Scholar.Integrate
 
   general_schema = [
@@ -41,7 +42,40 @@ defmodule Scholar.Metrics.Classification do
           * `:micro` - Calculate metrics globally by counting the total true positives,
           false negatives and false positives.
 
-          * `:none` - The f1 scores for each class are returned.
+          * `:none` - The F-score values for each class are returned.
+          """
+        ]
+      ]
+
+  fbeta_score_schema = f1_score_schema
+
+  precision_recall_fscore_support_schema =
+    general_schema ++
+      [
+        average: [
+          type: {:in, [:micro, :macro, :weighted, :none]},
+          default: :none,
+          doc: """
+          This determines the type of averaging performed on the data.
+
+          * `:macro` - Calculate metrics for each label, and find their unweighted mean.
+          This does not take label imbalance into account.
+
+          * `:weighted` - Calculate metrics for each label, and find their average weighted by
+          support (the number of true instances for each label).
+
+          * `:micro` - Calculate metrics globally by counting the total true positives,
+          false negatives and false positives.
+
+          * `:none` - The F-score values for each class are returned.
+          """
+        ],
+        beta: [
+          type: {:custom, Scholar.Options, :beta, []},
+          default: 1,
+          doc: """
+          Determines the weight of recall in the combined score.
+          For values of `beta` > 1 it gives more weight to recall, while `beta` < 1 favors precision.
           """
         ]
       ]
@@ -128,6 +162,26 @@ defmodule Scholar.Metrics.Classification do
     ]
   ]
 
+  log_loss_schema =
+    general_schema ++
+      [
+        normalize: [
+          type: :boolean,
+          default: true,
+          doc: """
+          If `true`, return the mean loss over the samples.
+          Otherwise, return the sum of losses over the samples.
+          """
+        ],
+        sample_weights: [
+          type: {:custom, Scholar.Options, :weights, []},
+          default: 1.0,
+          doc: """
+          Sample weights of the observations.
+          """
+        ]
+      ]
+
   top_k_accuracy_score_schema =
     general_schema ++
       [
@@ -163,9 +217,14 @@ defmodule Scholar.Metrics.Classification do
   @confusion_matrix_schema NimbleOptions.new!(confusion_matrix_schema)
   @balanced_accuracy_schema NimbleOptions.new!(balanced_accuracy_schema)
   @cohen_kappa_schema NimbleOptions.new!(cohen_kappa_schema)
+  @fbeta_score_schema NimbleOptions.new!(fbeta_score_schema)
   @f1_score_schema NimbleOptions.new!(f1_score_schema)
+  @precision_recall_fscore_support_schema NimbleOptions.new!(
+                                            precision_recall_fscore_support_schema
+                                          )
   @brier_score_loss_schema NimbleOptions.new!(brier_score_loss_schema)
   @accuracy_schema NimbleOptions.new!(accuracy_schema)
+  @log_loss_schema NimbleOptions.new!(log_loss_schema)
   @top_k_accuracy_score_schema NimbleOptions.new!(top_k_accuracy_score_schema)
   @zero_one_loss_schema NimbleOptions.new!(zero_one_loss_schema)
 
@@ -586,86 +645,243 @@ defmodule Scholar.Metrics.Classification do
   end
 
   @doc """
-  Calculates F1 score given rank-1 tensors which represent
+  Calculates F-beta score given rank-1 tensors which represent
   the expected (`y_true`) and predicted (`y_pred`) classes.
 
   If all examples are true negatives, then the result is 0 to
   avoid zero division.
 
+  #{~S'''
+  $$F_\beta = (1 + \beta^2) \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{(\beta^2 \cdot \mathrm{precision}) + \mathrm{recall}}$$
+  '''}
+
   ## Options
 
-  #{NimbleOptions.docs(@f1_score_schema)}
+  #{NimbleOptions.docs(@fbeta_score_schema)}
 
   ## Examples
 
       iex> y_true = Nx.tensor([0, 1, 1, 1, 1, 0, 2, 1, 0, 1], type: :u32)
       iex> y_pred = Nx.tensor([0, 2, 1, 1, 2, 2, 2, 0, 0, 1], type: :u32)
-      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3)
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.u32(1), num_classes: 3)
       #Nx.Tensor<
         f32[3]
         [0.6666666865348816, 0.6666666865348816, 0.4000000059604645]
       >
-      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :macro)
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.u32(2), num_classes: 3)
+      #Nx.Tensor<
+        f32[3]
+        [0.6666666865348816, 0.5555555820465088, 0.625]
+      >
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.f32(0.5), num_classes: 3)
+      #Nx.Tensor<
+        f32[3]
+        [0.6666666865348816, 0.8333333134651184, 0.29411765933036804]
+      >
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.u32(2), num_classes: 3, average: :macro)
       #Nx.Tensor<
         f32
-        0.5777778029441833
+        0.6157407760620117
       >
-      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :weighted)
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.u32(2), num_classes: 3, average: :weighted)
       #Nx.Tensor<
         f32
-        0.6399999856948853
+        0.5958333611488342
       >
-      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :micro)
+      iex> Scholar.Metrics.Classification.fbeta_score(y_true, y_pred, Nx.f32(0.5), num_classes: 3, average: :micro)
       #Nx.Tensor<
         f32
         0.6000000238418579
       >
-      iex> Scholar.Metrics.Classification.f1_score(Nx.tensor([1,0,1,0]), Nx.tensor([0, 1, 0, 1]), num_classes: 2, average: :none)
+      iex> Scholar.Metrics.Classification.fbeta_score(Nx.tensor([1, 0, 1, 0]), Nx.tensor([0, 1, 0, 1]), Nx.tensor(0.5), num_classes: 2, average: :none)
+      #Nx.Tensor<
+        f32[2]
+        [0.0, 0.0]
+      >
+      iex> Scholar.Metrics.Classification.fbeta_score(Nx.tensor([1, 0, 1, 0]), Nx.tensor([0, 1, 0, 1]), 0.5, num_classes: 2, average: :none)
       #Nx.Tensor<
         f32[2]
         [0.0, 0.0]
       >
   """
-  deftransform f1_score(y_true, y_pred, opts \\ []) do
-    f1_score_n(y_true, y_pred, NimbleOptions.validate!(opts, @f1_score_schema))
+  deftransform fbeta_score(y_true, y_pred, beta, opts \\ []) do
+    fbeta_score_n(y_true, y_pred, beta, NimbleOptions.validate!(opts, @fbeta_score_schema))
   end
 
-  defnp f1_score_n(y_true, y_pred, opts) do
-    check_shape(y_pred, y_true)
-    num_classes = check_num_classes(opts[:num_classes])
+  defnp fbeta_score_n(y_true, y_pred, beta, opts) do
+    {_precision, _recall, per_class_fscore, _support} =
+      precision_recall_fscore_support_n(y_true, y_pred, beta, opts)
 
-    case opts[:average] do
+    per_class_fscore
+  end
+
+  defnp fbeta_score_v(confusion_matrix, average) do
+    true_positive = Nx.take_diagonal(confusion_matrix)
+    false_positive = Nx.sum(confusion_matrix, axes: [0]) - true_positive
+    false_negative = Nx.sum(confusion_matrix, axes: [1]) - true_positive
+
+    case average do
       :micro ->
-        accuracy(y_true, y_pred)
+        true_positive = Nx.sum(true_positive)
+        false_positive = Nx.sum(false_positive)
+        false_negative = Nx.sum(false_negative)
+
+        {true_positive, false_positive, false_negative}
 
       _ ->
-        cm = confusion_matrix(y_true, y_pred, num_classes: num_classes)
-        true_positive = Nx.take_diagonal(cm)
-        false_positive = Nx.sum(cm, axes: [0]) - true_positive
-        false_negative = Nx.sum(cm, axes: [1]) - true_positive
+        {true_positive, false_positive, false_negative}
+    end
+  end
+
+  @doc """
+  Calculates precision, recall, F-score and support for each
+  class. It also supports a `beta` argument which weights
+  recall more than precision by it's value.
+
+  ## Options
+
+  #{NimbleOptions.docs(@precision_recall_fscore_support_schema)}
+
+  ## Examples
 
-        precision = safe_division(true_positive, true_positive + false_positive)
+      iex> y_true = Nx.tensor([0, 1, 1, 1, 1, 0, 2, 1, 0, 1], type: :u32)
+      iex> y_pred = Nx.tensor([0, 2, 1, 1, 2, 2, 2, 0, 0, 1], type: :u32)
+      iex> Scholar.Metrics.Classification.precision_recall_fscore_support(y_true, y_pred, num_classes: 3)
+      {Nx.f32([0.6666666865348816, 1.0, 0.25]),
+       Nx.f32([0.6666666865348816, 0.5, 1.0]),
+       Nx.f32([0.6666666865348816, 0.6666666865348816, 0.4000000059604645]),
+       Nx.u64([3, 6, 1])}
+      iex> Scholar.Metrics.Classification.precision_recall_fscore_support(y_true, y_pred, num_classes: 3, average: :macro)
+      {Nx.f32([0.6666666865348816, 1.0, 0.25]),
+       Nx.f32([0.6666666865348816, 0.5, 1.0]),
+       Nx.f32(0.5777778029441833),
+       Nx.Constants.nan()}
+      iex> Scholar.Metrics.Classification.precision_recall_fscore_support(y_true, y_pred, num_classes: 3, average: :weighted)
+      {Nx.f32([0.6666666865348816, 1.0, 0.25]),
+       Nx.f32([0.6666666865348816, 0.5, 1.0]),
+       Nx.f32(0.6399999856948853),
+       Nx.Constants.nan()}
+      iex> Scholar.Metrics.Classification.precision_recall_fscore_support(y_true, y_pred, num_classes: 3, average: :micro)
+      {Nx.f32(0.6000000238418579),
+       Nx.f32(0.6000000238418579),
+       Nx.f32(0.6000000238418579),
+       Nx.Constants.nan()}
+
+      iex> y_true = Nx.tensor([1, 0, 1, 0], type: :u32)
+      iex> y_pred = Nx.tensor([0, 1, 0, 1], type: :u32)
+      iex> opts = [beta: 2, num_classes: 2, average: :none]
+      iex> Scholar.Metrics.Classification.precision_recall_fscore_support(y_true, y_pred, opts)
+      {Nx.f32([0.0, 0.0]),
+       Nx.f32([0.0, 0.0]),
+       Nx.f32([0.0, 0.0]),
+       Nx.u64([2, 2])}
+  """
+  deftransform precision_recall_fscore_support(y_true, y_pred, opts) do
+    opts = NimbleOptions.validate!(opts, @precision_recall_fscore_support_schema)
+    {beta, opts} = Keyword.pop(opts, :beta)
 
-        recall = safe_division(true_positive, true_positive + false_negative)
+    precision_recall_fscore_support_n(
+      y_true,
+      y_pred,
+      beta,
+      opts
+    )
+  end
 
-        per_class_f1 = safe_division(2 * precision * recall, precision + recall)
+  defnp precision_recall_fscore_support_n(y_true, y_pred, beta, opts) do
+    check_shape(y_pred, y_true)
+    num_classes = check_num_classes(opts[:num_classes])
+    average = opts[:average]
+
+    confusion_matrix = confusion_matrix(y_true, y_pred, num_classes: num_classes)
+    {true_positive, false_positive, false_negative} = fbeta_score_v(confusion_matrix, average)
 
-        case opts[:average] do
-          :none ->
-            per_class_f1
+    precision = safe_division(true_positive, true_positive + false_positive)
+    recall = safe_division(true_positive, true_positive + false_negative)
 
-          :macro ->
-            Nx.mean(per_class_f1)
+    per_class_fscore =
+      cond do
+        # Should only be +Inf
+        Nx.is_infinity(beta) ->
+          recall
+
+        beta == 0 ->
+          precision
 
-          :weighted ->
-            support = (y_true == Nx.iota({num_classes, 1})) |> Nx.sum(axes: [1])
+        true ->
+          beta2 = Nx.pow(beta, 2)
+          safe_division((1 + beta2) * precision * recall, beta2 * precision + recall)
+      end
 
-            safe_division(per_class_f1 * support, Nx.sum(support))
-            |> Nx.sum()
-        end
+    case average do
+      :none ->
+        support = (y_true == Nx.iota({num_classes, 1})) |> Nx.sum(axes: [1])
+
+        {precision, recall, per_class_fscore, support}
+
+      :micro ->
+        {precision, recall, per_class_fscore, Nx.Constants.nan()}
+
+      :macro ->
+        {precision, recall, Nx.mean(per_class_fscore), Nx.Constants.nan()}
+
+      :weighted ->
+        support = (y_true == Nx.iota({num_classes, 1})) |> Nx.sum(axes: [1])
+
+        per_class_fscore =
+          (per_class_fscore * support)
+          |> safe_division(Nx.sum(support))
+          |> Nx.sum()
+
+        {precision, recall, per_class_fscore, Nx.Constants.nan()}
     end
   end
 
+  @doc """
+  Calculates F1 score given rank-1 tensors which represent
+  the expected (`y_true`) and predicted (`y_pred`) classes.
+
+  If all examples are true negatives, then the result is 0 to
+  avoid zero division.
+
+  ## Options
+
+  #{NimbleOptions.docs(@f1_score_schema)}
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([0, 1, 1, 1, 1, 0, 2, 1, 0, 1], type: :u32)
+      iex> y_pred = Nx.tensor([0, 2, 1, 1, 2, 2, 2, 0, 0, 1], type: :u32)
+      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3)
+      #Nx.Tensor<
+        f32[3]
+        [0.6666666865348816, 0.6666666865348816, 0.4000000059604645]
+      >
+      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :macro)
+      #Nx.Tensor<
+        f32
+        0.5777778029441833
+      >
+      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :weighted)
+      #Nx.Tensor<
+        f32
+        0.6399999856948853
+      >
+      iex> Scholar.Metrics.Classification.f1_score(y_true, y_pred, num_classes: 3, average: :micro)
+      #Nx.Tensor<
+        f32
+        0.6000000238418579
+      >
+      iex> Scholar.Metrics.Classification.f1_score(Nx.tensor([1, 0, 1, 0]), Nx.tensor([0, 1, 0, 1]), num_classes: 2, average: :none)
+      #Nx.Tensor<
+        f32[2]
+        [0.0, 0.0]
+      >
+  """
+  deftransform f1_score(y_true, y_pred, opts \\ []) do
+    fbeta_score_n(y_true, y_pred, 1, NimbleOptions.validate!(opts, @f1_score_schema))
+  end
+
   @doc """
   Zero-one classification loss.
 
@@ -1039,6 +1255,91 @@ defmodule Scholar.Metrics.Classification do
     1 - Nx.sum(weights_matrix * cm) / Nx.sum(weights_matrix * expected)
   end
 
+  @doc """
+  Computes the log loss, aka logistic loss or cross-entropy loss.
+
+  The log-loss is a measure of how well a forecaster performs, with smaller
+  values being better. For each sample, a forecaster outputs a probability for
+  each class, from which the log loss is computed by averaging the negative log
+  of the probability forecasted for the true class over a number of samples.
+
+  `y_true` should contain `num_classes` unique values, and the sum of `y_prob`
+  along axis 1 should be 1 to respect the law of total probability.
+
+  ## Options
+
+  #{NimbleOptions.docs(@log_loss_schema)}
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([0, 0, 1, 1])
+      iex> y_prob = Nx.tensor([[0.9, 0.1], [0.8, 0.2], [0.3, 0.7], [0.01, 0.99]])
+      iex> Scholar.Metrics.Classification.log_loss(y_true, y_prob, num_classes: 2)
+      #Nx.Tensor<
+        f32
+        0.17380733788013458
+      >
+      iex> Scholar.Metrics.Classification.log_loss(y_true, y_prob, num_classes: 2, normalize: false)
+      #Nx.Tensor<
+        f32
+        0.6952293515205383
+      >
+      iex> weights = Nx.tensor([0.7, 2.3, 1.3, 0.34])
+      iex(361)> Scholar.Metrics.Classification.log_loss(y_true, y_prob, num_classes: 2, sample_weights: weights)
+      #Nx.Tensor<
+        f32
+        0.22717177867889404
+      >
+  """
+  deftransform log_loss(y_true, y_prob, opts \\ []) do
+    log_loss_n(
+      y_true,
+      y_prob,
+      NimbleOptions.validate!(opts, @log_loss_schema)
+    )
+  end
+
+  defnp log_loss_n(y_true, y_prob, opts) do
+    assert_rank!(y_true, 1)
+    assert_rank!(y_prob, 2)
+
+    if Nx.axis_size(y_true, 0) != Nx.axis_size(y_prob, 0) do
+      raise ArgumentError, "y_true and y_prob must have the same size along axis 0"
+    end
+
+    num_classes = opts[:num_classes]
+
+    if Nx.axis_size(y_prob, 1) != num_classes do
+      raise ArgumentError, "y_prob must have a size of num_classes along axis 1"
+    end
+
+    weights =
+      validate_weights(
+        opts[:sample_weights],
+        Nx.axis_size(y_true, 0),
+        type: to_float_type(y_prob)
+      )
+
+    y_true_onehot =
+      ordinal_encode(y_true, num_classes: num_classes)
+      |> one_hot_encode(num_classes: num_classes)
+
+    y_prob = Nx.clip(y_prob, 0, 1)
+
+    sample_loss =
+      Nx.multiply(y_true_onehot, y_prob)
+      |> Nx.sum(axes: [-1])
+      |> Nx.log()
+      |> Nx.negate()
+
+    if opts[:normalize] do
+      Nx.weighted_mean(sample_loss, weights)
+    else
+      Nx.multiply(sample_loss, weights)
+      |> Nx.sum()
+    end
+  end
+
   @doc """
   Top-k Accuracy classification score.
 
@@ -1147,4 +1448,42 @@ defmodule Scholar.Metrics.Classification do
     assert_rank!(y_true, 1)
     assert_same_shape!(y_true, y_pred)
   end
+
+  @doc """
+  Matthews Correlation Coefficient (MCC) provides a measure of the quality of binary classifications.
+
+  It returns a value between -1 and 1 where 1 represents a perfect prediction, 0 represents no better
+  than random prediction, and -1 indicates total disagreement between prediction and observation.
+  """
+  defn mcc(y_true, y_pred) do
+    true_positives = binary_true_positives(y_true, y_pred)
+    true_negatives = binary_true_negatives(y_true, y_pred)
+    false_positives = binary_false_positives(y_true, y_pred)
+    false_negatives = binary_false_negatives(y_true, y_pred)
+
+    mcc_numerator = true_positives * true_negatives - false_positives * false_negatives
+
+    mcc_denominator =
+      Nx.sqrt(
+        (true_positives + false_positives) *
+          (true_positives + false_negatives) *
+          (true_negatives + false_positives) *
+          (true_negatives + false_negatives)
+      )
+
+    zero_tensor = Nx.tensor([0.0], type: :f32)
+
+    if Nx.all(
+         true_positives == zero_tensor and
+           true_negatives == zero_tensor
+       ) do
+      Nx.tensor([-1.0], type: :f32)
+    else
+      Nx.select(
+        mcc_denominator == zero_tensor,
+        zero_tensor,
+        mcc_numerator / mcc_denominator
+      )
+    end
+  end
 end
diff --git a/lib/scholar/metrics/clustering.ex b/lib/scholar/metrics/clustering.ex
index 7150bd96..d716faca 100644
--- a/lib/scholar/metrics/clustering.ex
+++ b/lib/scholar/metrics/clustering.ex
@@ -26,6 +26,8 @@ defmodule Scholar.Metrics.Clustering do
   clustering configuration is appropriate. If many points have a low or negative
   value, then the clustering configuration may have too many or too few clusters.
 
+  Time complexity of silhouette score is $O(N^2)$ where $N$ is the number of samples.
+
   ## Options
 
   #{NimbleOptions.docs(@opts_schema)}
diff --git a/lib/scholar/metrics/ranking.ex b/lib/scholar/metrics/ranking.ex
new file mode 100644
index 00000000..45a08447
--- /dev/null
+++ b/lib/scholar/metrics/ranking.ex
@@ -0,0 +1,97 @@
+defmodule Scholar.Metrics.Ranking do
+  @moduledoc """
+  Provides metrics and calculations related to ranking quality.
+
+  Ranking metrics evaluate the quality of ordered lists of items,
+  often used in information retrieval and recommendation systems.
+
+  This module currently supports the following ranking metrics:
+    * Discounted Cumulative Gain (DCG)
+  """
+
+  import Nx.Defn
+  import Scholar.Shared
+  require Nx
+
+  @dcg_opts [
+    k: [
+      type: {:custom, Scholar.Options, :positive_number, []},
+      doc: "Truncation parameter to consider only the top-k elements."
+    ]
+  ]
+
+  @dcg_opts_schema NimbleOptions.new!(@dcg_opts)
+
+  deftransform dcg(y_true, y_score, opts \\ []) do
+    dcg_n(y_true, y_score, NimbleOptions.validate!(opts, @dcg_opts_schema))
+  end
+
+  @doc """
+  ## Options
+  #{NimbleOptions.docs(@dcg_opts_schema)}
+
+  Computes the DCG based on true relevance scores (`y_true`) and their respective predicted scores (`y_score`).
+  """
+  defn dcg_n(y_true, y_score, opts) do
+    y_true_shape = Nx.shape(y_true)
+    y_score_shape = Nx.shape(y_score)
+
+    check_shape(y_true_shape, y_score_shape)
+
+    {adjusted_y_true, adjusted_y_score} = handle_ties(y_true, y_score)
+
+    sorted_indices = Nx.argsort(adjusted_y_score, axis: 0, direction: :desc)
+    sorted_y_true = Nx.take(adjusted_y_true, sorted_indices)
+
+    truncated_y_true = truncate_at_k(sorted_y_true, opts)
+    dcg_value(truncated_y_true)
+  end
+
+  defnp check_shape(y_true, y_pred) do
+    assert_same_shape!(y_true, y_pred)
+  end
+
+  defnp handle_ties(y_true, y_score) do
+    sorted_indices = Nx.argsort(y_score, axis: 0, direction: :desc)
+
+    sorted_y_true = Nx.take(y_true, sorted_indices)
+    sorted_y_score = Nx.take(y_score, sorted_indices)
+
+    tie_sorted_indices = Nx.argsort(sorted_y_true, axis: 0, direction: :desc)
+    adjusted_y_true = Nx.take(sorted_y_true, tie_sorted_indices)
+    adjusted_y_score = Nx.take(sorted_y_score, tie_sorted_indices)
+
+    {adjusted_y_true, adjusted_y_score}
+  end
+
+  defnp dcg_value(y_true) do
+    float_y_true = Nx.as_type(y_true, :f32)
+
+    log_tensor =
+      y_true
+      |> Nx.shape()
+      |> Nx.iota()
+      |> Nx.as_type(:f32)
+      |> Nx.add(2.0)
+      |> Nx.log2()
+
+    div_result = Nx.divide(float_y_true, log_tensor)
+
+    Nx.sum(div_result)
+  end
+
+  defnp truncate_at_k(tensor, opts) do
+    case opts[:k] do
+      nil ->
+        tensor
+
+      _ ->
+        if opts[:k] > Nx.axis_size(tensor, 0) do
+          tensor
+        else
+          {top_k, _rest} = Nx.split(tensor, opts[:k], axis: 0)
+          top_k
+        end
+    end
+  end
+end
diff --git a/lib/scholar/metrics/regression.ex b/lib/scholar/metrics/regression.ex
index 725f7b99..aa2385ad 100644
--- a/lib/scholar/metrics/regression.ex
+++ b/lib/scholar/metrics/regression.ex
@@ -71,8 +71,7 @@ defmodule Scholar.Metrics.Regression do
       >
   """
   defn mean_square_error(y_true, y_pred) do
-    diff = y_true - y_pred
-    (diff * diff) |> Nx.mean()
+    mean_tweedie_deviance_n(y_true, y_pred, 0)
   end
 
   @doc ~S"""
@@ -133,6 +132,170 @@ defmodule Scholar.Metrics.Regression do
     |> Nx.mean()
   end
 
+  @doc """
+  Calculates the mean Tweedie deviance of predictions
+  with respect to targets. Includes the Gaussian, Poisson,
+  Gamma and inverse-Gaussian families as special cases.
+
+  #{~S'''
+  $$d(y,\mu) =
+  \begin{cases}
+  (y-\mu)^2, & \text{for }p=0\\\\
+  2(y \log(y/\mu) + \mu - y), & \text{for }p=1\\\\
+  2(\log(\mu/y) + y/\mu - 1), & \text{for }p=2\\\\
+  2\left(\frac{\max(y,0)^{2-p}}{(1-p)(2-p)}-\frac{y\mu^{1-p}}{1-p}+\frac{\mu^{2-p}}{2-p}\right), & \text{for }p<0 \vee p>2
+  \end{cases}$$
+  '''}
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      iex> y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      iex> Scholar.Metrics.Regression.mean_tweedie_deviance(y_true, y_pred, 1)
+      #Nx.Tensor<
+        f32
+        0.18411168456077576
+      >
+  """
+  defn mean_tweedie_deviance(y_true, y_pred, power) do
+    mean_tweedie_deviance_n(y_true, y_pred, power)
+  end
+
+  @doc """
+  Similar to `mean_tweedie_deviance/3` but raises `RuntimeError` if the
+  inputs cannot be used with the given power argument.
+
+  Note: This function cannot be used in `defn`.
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      iex> y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      iex> Scholar.Metrics.Regression.mean_tweedie_deviance!(y_true, y_pred, 1)
+      #Nx.Tensor<
+        f32
+        0.18411168456077576
+      >
+  """
+  def mean_tweedie_deviance!(y_true, y_pred, power) do
+    message = "mean Tweedie deviance with power=#{power} can only be used on "
+
+    case check_tweedie_deviance_power(y_true, y_pred, power) |> Nx.to_number() do
+      1 -> :ok
+      2 -> raise message <> "strictly positive y_pred"
+      4 -> raise message <> "non-negative y_true and strictly positive y_pred"
+      5 -> raise message <> "strictly positive y_true and strictly positive y_pred"
+      100 -> raise "something went wrong, branch should never appear"
+    end
+
+    mean_tweedie_deviance_n(y_true, y_pred, power)
+  end
+
+  defnp mean_tweedie_deviance_n(y_true, y_pred, power) do
+    deviance =
+      cond do
+        power < 0 ->
+          2 *
+            (
+              Nx.pow(max(y_true, 0), 2 - power) / ((1 - power) * (2 - power))
+              -y_true * Nx.pow(y_pred, 1 - power) / (1 - power)
+              +Nx.pow(y_pred, 2 - power) / (2 - power)
+            )
+
+        # Normal distribution
+        power == 0 ->
+          Nx.pow(y_true - y_pred, 2)
+
+        # Poisson distribution
+        power == 1 ->
+          2 * (y_true * Nx.log(y_true / y_pred) + y_pred - y_true)
+
+        # Gamma distribution
+        power == 2 ->
+          2 * (Nx.log(y_pred / y_true) + y_true / y_pred - 1)
+
+        # 1 < power < 2 -> Compound Poisson distribution, non-negative with mass at zero
+        # power == 3 -> Inverse-Gaussian distribution
+        # power > 2 -> Stable distribution, with support on the positive reals
+        true ->
+          2 *
+            (
+              Nx.pow(y_true, 2 - power) / ((1 - power) * (2 - power))
+              -y_true * Nx.pow(y_pred, 1 - power) / (1 - power)
+              +Nx.pow(y_pred, 2 - power) / (2 - power)
+            )
+      end
+
+    Nx.mean(deviance)
+  end
+
+  defnp check_tweedie_deviance_power(y_true, y_pred, power) do
+    cond do
+      power < 0 ->
+        if Nx.all(y_pred > 0) do
+          Nx.u8(1)
+        else
+          Nx.u8(2)
+        end
+
+      power == 0 ->
+        Nx.u8(1)
+
+      power >= 1 and power < 2 ->
+        if Nx.all(y_true >= 0) and Nx.all(y_pred > 0) do
+          Nx.u8(1)
+        else
+          Nx.u8(4)
+        end
+
+      power >= 2 ->
+        if Nx.all(y_true > 0) and Nx.all(y_pred > 0) do
+          Nx.u8(1)
+        else
+          Nx.u8(5)
+        end
+
+      true ->
+        Nx.u8(100)
+    end
+  end
+
+  @doc """
+  Calculates the mean Poisson deviance of predictions
+  with respect to targets.
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      iex> y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      iex> Scholar.Metrics.Regression.mean_poisson_deviance(y_true, y_pred)
+      #Nx.Tensor<
+        f32
+        0.18411168456077576
+      >
+  """
+  defn mean_poisson_deviance(y_true, y_pred) do
+    mean_tweedie_deviance_n(y_true, y_pred, 1)
+  end
+
+  @doc """
+  Calculates the mean Gamma deviance of predictions
+  with respect to targets.
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      iex> y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      iex> Scholar.Metrics.Regression.mean_gamma_deviance(y_true, y_pred)
+      #Nx.Tensor<
+        f32
+        0.115888312458992
+      >
+  """
+  defn mean_gamma_deviance(y_true, y_pred) do
+    mean_tweedie_deviance_n(y_true, y_pred, 2)
+  end
+
   @doc """
   Calculates the $R^2$ score of predictions with respect to targets.
 
@@ -292,6 +455,46 @@ defmodule Scholar.Metrics.Regression do
     end
   end
 
+  @doc """
+  $D^2$ regression score function, fraction of Tweedie
+  deviance explained.
+
+  Best possible score is 1.0, lower values are worse and it
+  can also be negative.
+
+  Since it uses the mean Tweedie deviance, it also includes
+  the Gaussian, Poisson, Gamma and inverse-Gaussian
+  distribution families as special cases.
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      iex> y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      iex> Scholar.Metrics.Regression.d2_tweedie_score(y_true, y_pred, 1)
+      #Nx.Tensor<
+        f32
+        0.32202935218811035
+      >
+  """
+  defn d2_tweedie_score(y_true, y_pred, power) do
+    if Nx.size(y_pred) < 2 do
+      Nx.Constants.nan()
+    else
+      d2_tweedie_score_n(y_true, y_pred, power)
+    end
+  end
+
+  defnp d2_tweedie_score_n(y_true, y_pred, power) do
+    y_true = Nx.squeeze(y_true)
+    y_pred = Nx.squeeze(y_pred)
+
+    numerator = mean_tweedie_deviance_n(y_true, y_pred, power)
+    y_avg = Nx.mean(y_true)
+    denominator = mean_tweedie_deviance_n(y_true, y_avg, power)
+
+    1 - numerator / denominator
+  end
+
   @doc ~S"""
   Calculates the maximum residual error.
 
diff --git a/lib/scholar/naive_bayes/complement.ex b/lib/scholar/naive_bayes/complement.ex
index b81145c2..fce02c9c 100644
--- a/lib/scholar/naive_bayes/complement.ex
+++ b/lib/scholar/naive_bayes/complement.ex
@@ -6,6 +6,9 @@ defmodule Scholar.NaiveBayes.Complement do
   that each class has roughly the same representation. It is particularly
   suited for imbalanced data sets.
 
+  Time complexity is $O(K * N * C)$ where $N$ is the number of samples and $K$ is the number of features,
+  and $C$ is the number of classes.
+
   Reference:
 
   * [1] - [Paper about Complement Naive Bayes Algorithm](https://cdn.aaai.org/ICML/2003/ICML03-081.pdf)
diff --git a/lib/scholar/naive_bayes/gaussian.ex b/lib/scholar/naive_bayes/gaussian.ex
index 452a42dd..315061b5 100644
--- a/lib/scholar/naive_bayes/gaussian.ex
+++ b/lib/scholar/naive_bayes/gaussian.ex
@@ -7,6 +7,9 @@ defmodule Scholar.NaiveBayes.Gaussian do
 
   The parameters $\sigma\_{y}$ and $\mu\_{y}$ are estimated using maximum likelihood.
 
+  Time complexity is $O(K * N * C)$ where $N$ is the number of samples and $K$ is the number of features,
+  and $C$ is the number of classes.
+
   Reference:
 
   * [1] - [Detailed explanation of algorithm used to update feature means and variance online by Chan, Golub, and LaVeque](http://i.stanford.edu/pub/cstr/reports/cs/tr/79/773/CS-TR-79-773.pdf)
diff --git a/lib/scholar/naive_bayes/multinomial.ex b/lib/scholar/naive_bayes/multinomial.ex
index 06d5ba0f..33e4c31a 100644
--- a/lib/scholar/naive_bayes/multinomial.ex
+++ b/lib/scholar/naive_bayes/multinomial.ex
@@ -1,6 +1,9 @@
 defmodule Scholar.NaiveBayes.Multinomial do
   @moduledoc """
   Naive Bayes classifier for multinomial models.
+
+  Time complexity is $O(K * N * C)$ where $N$ is the number of samples and $K$ is the number of features,
+  and $C$ is the number of classes.
   """
   import Nx.Defn
   import Scholar.Shared
diff --git a/lib/scholar/neighbors/k_nearest_neighbors.ex b/lib/scholar/neighbors/k_nearest_neighbors.ex
index 0223a3b6..a41ee5c8 100644
--- a/lib/scholar/neighbors/k_nearest_neighbors.ex
+++ b/lib/scholar/neighbors/k_nearest_neighbors.ex
@@ -1,6 +1,9 @@
 defmodule Scholar.Neighbors.KNearestNeighbors do
   @moduledoc """
-  The K-Nearest Neighbors. It implements both classification and regression.
+  The K-Nearest Neighbors.
+
+  It implements both classification and regression. This implements the linear
+  version of kNN and therefore it has time complexity $O(N^2)$ for $N$ samples.
   """
   import Nx.Defn
   import Scholar.Shared
@@ -162,7 +165,7 @@ defmodule Scholar.Neighbors.KNearestNeighbors do
 
   ## Return Values
 
-    It returns a tensor with predicted class labels
+  It returns a tensor with predicted class labels.
 
   ## Examples
 
@@ -210,7 +213,7 @@ defmodule Scholar.Neighbors.KNearestNeighbors do
 
   ## Return Values
 
-    It returns a tensor with probabilities of classes. They are arranged in lexicographic order.
+  It returns a tensor with probabilities of classes. They are arranged in lexicographic order.
 
   ## Examples
 
diff --git a/lib/scholar/neighbors/kd_tree.ex b/lib/scholar/neighbors/kd_tree.ex
new file mode 100644
index 00000000..c80077d8
--- /dev/null
+++ b/lib/scholar/neighbors/kd_tree.ex
@@ -0,0 +1,350 @@
+defmodule Scholar.Neighbors.KDTree do
+  @moduledoc """
+  Implements a kd-tree, a space-partitioning data structure for organizing points
+  in a k-dimensional space.
+
+  This is implemented as one-dimensional tensor with indices pointed to highest
+  dimension of the given tensor. Traversal starts by calling `root/0` and then
+  accessing the `left_child/1` and `right_child/1`. The tree is left-balanced.
+
+  Two construction modes are available:
+
+    * `bounded/2` - the tensor has min and max values with an amplitude given by `max - min`.
+      It is also guaranteed that the `amplitude * levels(tensor) + 1` does not overflow
+      the tensor. See `amplitude/1` to verify if this holds. This implementation happens
+      fully within `defn`. This version is orders of magnitude faster than the `unbounded/2`
+      one.
+
+    * `unbounded/2` - there are no known bounds (min and max values) to the tensor.
+      This implementation is recursive and goes in and out of the `defn`, therefore
+      it cannot be called inside `defn`.
+
+  Each level traverses over the last axis of tensor, the index for a level can be
+  computed as: `rem(level, Nx.axis_size(tensor, -1))`.
+
+  ## References
+
+    * [GPU-friendly, Parallel, and (Almost-)In-Place Construction of Left-Balanced k-d Trees](https://arxiv.org/pdf/2211.00120.pdf).
+  """
+
+  import Nx.Defn
+
+  @derive {Nx.Container, keep: [:levels], containers: [:indexes, :data]}
+  @enforce_keys [:levels, :indexes, :data]
+  defstruct [:levels, :indexes, :data]
+
+  @doc """
+  Builds a KDTree without known min-max bounds.
+
+  If your tensor has known bounds (for example, -1 and 1),
+  consider using the `bounded/2` version which is often orders of
+  magnitude more efficient.
+
+  ## Options
+
+    * `:compiler` - the default compiler to use for internal defn operations
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.unbounded(Nx.iota({5, 2}), compiler: EXLA)
+      %Scholar.Neighbors.KDTree{
+        data: Nx.iota({5, 2}),
+        levels: 3,
+        indexes: Nx.u32([3, 1, 4, 0, 2])
+      }
+
+  """
+  def unbounded(tensor, opts \\ []) do
+    levels = levels(tensor)
+    {size, _dims} = Nx.shape(tensor)
+
+    indexes =
+      if size > 2 do
+        subtree_size = unbounded_subtree_size(1, levels, size)
+        {left, mid, right} = Nx.Defn.jit_apply(&root_slice(&1, subtree_size), [tensor], opts)
+
+        acc = <<Nx.to_number(mid)::32-unsigned-native-integer>>
+        acc = recur([{1, left}, {2, right}], [], acc, tensor, 1, levels, opts)
+        Nx.from_binary(acc, :u32)
+      else
+        Nx.argsort(tensor[[.., 0]], direction: :desc, type: :u32)
+      end
+
+    %__MODULE__{levels: levels, indexes: indexes, data: tensor}
+  end
+
+  defp recur([{_i, %Nx.Tensor{shape: {1}} = leaf} | rest], next, acc, tensor, level, levels, opts) do
+    [leaf] = Nx.to_flat_list(leaf)
+    acc = <<acc::binary, leaf::32-unsigned-native-integer>>
+    recur(rest, next, acc, tensor, level, levels, opts)
+  end
+
+  defp recur([{i, %Nx.Tensor{shape: {2}} = node} | rest], next, acc, tensor, level, levels, opts) do
+    acc = <<acc::binary, Nx.to_number(node[1])::32-unsigned-native-integer>>
+    next = [{left_child(i), Nx.slice(node, [0], [1])} | next]
+    recur(rest, next, acc, tensor, level, levels, opts)
+  end
+
+  defp recur([{i, indexes} | rest], next, acc, tensor, level, levels, opts) do
+    %Nx.Tensor{shape: {size, dims}} = tensor
+    k = rem(level, dims)
+    subtree_size = unbounded_subtree_size(left_child(i), levels, size)
+
+    {left, mid, right} =
+      Nx.Defn.jit_apply(&recur_slice(&1, &2, &3, subtree_size), [tensor, indexes, k], opts)
+
+    next = [{right_child(i), right}, {left_child(i), left} | next]
+    acc = <<acc::binary, Nx.to_number(mid)::32-unsigned-native-integer>>
+    recur(rest, next, acc, tensor, level, levels, opts)
+  end
+
+  defp recur([], [], acc, _tensor, _level, _levels, _opts) do
+    acc
+  end
+
+  defp recur([], next, acc, tensor, level, levels, opts) do
+    recur(Enum.reverse(next), [], acc, tensor, level + 1, levels, opts)
+  end
+
+  defp root_slice(tensor, subtree_size) do
+    indexes = Nx.argsort(tensor[[.., 0]], type: :u32)
+
+    {Nx.slice(indexes, [0], [subtree_size]), indexes[subtree_size],
+     Nx.slice(indexes, [subtree_size + 1], [Nx.size(indexes) - subtree_size - 1])}
+  end
+
+  defp recur_slice(tensor, indexes, k, subtree_size) do
+    sorted = Nx.argsort(Nx.take(tensor, indexes)[[.., k]], type: :u32)
+    indexes = Nx.take(indexes, sorted)
+
+    {Nx.slice(indexes, [0], [subtree_size]), indexes[subtree_size],
+     Nx.slice(indexes, [subtree_size + 1], [Nx.size(indexes) - subtree_size - 1])}
+  end
+
+  defp unbounded_subtree_size(i, levels, size) do
+    import Bitwise
+    diff = levels - unbounded_level(i) - 1
+    shifted = 1 <<< diff
+    fllc_s = (i <<< diff) + shifted - 1
+    shifted - 1 + min(max(0, size - fllc_s), shifted)
+  end
+
+  defp unbounded_level(i) when is_integer(i), do: floor(:math.log2(i + 1))
+
+  @doc """
+  Builds a KDTree with known min-max bounds entirely within `defn`.
+
+  This requires the amplitude `|max - min|` of the tensor to be given
+  such that `max + (amplitude + 1) * (size - 1)` does not overflow the
+  maximum tensor type.
+
+  For example, a tensor where all values are between 0 and 1 has amplitude
+  1. Values between -1 and 1 has amplitude 2. If your tensor is normalized
+  to floating points, then it is most likely bounded (given their high
+  precision). You can use `amplitude/1` to check your assumptions.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.bounded(Nx.iota({5, 2}), 10)
+      %Scholar.Neighbors.KDTree{
+        data: Nx.iota({5, 2}),
+        levels: 3,
+        indexes: Nx.u32([3, 1, 4, 0, 2])
+      }
+  """
+  deftransform bounded(tensor, amplitude) do
+    %__MODULE__{levels: levels(tensor), indexes: bounded_n(tensor, amplitude), data: tensor}
+  end
+
+  defnp bounded_n(tensor, amplitude) do
+    levels = levels(tensor)
+    {size, dims} = Nx.shape(tensor)
+    band = amplitude + 1
+    tags = Nx.broadcast(Nx.u32(0), {size})
+
+    {level, tags, _tensor, _band} =
+      while {level = Nx.u32(0), tags, tensor, band}, level < levels - 1 do
+        k = rem(level, dims)
+        indexes = Nx.argsort(tensor[[.., k]] + band * tags, type: :u32)
+        tags = update_tags(tags, indexes, level, levels, size)
+        {level + 1, tags, tensor, band}
+      end
+
+    k = rem(level, dims)
+    Nx.argsort(tensor[[.., k]] + band * tags, type: :u32)
+  end
+
+  defnp update_tags(tags, indexes, level, levels, size) do
+    pos = Nx.argsort(indexes, type: :u32)
+
+    pivot =
+      bounded_segment_begin(tags, levels, size) +
+        bounded_subtree_size(left_child(tags), levels, size)
+
+    Nx.select(
+      pos < (1 <<< level) - 1,
+      tags,
+      Nx.select(
+        pos < pivot,
+        left_child(tags),
+        Nx.select(
+          pos > pivot,
+          right_child(tags),
+          tags
+        )
+      )
+    )
+  end
+
+  defnp bounded_subtree_size(i, levels, size) do
+    diff = levels - bounded_level(i) - 1
+    shifted = 1 <<< diff
+    first_lowest_level = (i <<< diff) + shifted - 1
+    # Use select instead of max to deal with overflows
+    lowest_level = Nx.select(first_lowest_level > size, Nx.u32(0), size - first_lowest_level)
+    shifted - 1 + min(lowest_level, shifted)
+  end
+
+  defnp bounded_segment_begin(i, levels, size) do
+    level = bounded_level(i)
+    top = (1 <<< level) - 1
+    diff = levels - level - 1
+    shifted = 1 <<< diff
+    left_siblings = i - top
+
+    top + left_siblings * (shifted - 1) +
+      min(left_siblings * shifted, size - (1 <<< (levels - 1)) + 1)
+  end
+
+  # Since this property relies on u32, let's check the tensor type.
+  deftransformp bounded_level(%Nx.Tensor{type: {:u, 32}} = i) do
+    Nx.subtract(31, Nx.count_leading_zeros(Nx.add(i, 1)))
+  end
+
+  @doc """
+  Returns the amplitude of a bounded tensor.
+
+  If -1 is returned, it means the tensor cannot use the `bounded` algorithm
+  to generate a KDTree and `unbounded/2` must be used instead.
+
+  This cannot be invoked inside a `defn`.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.amplitude(Nx.iota({10, 2}))
+      19
+      iex> Scholar.Neighbors.KDTree.amplitude(Nx.iota({20, 2}, type: :f32))
+      39.0
+      iex> Scholar.Neighbors.KDTree.amplitude(Nx.iota({20, 2}, type: :u8))
+      -1
+      iex> Scholar.Neighbors.KDTree.amplitude(Nx.negate(Nx.iota({10, 2})))
+      19
+
+  """
+  def amplitude(tensor) do
+    max = tensor |> Nx.reduce_max() |> Nx.to_number()
+    min = tensor |> Nx.reduce_min() |> Nx.to_number()
+    amplitude = abs(max - min)
+    limit = tensor.type |> Nx.Constants.max_finite() |> Nx.to_number()
+
+    if max + (amplitude + 1) * (Nx.axis_size(tensor, 0) - 1) > limit do
+      -1
+    else
+      amplitude
+    end
+  end
+
+  @doc """
+  Returns the number of resulting levels in a KDTree for `tensor`.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.levels(Nx.iota({10, 3}))
+      4
+  """
+  deftransform levels(%Nx.Tensor{} = tensor) do
+    case Nx.shape(tensor) do
+      {size, _dims} -> ceil(:math.log2(size + 1))
+      _ -> raise ArgumentError, "KDTrees requires a tensor of rank 2"
+    end
+  end
+
+  @doc """
+  Returns the root index.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.root()
+      0
+
+  """
+  deftransform root, do: 0
+
+  @doc """
+  Returns the parent of child `i`.
+
+  It is your responsibility to guarantee the result is positive.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.parent(1)
+      0
+      iex> Scholar.Neighbors.KDTree.parent(2)
+      0
+
+      iex> Scholar.Neighbors.KDTree.parent(Nx.u32(3))
+      #Nx.Tensor<
+        u32
+        1
+      >
+
+  """
+  deftransform parent(i) when is_integer(i), do: div(i - 1, 2)
+  deftransform parent(%Nx.Tensor{} = t), do: Nx.quotient(Nx.subtract(t, 1), 2)
+
+  @doc """
+  Returns the index of the left child of i.
+
+  It is your responsibility to guarantee the result
+  is not greater than the leading axis of the tensor.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.left_child(0)
+      1
+      iex> Scholar.Neighbors.KDTree.left_child(1)
+      3
+
+      iex> Scholar.Neighbors.KDTree.left_child(Nx.u32(3))
+      #Nx.Tensor<
+        u32
+        7
+      >
+
+  """
+  deftransform left_child(i) when is_integer(i), do: 2 * i + 1
+  deftransform left_child(%Nx.Tensor{} = t), do: Nx.add(Nx.multiply(2, t), 1)
+
+  @doc """
+  Returns the index of the right child of i.
+
+  It is your responsibility to guarantee the result
+  is not greater than the leading axis of the tensor.
+
+  ## Examples
+
+      iex> Scholar.Neighbors.KDTree.right_child(0)
+      2
+      iex> Scholar.Neighbors.KDTree.right_child(1)
+      4
+
+      iex> Scholar.Neighbors.KDTree.right_child(Nx.u32(3))
+      #Nx.Tensor<
+        u32
+        8
+      >
+
+  """
+  deftransform right_child(i) when is_integer(i), do: 2 * i + 2
+  deftransform right_child(%Nx.Tensor{} = t), do: Nx.add(Nx.multiply(2, t), 2)
+end
diff --git a/lib/scholar/neighbors/radius_nearest_neighbors.ex b/lib/scholar/neighbors/radius_nearest_neighbors.ex
index 66c378b1..b1eca0e3 100644
--- a/lib/scholar/neighbors/radius_nearest_neighbors.ex
+++ b/lib/scholar/neighbors/radius_nearest_neighbors.ex
@@ -1,6 +1,8 @@
 defmodule Scholar.Neighbors.RadiusNearestNeighbors do
   @moduledoc """
-  The Radius Nearest Neighbors. It implements both classification and regression.
+  The Radius Nearest Neighbors.
+
+  It implements both classification and regression.
   """
   import Nx.Defn
   import Scholar.Shared
diff --git a/lib/scholar/options.ex b/lib/scholar/options.ex
index a779d572..e0173ad1 100644
--- a/lib/scholar/options.ex
+++ b/lib/scholar/options.ex
@@ -100,4 +100,12 @@ defmodule Scholar.Options do
     {:error,
      "expected metric to be a :cosine or tuple {:minkowski, p} where p is a positive number or :infinity, got: #{inspect(metric)}"}
   end
+
+  def beta(beta) do
+    if (is_number(beta) and beta >= 0) or (Nx.is_tensor(beta) and Nx.rank(beta) == 0) do
+      {:ok, beta}
+    else
+      {:error, "expect 'beta' to be in the range [0, inf]"}
+    end
+  end
 end
diff --git a/lib/scholar/stats.ex b/lib/scholar/stats.ex
index 188a0df4..e3cf20a8 100644
--- a/lib/scholar/stats.ex
+++ b/lib/scholar/stats.ex
@@ -181,6 +181,9 @@ defmodule Scholar.Stats do
     * $Cov(X\_i, X\_j)$ is covariance between features $X_i$ and $X_j$
   '''}
 
+  Time complexity of correlation estimation is $O(N * K^2)$ where $N$ is the number of samples
+  and $K$ is the number of features.
+
   ## Example
 
       iex> Scholar.Stats.correlation_matrix(Nx.tensor([[3, 6, 5], [26, 75, 3], [23, 4, 1]]))
diff --git a/mix.exs b/mix.exs
index 4908188d..02acd3bb 100644
--- a/mix.exs
+++ b/mix.exs
@@ -31,10 +31,11 @@ defmodule Scholar.MixProject do
     [
       {:ex_doc, "~> 0.30", only: :docs},
       # {:nx, "~> 0.6", override: true},
-      {:nx, github: "elixir-nx/nx", sparse: "nx", override: true},
+      {:nx, github: "elixir-nx/nx", sparse: "nx", override: true, branch: "v0.6"},
       {:nimble_options, "~> 0.5.2 or ~> 1.0"},
       {:exla, "~> 0.6", optional: true},
-      {:polaris, "~> 0.1"}
+      {:polaris, "~> 0.1"},
+      {:benchee, "~> 1.0", only: :dev}
     ]
   end
 
@@ -49,11 +50,12 @@ defmodule Scholar.MixProject do
 
   defp docs do
     [
-      main: "Scholar",
+      main: "readme",
       source_url: @source_url,
       logo: "images/scholar_simplified.png",
       extra_section: "Guides",
       extras: [
+        "README.md",
         "notebooks/linear_regression.livemd",
         "notebooks/k_means.livemd",
         "notebooks/k_nearest_neighbors.livemd",
diff --git a/mix.lock b/mix.lock
index a69d4862..c17916d2 100644
--- a/mix.lock
+++ b/mix.lock
@@ -1,6 +1,8 @@
 %{
+  "benchee": {:hex, :benchee, "1.1.0", "f3a43817209a92a1fade36ef36b86e1052627fd8934a8b937ac9ab3a76c43062", [:mix], [{:deep_merge, "~> 1.0", [hex: :deep_merge, repo: "hexpm", optional: false]}, {:statistex, "~> 1.0", [hex: :statistex, repo: "hexpm", optional: false]}], "hexpm", "7da57d545003165a012b587077f6ba90b89210fd88074ce3c60ce239eb5e6d93"},
   "complex": {:hex, :complex, "0.5.0", "af2d2331ff6170b61bb738695e481b27a66780e18763e066ee2cd863d0b1dd92", [:mix], [], "hexpm", "2683bd3c184466cfb94fad74cbfddfaa94b860e27ad4ca1bffe3bff169d91ef1"},
-  "earmark_parser": {:hex, :earmark_parser, "1.4.33", "3c3fd9673bb5dcc9edc28dd90f50c87ce506d1f71b70e3de69aa8154bc695d44", [:mix], [], "hexpm", "2d526833729b59b9fdb85785078697c72ac5e5066350663e5be6a1182da61b8f"},
+  "deep_merge": {:hex, :deep_merge, "1.0.0", "b4aa1a0d1acac393bdf38b2291af38cb1d4a52806cf7a4906f718e1feb5ee961", [:mix], [], "hexpm", "ce708e5f094b9cd4e8f2be4f00d2f4250c4095be93f8cd6d018c753894885430"},
+  "earmark_parser": {:hex, :earmark_parser, "1.4.37", "2ad73550e27c8946648b06905a57e4d454e4d7229c2dafa72a0348c99d8be5f7", [:mix], [], "hexpm", "6b19783f2802f039806f375610faa22da130b8edc21209d0bff47918bb48360e"},
   "elixir_make": {:hex, :elixir_make, "0.7.7", "7128c60c2476019ed978210c245badf08b03dbec4f24d05790ef791da11aa17c", [:mix], [{:castore, "~> 0.1 or ~> 1.0", [hex: :castore, repo: "hexpm", optional: true]}], "hexpm", "5bc19fff950fad52bbe5f211b12db9ec82c6b34a9647da0c2224b8b8464c7e6c"},
   "ex_doc": {:hex, :ex_doc, "0.30.6", "5f8b54854b240a2b55c9734c4b1d0dd7bdd41f71a095d42a70445c03cf05a281", [:mix], [{:earmark_parser, "~> 1.4.31", [hex: :earmark_parser, repo: "hexpm", optional: false]}, {:makeup_elixir, "~> 0.14", [hex: :makeup_elixir, repo: "hexpm", optional: false]}, {:makeup_erlang, "~> 0.1", [hex: :makeup_erlang, repo: "hexpm", optional: false]}], "hexpm", "bd48f2ddacf4e482c727f9293d9498e0881597eae6ddc3d9562bd7923375109f"},
   "exla": {:hex, :exla, "0.6.0", "af63e45ce41ad25630967923147d14292a0cc48e507b8a3cf3bf3d5483099a28", [:make, :mix], [{:elixir_make, "~> 0.6", [hex: :elixir_make, repo: "hexpm", optional: false]}, {:nx, "~> 0.6.0", [hex: :nx, repo: "hexpm", optional: false]}, {:telemetry, "~> 0.4.0 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}, {:xla, "~> 0.5.0", [hex: :xla, repo: "hexpm", optional: false]}], "hexpm", "5f6a4a105ea9ab207b9aa4de5a294730e2bfe9639f4b8d37a7c00da131090d7a"},
@@ -9,8 +11,9 @@
   "makeup_erlang": {:hex, :makeup_erlang, "0.1.2", "ad87296a092a46e03b7e9b0be7631ddcf64c790fa68a9ef5323b6cbb36affc72", [:mix], [{:makeup, "~> 1.0", [hex: :makeup, repo: "hexpm", optional: false]}], "hexpm", "f3f5a1ca93ce6e092d92b6d9c049bcda58a3b617a8d888f8e7231c85630e8108"},
   "nimble_options": {:hex, :nimble_options, "0.5.2", "42703307b924880f8c08d97719da7472673391905f528259915782bb346e0a1b", [:mix], [], "hexpm", "4da7f904b915fd71db549bcdc25f8d56f378ef7ae07dc1d372cbe72ba950dce0"},
   "nimble_parsec": {:hex, :nimble_parsec, "1.3.1", "2c54013ecf170e249e9291ed0a62e5832f70a476c61da16f6aac6dca0189f2af", [:mix], [], "hexpm", "2682e3c0b2eb58d90c6375fc0cc30bc7be06f365bf72608804fb9cffa5e1b167"},
-  "nx": {:git, "https://github.com/elixir-nx/nx.git", "a0b7e2e5cc7a62a55cd2e7bbc3e44ba2ac1c996b", [sparse: "nx"]},
+  "nx": {:git, "https://github.com/elixir-nx/nx.git", "ef464cfd0935eb4c2c1fa9a40f099b098a0b95bf", [sparse: "nx", branch: "v0.6"]},
   "polaris": {:hex, :polaris, "0.1.0", "dca61b18e3e801ecdae6ac9f0eca5f19792b44a5cb4b8d63db50fc40fc038d22", [:mix], [{:nx, "~> 0.5", [hex: :nx, repo: "hexpm", optional: false]}], "hexpm", "13ef2b166650e533cb24b10e2f3b8ab4f2f449ba4d63156e8c569527f206e2c2"},
+  "statistex": {:hex, :statistex, "1.0.0", "f3dc93f3c0c6c92e5f291704cf62b99b553253d7969e9a5fa713e5481cd858a5", [:mix], [], "hexpm", "ff9d8bee7035028ab4742ff52fc80a2aa35cece833cf5319009b52f1b5a86c27"},
   "telemetry": {:hex, :telemetry, "1.2.1", "68fdfe8d8f05a8428483a97d7aab2f268aaff24b49e0f599faa091f1d4e7f61c", [:rebar3], [], "hexpm", "dad9ce9d8effc621708f99eac538ef1cbe05d6a874dd741de2e689c47feafed5"},
   "xla": {:hex, :xla, "0.5.0", "fb8a02c02e5a4f4531fbf18a90c325e471037f983f0115d23f510e7dd9a6aa65", [:make, :mix], [{:elixir_make, "~> 0.4", [hex: :elixir_make, repo: "hexpm", optional: false]}], "hexpm", "571ac797a4244b8ba8552ed0295a54397bd896708be51e4da6cbb784f6678061"},
 }
diff --git a/notebooks/k_means.livemd b/notebooks/k_means.livemd
index dd8aa3ff..e7b99523 100644
--- a/notebooks/k_means.livemd
+++ b/notebooks/k_means.livemd
@@ -12,22 +12,16 @@ Mix.install([
   {:scidata, "~> 0.1.10"},
   {:req, "~> 0.3.9"},
   {:kino, "~> 0.10.0"},
-  {:kino_vega_lite, "~> 0.1.9"}
+  {:kino_vega_lite, "~> 0.1.9"},
+  {:tucan, "~> 0.2.1"}
 ])
 ```
 
-<!-- livebook:{"output":true} -->
-
-```
-:ok
-```
-
 ## Introduction
 
 The main purpose of this livebook is to introduce the **KMeans** clustering algorithm. We will explore KMeans in three different use cases.
 
 ```elixir
-alias VegaLite, as: Vl
 alias Scholar.Cluster.KMeans
 require Explorer.DataFrame, as: DF
 Nx.global_default_backend(EXLA.Backend)
@@ -36,14 +30,6 @@ key = Nx.Random.key(42)
 
 <!-- livebook:{"output":true} -->
 
-```
-
-02:30:02.231 [info] TfrtCpuClient created.
-
-```
-
-<!-- livebook:{"output":true} -->
-
 ```
 #Nx.Tensor<
   u32[2]
@@ -143,66 +129,46 @@ DF.summarise(
 We see that `petal_length` and `petal_width` are the most distinguishing features. Let's explore them a little bit more.
 
 ```elixir
-Vl.new(title: [text: "Histograms of petal_length column by species", offset: 25, anchor: :middle])
-|> Vl.data_from_values(df)
-|> Vl.facet(
-  [field: "species"],
-  Vl.new(width: 200, height: 200)
-  |> Vl.mark(:bar)
-  |> Vl.encode_field(:x, "petal_length", type: :quantitative, bin: true)
-  |> Vl.encode(:y, aggregate: :count, scale: [domain: [0, 55]])
-)
+Tucan.histogram(df, "petal_length", color_by: "species")
+|> Tucan.facet_by(:column, "species")
+|> Tucan.Scale.set_y_domain(0, 55)
+|> Tucan.set_size(200, 200)
+|> Tucan.set_title("Histograms of petal_length column by species", offset: 25, anchor: :middle)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
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of petal_length column by species"},"transform":[{"as":"bin_petal_length","bin":true,"field":"petal_length"},{"aggregate":[{"as":"count_petal_length","op":"count"}],"groupby":["bin_petal_length","bin_petal_length_end","species"]}],"width":200}
 ```
 
 ```elixir
-Vl.new(
-  width: 300,
-  height: 300,
-  title: [
-    text: "Scatterplot of data samples projected on plane petal_width x petal_length",
-    offset: 25
-  ]
+Tucan.scatter(df, "petal_length", "petal_width", filled: true, color_by: "species")
+|> Tucan.set_size(300, 300)
+|> Tucan.set_title("Scatterplot of data samples projected on plane petal_width x petal_length",
+  offset: 25
 )
-|> Vl.data_from_values(df)
-|> Vl.mark(:circle)
-|> Vl.encode_field(:x, "petal_length", type: :quantitative)
-|> Vl.encode_field(:y, "petal_width", type: :quantitative)
-|> Vl.encode_field(:color, "species")
 ```
 
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 ```vega-lite
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"Iris-virginica"},{"petal_length":5.0,"petal_width":1.9,"sepal_length":6.3,"sepal_width":2.5,"species":"Iris-virginica"},{"petal_length":5.2,"petal_width":2.0,"sepal_length":6.5,"sepal_width":3.0,"species":"Iris-virginica"},{"petal_length":5.4,"petal_width":2.3,"sepal_length":6.2,"sepal_width":3.4,"species":"Iris-virginica"},{"petal_length":5.1,"petal_width":1.8,"sepal_length":5.9,"sepal_width":3.0,"species":"Iris-virginica"}]},"encoding":{"color":{"field":"species","type":"nominal"},"x":{"field":"petal_length","scale":{"zero":false},"type":"quantitative"},"y":{"field":"petal_width","scale":{"zero":false},"type":"quantitative"}},"height":300,"mark":{"fillOpacity":1,"filled":true,"type":"point"},"title":{"offset":25,"text":"Scatterplot of data samples projected on plane petal_width x petal_length"},"width":300}
 ```
 
 ```elixir
-Vl.new(
-  title: [
-    text: "Scatterplot of data samples projected on plane petal_width x petal_length by species",
-    offset: 25
-  ]
-)
-|> Vl.data_from_values(df)
-|> Vl.facet(
-  [field: "species"],
-  Vl.new(width: 200, height: 200)
-  |> Vl.mark(:point)
-  |> Vl.encode_field(:x, "petal_length", type: :quantitative)
-  |> Vl.encode_field(:y, "petal_width", type: :quantitative)
+Tucan.scatter(df, "petal_length", "petal_width")
+|> Tucan.facet_by(:column, "species")
+|> Tucan.set_title(
+  "Scatterplot of data samples projected on plane petal_width x petal_length by species",
+  offset: 25
 )
 ```
 
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"Iris-virginica"},{"petal_length":5.0,"petal_width":1.9,"sepal_length":6.3,"sepal_width":2.5,"species":"Iris-virginica"},{"petal_length":5.2,"petal_width":2.0,"sepal_length":6.5,"sepal_width":3.0,"species":"Iris-virginica"},{"petal_length":5.4,"petal_width":2.3,"sepal_length":6.2,"sepal_width":3.4,"species":"Iris-virginica"},{"petal_length":5.1,"petal_width":1.8,"sepal_length":5.9,"sepal_width":3.0,"species":"Iris-virginica"}]},"encoding":{"column":{"field":"species"},"x":{"field":"petal_length","scale":{"zero":false},"type":"quantitative"},"y":{"field":"petal_width","scale":{"zero":false},"type":"quantitative"}},"mark":{"fillOpacity":1,"type":"point"},"title":{"offset":25,"text":"Scatterplot of data samples projected on plane petal_width x petal_length by species"}}
 ```
 
 Now we have a better understanding of the data. Iris species have different petal widths and petal lengths. Iris *Setosa* has the smallest petal, *Versicolor* is medium size, and *Virginica* has the largest petal. We can ascertain that our analysis is correct and plot the so-called **Elbow plot**. The Elbow plot is a plot which presents Inertia vs the number of clusters. If there is a characteristic elbow, then we have a strong suggestion that the number of clusters is correct. Let's train KMeans models for a different number of clusters from range 1 to 11.
@@ -227,21 +193,18 @@ inertias = for model <- models, do: Nx.to_number(model.inertia)
 ```
 
 ```elixir
-Vl.new(width: 600, height: 300, title: "Elbow Plot")
-|> Vl.data_from_values(num_clusters: clusterings, inertia: inertias)
-|> Vl.mark(:line)
-|> Vl.encode_field(:x, "num_clusters",
-  title: "Number of Clusters",
-  type: :ordinal,
-  axis: [label_angle: 0]
+Tucan.lineplot([num_clusters: clusterings, inertia: inertias], "num_clusters", "inertia",
+  x: [type: :nominal, axis: [label_angle: 0]],
+  title: "Elbow Plot"
 )
-|> Vl.encode_field(:y, "inertia", title: "Inertia", type: :quantitative)
+|> Tucan.Axes.set_xy_titles("Number of Clusters", "Inertia")
+|> Tucan.set_size(600, 300)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"inertia":680.8244,"num_clusters":1},{"inertia":152.36870647733906,"num_clusters":2},{"inertia":78.94084142614602,"num_clusters":3},{"inertia":57.44028021295475,"num_clusters":4},{"inertia":46.56163015873016,"num_clusters":5},{"inertia":38.95701115711985,"num_clusters":6},{"inertia":35.15943976939724,"num_clusters":7},{"inertia":30.324232174688056,"num_clusters":8},{"inertia":27.927083333333336,"num_clusters":9},{"inertia":26.371291306519566,"num_clusters":10},{"inertia":24.004956137000256,"num_clusters":11}]},"encoding":{"x":{"axis":{"labelAngle":0},"field":"num_clusters","title":"Number of Clusters","type":"ordinal"},"y":{"field":"inertia","title":"Inertia","type":"quantitative"}},"height":300,"mark":"line","title":"Elbow Plot","width":600}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"inertia":680.8244000000001,"num_clusters":1},{"inertia":152.36870647733906,"num_clusters":2},{"inertia":78.94084142614601,"num_clusters":3},{"inertia":57.44028021295475,"num_clusters":4},{"inertia":46.56163015873015,"num_clusters":5},{"inertia":38.95701115711985,"num_clusters":6},{"inertia":35.15943976939724,"num_clusters":7},{"inertia":30.324232174688056,"num_clusters":8},{"inertia":27.92708333333333,"num_clusters":9},{"inertia":26.371291306519566,"num_clusters":10},{"inertia":24.00495613700025,"num_clusters":11}]},"encoding":{"x":{"axis":{"labelAngle":0,"title":"Number of Clusters"},"field":"num_clusters","type":"nominal"},"y":{"axis":{"title":"Inertia"},"field":"inertia","type":"quantitative"}},"height":300,"mark":{"fillOpacity":1,"type":"line"},"title":"Elbow Plot","width":600}
 ```
 
 As you can see, we have the elbow when the number of clusters equals three. So this value of the parameter seems to be the best.
@@ -298,34 +261,25 @@ coords = [
   cluster_petal_width: best_model.clusters[[.., 3]] |> Nx.to_flat_list()
 ]
 
-Vl.new(
-  width: 300,
-  height: 300,
-  title: [
-    text:
-      "Scatterplot of data samples projected on plane petal_width x petal_length with calculated centroids",
-    offset: 25
-  ]
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(df)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "petal_length", type: :quantitative)
-  |> Vl.encode_field(:y, "petal_width", type: :quantitative)
-  |> Vl.encode_field(:color, "species"),
-  Vl.new()
-  |> Vl.data_from_values(coords)
-  |> Vl.mark(:circle, color: :green, size: 100)
-  |> Vl.encode_field(:x, "cluster_petal_length", type: :quantitative)
-  |> Vl.encode_field(:y, "cluster_petal_width", type: :quantitative)
+Tucan.layers([
+  Tucan.scatter(df, "petal_length", "petal_width", color_by: "species", filled: true),
+  Tucan.scatter(coords, "cluster_petal_length", "cluster_petal_width",
+    filled: true,
+    point_size: 100,
+    point_color: "green"
+  )
 ])
+|> Tucan.set_size(300, 300)
+|> Tucan.set_title(
+  "Scatterplot of data samples projected on plane petal_width x petal_length with calculated centroids",
+  offset: 25
+)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":300,"layer":[{"data":{"values":[{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.7,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.1,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.2,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.7,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.7,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.0,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.7,"petal_width":0.5,"species":"Iris-setosa"},{"petal_length":1.9,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.2,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.1,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.3,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.6,"species":"Iris-setosa"},{"petal_length":1.9,"petal_width":0.4,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.3,"species":"Iris-setosa"},{"petal_length":1.6,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.5,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":1.4,"petal_width":0.2,"species":"Iris-setosa"},{"petal_length":4.7,"petal_width":1.4,"species":"Iris-versicolor"},{"petal_length":4.5,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.9,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.0,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":4.6,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.5,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":4.7,"petal_width":1.6,"species":"Iris-versicolor"},{"petal_length":3.3,"petal_width":1.0,"species":"Iris-versicolor"},{"petal_length":4.6,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":3.9,"petal_width":1.4,"species":"Iris-versicolor"},{"petal_length":3.5,"petal_width":1.0,"species":"Iris-versicolor"},{"petal_length":4.2,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.0,"petal_width":1.0,"species":"Iris-versicolor"},{"petal_length":4.7,"petal_width":1.4,"species":"Iris-versicolor"},{"petal_length":3.6,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":4.4,"petal_width":1.4,"species":"Iris-versicolor"},{"petal_length":4.5,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.1,"petal_width":1.0,"species":"Iris-versicolor"},{"petal_length":4.5,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":3.9,"petal_width":1.1,"species":"Iris-versicolor"},{"petal_length":4.8,"petal_width":1.8,"species":"Iris-versicolor"},{"petal_length":4.0,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":4.9,"petal_width":1.5,"species":"Iris-versicolor"},{"petal_length":4.7,"petal_width":1.2,"species":"Iris-versicolor"},{"petal_length":4.3,"petal_width":1.3,"species":"Iris-versicolor"},{"petal_length":4.4,"petal_width":1.4,"species":"Iris-versicolor"},{"pet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of data samples projected on plane petal_width x petal_length with calculated centroids"},"width":300}
 ```
 
 As we expect 😎
@@ -1203,25 +1157,20 @@ data = [
   inertia: for(model <- models, do: Nx.to_number(model.inertia))
 ]
 
-Vl.new(width: 600, height: 300, title: "Elbow Plot")
-|> Vl.data_from_values(data)
-|> Vl.mark(:line)
-|> Vl.encode_field(:x, "num_clusters",
-  title: "Number of Clusters",
-  type: :ordinal,
-  axis: [label_angle: 0]
-)
-|> Vl.encode_field(:y, "inertia",
-  title: "Inertia",
-  type: :quantitative,
-  scale: [domain: [4800, 11500]]
+Tucan.lineplot(data, "num_clusters", "inertia",
+  x: [type: :ordinal, axis: [label_angle: 0]],
+  width: 600,
+  height: 300
 )
+|> Tucan.Axes.set_xy_titles("Number of Clusters", "Inertia")
+|> Tucan.Scale.set_y_domain(4800, 11500)
+|> Tucan.set_title("Elbow Plot")
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"inertia":10950.6201171875,"num_clusters":2},{"inertia":9246.3125,"num_clusters":3},{"inertia":8447.5419921875,"num_clusters":4},{"inertia":7935.5498046875,"num_clusters":5},{"inertia":7484.12109375,"num_clusters":6},{"inertia":7091.55810546875,"num_clusters":7},{"inertia":6868.54296875,"num_clusters":8},{"inertia":6582.2734375,"num_clusters":9},{"inertia":6426.0517578125,"num_clusters":10},{"inertia":6238.46923828125,"num_clusters":11},{"inertia":6081.9736328125,"num_clusters":12},{"inertia":5876.912109375,"num_clusters":13},{"inertia":5797.251953125,"num_clusters":14},{"inertia":5662.34521484375,"num_clusters":15},{"inertia":5568.4345703125,"num_clusters":16},{"inertia":5398.72412109375,"num_clusters":17},{"inertia":5336.95263671875,"num_clusters":18},{"inertia":5233.1396484375,"num_clusters":19},{"inertia":5173.603515625,"num_clusters":20}]},"encoding":{"x":{"axis":{"labelAngle":0},"field":"num_clusters","title":"Number of Clusters","type":"ordinal"},"y":{"field":"inertia","scale":{"domain":[4800,11500]},"title":"Inertia","type":"quantitative"}},"height":300,"mark":"line","title":"Elbow Plot","width":600}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"inertia":10950.62109375,"num_clusters":2},{"inertia":9246.3134765625,"num_clusters":3},{"inertia":8447.5419921875,"num_clusters":4},{"inertia":7935.54931640625,"num_clusters":5},{"inertia":7484.1201171875,"num_clusters":6},{"inertia":7091.55810546875,"num_clusters":7},{"inertia":6868.54248046875,"num_clusters":8},{"inertia":6582.2734375,"num_clusters":9},{"inertia":6426.0517578125,"num_clusters":10},{"inertia":6238.46923828125,"num_clusters":11},{"inertia":6081.97265625,"num_clusters":12},{"inertia":5876.912109375,"num_clusters":13},{"inertia":5797.251953125,"num_clusters":14},{"inertia":5662.3447265625,"num_clusters":15},{"inertia":5568.43408203125,"num_clusters":16},{"inertia":5398.724609375,"num_clusters":17},{"inertia":5336.9521484375,"num_clusters":18},{"inertia":5233.13916015625,"num_clusters":19},{"inertia":5173.60400390625,"num_clusters":20}]},"encoding":{"x":{"axis":{"labelAngle":0,"title":"Number of Clusters"},"field":"num_clusters","type":"ordinal"},"y":{"axis":{"title":"Inertia"},"field":"inertia","scale":{"domain":[4800,11500]},"type":"quantitative"}},"height":300,"mark":{"fillOpacity":1,"type":"line"},"title":{"text":"Elbow Plot"},"width":600}
 ```
 
 Look that this time there is no elbow on a plot. We need to use a different method to predict the number of classes. Now we will use *Silhouette Score*. It is a metric that indicates the quality of clustering. The higher score we achieve, the better clustering we get. However, we should be aware that Silhouette Score is just a heuristic and not always works.
@@ -1247,25 +1196,21 @@ silhouette_scores =
 ```elixir
 data = [num_clusters: nums_clusters, silhouette_scores: silhouette_scores]
 
-Vl.new(width: 600, height: 300, title: "Silhouette score vs Number of Clusters")
-|> Vl.data_from_values(data)
-|> Vl.mark(:line, point: [point: true, color: :dark_blue])
-|> Vl.encode_field(:x, "num_clusters",
-  title: "Number of Clusters",
-  type: :ordinal,
-  axis: [label_angle: 0]
-)
-|> Vl.encode_field(:y, "silhouette_scores",
-  title: "Silhouette score",
-  type: :quantitative,
-  scale: [domain: [0.088, 0.205]]
+Tucan.lineplot(data, "num_clusters", "silhouette_scores",
+  points: true,
+  point_color: "darkBlue",
+  x: [type: :ordinal, axis: [label_angle: 0]]
 )
+|> Tucan.Axes.set_xy_titles("Number of Clusters", "Silhouette score")
+|> Tucan.Scale.set_y_domain(0.088, 0.205)
+|> Tucan.set_size(600, 300)
+|> Tucan.set_title("Silhouette score vs Number of Clusters")
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"num_clusters":2,"silhouette_scores":0.1867797076702118},{"num_clusters":3,"silhouette_scores":0.19426067173480988},{"num_clusters":4,"silhouette_scores":0.18798942863941193},{"num_clusters":5,"silhouette_scores":0.16196762025356293},{"num_clusters":6,"silhouette_scores":0.14662104845046997},{"num_clusters":7,"silhouette_scores":0.15014168620109558},{"num_clusters":8,"silhouette_scores":0.1334874927997589},{"num_clusters":9,"silhouette_scores":0.12096332758665085},{"num_clusters":10,"silhouette_scores":0.12907366454601288},{"num_clusters":11,"silhouette_scores":0.12029680609703064},{"num_clusters":12,"silhouette_scores":0.12559780478477478},{"num_clusters":13,"silhouette_scores":0.12784500420093536},{"num_clusters":14,"silhouette_scores":0.12478214502334595},{"num_clusters":15,"silhouette_scores":0.1155780702829361},{"num_clusters":16,"silhouette_scores":0.11121585220098495},{"num_clusters":17,"silhouette_scores":0.11069852113723755},{"num_clusters":18,"silhouette_scores":0.10738851875066757},{"num_clusters":19,"silhouette_scores":0.10977344214916229},{"num_clusters":20,"silhouette_scores":0.10331624001264572}]},"encoding":{"x":{"axis":{"labelAngle":0},"field":"num_clusters","title":"Number of Clusters","type":"ordinal"},"y":{"field":"silhouette_scores","scale":{"domain":[0.088,0.205]},"title":"Silhouette score","type":"quantitative"}},"height":300,"mark":{"point":{"color":"darkBlue","point":true},"type":"line"},"title":"Silhouette score vs Number of Clusters","width":600}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"num_clusters":2,"silhouette_scores":0.18677975237369537},{"num_clusters":3,"silhouette_scores":0.1942606419324875},{"num_clusters":4,"silhouette_scores":0.18798941373825073},{"num_clusters":5,"silhouette_scores":0.16196760535240173},{"num_clusters":6,"silhouette_scores":0.14662104845046997},{"num_clusters":7,"silhouette_scores":0.15014170110225677},{"num_clusters":8,"silhouette_scores":0.13348747789859772},{"num_clusters":9,"silhouette_scores":0.12096334248781204},{"num_clusters":10,"silhouette_scores":0.12907366454601288},{"num_clusters":11,"silhouette_scores":0.12029680609703064},{"num_clusters":12,"silhouette_scores":0.1255977749824524},{"num_clusters":13,"silhouette_scores":0.12784500420093536},{"num_clusters":14,"silhouette_scores":0.12478211522102356},{"num_clusters":15,"silhouette_scores":0.1155780628323555},{"num_clusters":16,"silhouette_scores":0.11121582984924316},{"num_clusters":17,"silhouette_scores":0.11069852113723755},{"num_clusters":18,"silhouette_scores":0.10738851875066757},{"num_clusters":19,"silhouette_scores":0.10977346450090408},{"num_clusters":20,"silhouette_scores":0.10331626981496811}]},"encoding":{"x":{"axis":{"labelAngle":0,"title":"Number of Clusters"},"field":"num_clusters","type":"ordinal"},"y":{"axis":{"title":"Silhouette score"},"field":"silhouette_scores","scale":{"domain":[0.088,0.205]},"type":"quantitative"}},"height":300,"mark":{"fillOpacity":1,"point":{"color":"darkBlue"},"type":"line"},"title":{"text":"Silhouette score vs Number of Clusters"},"width":600}
 ```
 
 As we can see, the model with num_clusters equal to 3 has the highest Silhouette Score. Now we will visualize this clusterization.
diff --git a/notebooks/k_nearest_neighbors.livemd b/notebooks/k_nearest_neighbors.livemd
index fe7dc492..19001352 100644
--- a/notebooks/k_nearest_neighbors.livemd
+++ b/notebooks/k_nearest_neighbors.livemd
@@ -1,1048 +1,865 @@
-<!-- livebook:{"persist_outputs":true} -->
-
-# K-Nearest Neighbors
-
-```elixir
-Mix.install([
-  {:scholar, "~> 0.2.0"},
-  {:explorer, "~> 0.6.1"},
-  {:exla, "~> 0.6.0"},
-  {:nx, "~> 0.6.0", override: true},
-  {:req, "~> 0.3.9"},
-  {:kino_vega_lite, "~> 0.1.9"},
-  {:kino, "~> 0.10.0"},
-  {:scidata, "~> 0.1.10"},
-  {:kino_explorer, "~> 0.1.7"}
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-:ok
-```
-
-## Setup
-
-We will extensively use VegaLite, Explorer, and Scholar throughout this guide, so let's define some aliases:
-
-```elixir
-alias VegaLite, as: Vl
-require Explorer.DataFrame, as: DF
-require Explorer.Series, as: S
-require Explorer.Query, as: Q
-alias Scholar.Neighbors.KNearestNeighbors, as: KNN
-alias Scholar.Metrics.Classification
-alias Scholar.Metrics.Regression
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-Scholar.Metrics.Regression
-```
-
-And let's configure `EXLA.Backend` as our default across the notebook and all branched sections:
-
-```elixir
-Nx.global_default_backend(EXLA.Backend)
-seed = 42
-key = Nx.Random.key(42)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-
-02:33:33.173 [info] TfrtCpuClient created.
-
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  u32[2]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254101>
-  [0, 42]
->
-```
-
-## Introduction
-
-This notebook will cover the three primary applications of K-Nearest Neighbors: classification, regression, and
-anomaly detection.
-
-<!-- livebook:{"branch_parent_index":1} -->
-
-## Classification
-
-The process of classification using KNN is relatively straightforward. We start by working with a dataset where each sample is assigned a label. To predict the label of a new sample, we compute the distance between it and all the other samples in the dataset. Next, we select only the $k$ closest samples based on the distance metric, where $k$ is a user-defined parameter. We then examine the labels of these $k$ samples and choose the label that appears most frequently. This label is assigned as the predicted label for the new sample.
-
-Let's first grasp how kNN works visually with a small example.
-
-```elixir
-data =
-  DF.new(
-    x: [-1, 0.2, -0.5, -2.1, -2.3, -2.2, 0.1, 0.3, 0.4, 0.7, 1.3],
-    y: [-0.1, 0.4, 0.5, 0.4, 1.1, -1.0, -0.1, 0.2, 1.5, 1.6, 0.9],
-    label: [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
-  )
-
-point_to_predict = DF.new(x: [0.0], y: [0.0])
-
-k_eq_3 = DF.new(x: [0.45], y: [0.45], name: ["k = 3"])
-k_eq_5 = DF.new(x: [0.72], y: [0.72], name: ["k = 5"])
-
-Vl.new(
-  title: [
-    text: "Scatterplot showing KNN prediction process",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(data)
-  |> Vl.mark(:point, size: 200, filled: true)
-  |> Vl.encode_field(:shape, "label", type: :nominal)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: [domain: [-2.4, 1.5]],
-    axis: [grid: false]
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: [domain: [-1.2, 1.8]],
-    axis: [grid: false]
-  )
-  |> Vl.encode_field(:color, "label", type: :nominal, scale: [scheme: :plasma]),
-  Vl.new()
-  |> Vl.data_from_values(point_to_predict)
-  |> Vl.mark(:point, color: :green, size: 400, shape: :triangle, filled: true)
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative),
-  Vl.new()
-  |> Vl.data_from_values(point_to_predict)
-  |> Vl.mark(:arc,
-    outer_radius: 99,
-    inner_radius: 97,
-    color: :brown,
-    stroke_dash: [stroke_dash: [5, 5]]
-  )
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative),
-  Vl.new()
-  |> Vl.data_from_values(point_to_predict)
-  |> Vl.mark(:arc,
-    outer_radius: 170,
-    inner_radius: 168,
-    color: :blue
-  )
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative),
-  Vl.new()
-  |> Vl.data_from_values(k_eq_3)
-  |> Vl.mark(:text, size: 20, color: :brown)
-  |> Vl.encode_field(:text, "name", type: :nominal)
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative),
-  Vl.new()
-  |> Vl.data_from_values(k_eq_5)
-  |> Vl.mark(:text, size: 20, color: :blue)
-  |> Vl.encode_field(:text, "name", type: :nominal)
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative)
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"label":0,"x":-1.0,"y":-0.1},{"label":0,"x":0.2,"y":0.4},{"label":0,"x":-0.5,"y":0.5},{"label":0,"x":-2.1,"y":0.4},{"label":0,"x":-2.3,"y":1.1},{"label":0,"x":-2.2,"y":-1.0},{"label":1,"x":0.1,"y":-0.1},{"label":1,"x":0.3,"y":0.2},{"label":1,"x":0.4,"y":1.5},{"label":1,"x":0.7,"y":1.6},{"label":1,"x":1.3,"y":0.9}]},"encoding":{"color":{"field":"label","scale":{"scheme":"plasma"},"type":"nominal"},"shape":{"field":"label","type":"nominal"},"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.5]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-1.2,1.8]},"type":"quantitative"}},"mark":{"filled":true,"size":200,"type":"point"}},{"data":{"values":[{"x":0.0,"y":0.0}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"green","filled":true,"shape":"triangle","size":400,"type":"point"}},{"data":{"values":[{"x":0.0,"y":0.0}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"brown","innerRadius":97,"outerRadius":99,"type":"arc"}},{"data":{"values":[{"x":0.0,"y":0.0}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"blue","innerRadius":168,"outerRadius":170,"type":"arc"}},{"data":{"values":[{"name":"k = 3","x":0.45,"y":0.45}]},"encoding":{"text":{"field":"name","type":"nominal"},"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"brown","size":20,"type":"text"}},{"data":{"values":[{"name":"k = 5","x":0.72,"y":0.72}]},"encoding":{"text":{"field":"name","type":"nominal"},"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"blue","size":20,"type":"text"}}],"title":{"offset":20,"text":"Scatterplot showing KNN prediction process"},"width":630}
-```
-
-Note that the final prediction may vary depending on the value of $k$. For example, with $k = 3$, we would predict the green triangle as an orange square (1), whereas with $k = 5$, the purple circle (0) would be the final prediction.
-
-Let's now test this using Scholar code. First, we will define our data.
-
-```elixir
-x = Nx.stack(DF.discard(data, "label"), axis: 1)
-labels = Nx.stack(DF.select(data, "label"), axis: 1) |> Nx.squeeze(axes: [1])
-x_pred = Nx.stack(point_to_predict, axis: 1)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64[1][2]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254170>
-  [
-    [0.0, 0.0]
-  ]
->
-```
-
-Let's now try with $k = 3$.
-
-```elixir
-model = KNN.fit(x, labels, num_classes: 2, num_neighbors: 3)
-KNN.predict(model, x_pred)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  s64[1]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254247>
-  [1]
->
-```
-
-And $k = 5$.
-
-```elixir
-model = KNN.fit(x, labels, num_classes: 2, num_neighbors: 5)
-KNN.predict(model, x_pred)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  s64[1]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254320>
-  [0]
->
-```
-
-As we can see, the predictions match our intuition from analyzing the plot.
-
-Now, let's try KNN on a more complicated dataset: the Wine dataset. Our task will be to classify the quality of the wine. Before we load the dataset into `Explorer.DataFrame` for more efficient exploration, let's check some more detailed information about the dataset.
-
-```elixir
-info =
-  Req.get!(
-    "https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality.names"
-  ).body
-
-Kino.Markdown.new(info)
-```
-
-```elixir
-data =
-  Req.get!(
-    "https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv"
-  ).body
-
-df_data = DF.load_csv!(data, delimiter: ";", dtypes: %{"total sulfur dioxide": :float})
-tensor_data = Nx.stack(df_data, axis: 1)
-df_data
-```
-
-As we can see, there are no null values in the dataset. Now, let's check the size of the dataset.
-
-```elixir
-DF.shape(df_data)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-{4898, 12}
-```
-
-Let's check some statistical properties of the dataset. We will start with *skewness*, which measures the asymmetry of the probability distribution of a random variable about its mean. To better understand this concept, please take a look at the picture below.
-
-| ![Skewness](https://upload.wikimedia.org/wikipedia/commons/c/cc/Relationship_between_mean_and_median_under_different_skewness.png) |
-| :--------------------------------------------------------------------------------------------------------------------------------: |
-| Figure 1: A general relationship of mean and median under differently skewed unimodal distribution                                 |
-
-Now, let's check the skewness of our dataset using Scholar.Stats.skew function.
-
-```elixir
-Scholar.Stats.skew(tensor_data)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64[12]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254424>
-  [0.6475530855160632, 1.5764965159574844, 1.2815277799152376, 1.0767638711454446, 5.0217921696710315, 1.4063140718346212, 0.3905901775815236, 0.9774735389046988, 0.45764233925379794, 0.9768943947733456, 0.4871927332763434, 0.15574868141362447]
->
-```
-
-As we can see, all features have positive skewness, which means that their distributions are more similar to the left plot in the picture above.
-
-Moving on to another statistical function, let's discuss *kurtosis*. Kurtosis measures how much data is located in the tails of distributions. If the kurtosis is greater than 0, the distribution is said to be "platykurtic", indicating that it has more extreme values than a univariate normal distribution. Similarly, a "leptokurtic" distribution has positive kurtosis and less extreme values, while a "mesokurtic" distribution has the same kurtosis as a normal distribution. Let's check the kurtosis of our dataset.
-
-| ![Skewness](https://vitalflux.com/wp-content/uploads/2023/01/fourth-moment-kurtosis-640x334.png) |
-| :----------------------------------------------------------------------------------------------: |
-| Figure 2: Plot showing Platykurtic, Mesokurtic and Leptokurtic distributions                     |
-
-```elixir
-Scholar.Stats.kurtosis(tensor_data)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64[12]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254451>
-  [2.168736944824719, 5.08520490451785, 6.167374226819426, 3.4650542966046363, 37.52503905008619, 11.453415905047144, 0.5700448984658735, 9.78258726703508, 0.5290085383907339, 1.5880812942840778, -0.6989373013774784, 0.21508011570192975]
->
-```
-
-Almost all features have positive kurtosis (they are leptokurtic). `alcohol` has negative excess kurtosis, which means it is platykurtic. Below there is Kernel Density Estimate (KDE) to check how exactly this tail look like.
-
-```elixir
-# Increase the sample size (or use 1.0 to plot all data)
-sample = DF.sample(df_data, 0.5, seed: seed)
-
-Vl.new(
-  title: [
-    text: "KDE plots of Features",
-    anchor: :middle,
-    offset: 20
-  ],
-  width: 700,
-  height: 300
-)
-|> Vl.data_from_values(sample, only: ~w(alcohol density pH))
-|> Vl.concat([
-  Vl.new(
-    title: [
-      text: "KDE plot of alcohol feature",
-      offset: 20
-    ],
-    width: 350,
-    height: 300
-  )
-  |> Vl.transform(density: "alcohol")
-  |> Vl.mark(:area, color: "lightblue")
-  |> Vl.encode_field(:x, "value", type: :quantitative, title: "% of alcohol")
-  |> Vl.encode_field(:y, "density", type: :quantitative),
-  Vl.new(
-    title: [
-      text: "KDE plot of pH feature",
-      offset: 20
-    ],
-    width: 350,
-    height: 300
-  )
-  |> Vl.transform(density: "pH")
-  |> Vl.mark(:area, color: "lightgreen")
-  |> Vl.encode_field(:x, "value", type: :quantitative, title: "pH")
-  |> Vl.encode_field(:y, "density", type: :quantitative)
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
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alcohol":12.6,"density":0.99014,"pH":3.23},{"alcohol":11.3,"density":0.9914,"pH":3.06},{"alcohol":12.0,"density":0.99114,"pH":3.38},{"alcohol":10.7,"density":0.9925,"pH":3.43},{"alcohol":10.5,"density":0.99496,"pH":3.11},{"alcohol":9.6,"density":0.9938,"pH":3.25},{"alcohol":9.6,"density":0.9938,"pH":3.25},{"alcohol":12.6,"density":0.98956,"pH":3.45},{"alcohol":9.7,"density":0.99632,"pH":3.16},{"alcohol":12.2,"density":0.9925,"pH":3.27},{"alcohol":11.8,"density":0.9916,"pH":3.17},{"alcohol":11.9,"density":0.99116,"pH":3.15},{"alcohol":10.2,"density":0.99742,"pH":3.24},{"alcohol":8.8,"density":0.99916,"pH":3.13},{"alcohol":10.2,"density":0.99514,"pH":3.1},{"alcohol":10.0,"density":0.99566,"pH":3.12},{"alcohol":12.0,"density":0.99193,"pH":3.2},{"alcohol":9.6,"density":0.99587,"pH":3.04},{"alcohol":9.0,"density":0.99772,"pH":3.24},{"alcohol":12.7,"density":0.99117,"pH":3.17},{"alcohol":11.0,"density":0.99399,"pH":3.34},{"alcohol":9.1,"density":0.99741,"pH":3.1},{"alcohol":8.7,"density":1.00013,"pH":2.96},{"alcohol":10.1,"density":0.99622,"pH":3.38},{"alcohol":9.2,"density":1.00051,"pH":3.05},{"alcohol":9.4,"density":0.99803,"pH":3.47},{"alcohol":10.2,"density":0.99405,"pH":3.35},{"alcohol":8.8,"density":1.0,"pH":3.27},{"alcohol":10.3,"density":0.99256,"pH":3.3},{"alcohol":9.7,"density":0.99526,"pH":3.22},{"alcohol":9.0,"density":0.99713,"pH":3.15},{"alcohol":9.5,"density":0.99274,"pH":3.16},{"alcohol":12.4,"density":0.99066,"pH":2.98},{"alcohol":13.3,"density":0.99176,"pH":3.05},{"alcohol":11.1,"density":0.9912,"pH":3.13},{"alcohol":9.2,"density":0.99771,"pH":3.56},{"alcohol":10.1,"density":0.99411,"pH":3.36},{"alcohol":9.2,"density":0.99771,"pH":3.56},{"alcohol":10.1,"density":0.99411,"pH":3.36},{"alcohol":11.2,"density":0.99067,"pH":3.23},{"alcohol":9.8,"density":0.99558,"pH":3.14},{"alcohol":10.3,"density":0.99678,"pH":3.28},{"alcohol":9.3,"density":0.9979,"pH":3.39},{"alcohol":9.4,"density":0.99577,"pH":3.22},{"alcohol":10.6,"density":0.99246,"pH":3.28},{"alcohol":9.4,"density":0.99578,"pH":3.21},{"alcohol":8.9,"density":0.99888,"pH":3.11},{"alcohol":9.7,"density":0.99271,"pH":3.27},{"alcohol":9.8,"density":0.99441,"pH":3.17},{"alcohol":12.4,"density":0.98984,"pH":3.01},{"alcohol":10.1,"density":0.9926,"pH":3.14},{"alcohol":10.4,"density":0.99192,"pH":3.18},{"alcohol":9.9,"density":0.9979,"pH":3.48},{"alcohol":10.0,"density":0.99434,"pH":3.14},{"alcohol":12.0,"density":0.9948,"pH":3.03},{"alcohol":9.2,"density":0.998,"pH":3.0},{"alcohol":10.0,"density":0.99316,"pH":3.15},{"alcohol":9.2,"density":0.998,"pH":3.0},{"alcohol":9.5,"density":0.9924,"pH":3.06},{"alcohol":11.5,"density":0.99084,"pH":3.38},{"alcohol":9.6,"density":0.99492,"pH":3.14},{"alcohol":9.6,"density":0.99452,"pH":3.53}]},"height":300,"title":{"anchor":"middle","offset":20,"text":"KDE plots of Features"},"width":700}
-```
-
-The previous analysis indicates that the alcohol feature has more extreme values than pH. Now, we will create a correlation heatmap to investigate the relationships between the features in the dataset.
-
-```elixir
-correlation = Scholar.Covariance.correlation_matrix(tensor_data, biased: true)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64[12][12]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254489>
-  [
-    [1.0, -0.022697290146647113, 0.2891806976936754, 0.08902070136217163, 0.023085643656347757, -0.049395859081173187, 0.09106975615864087, 0.2653310138391866, -0.42585829099138195, -0.017142985021137338, -0.12088112319453302, -0.11366283071301796],
-    [-0.022697290146647113, 1.0000000000000007, -0.14947181064857518, 0.06428606009099526, 0.07051157147938472, -0.09701193927796008, 0.0892605035517784, 0.02711384546243434, -0.03191536827348892, -0.03572814690581474, 0.06771794277504414, -0.19472296892113428],
-    [0.2891806976936754, -0.14947181064857518, 1.0000000000000009, 0.09421162429049387, 0.11436444838681839, 0.09407722101469612, 0.12113079766441823, 0.14950257057002272, -0.16374821140062368, 0.06233094028523288, -0.07572873005717942, -0.009209090883975417],
-    [0.08902070136217163, 0.06428606009099526, 0.09421162429049387, 1.0000000000000002, 0.0886845359412256, 0.299098353693518, 0.40143931115992487, 0.8389664549045833, -0.19413345399025597, -0.026664365853858334, -0.45063122203172884, -0.09757682889469321],
-    [0.023085643656347757, 0.07051157147938472, ...],
-    ...
-  ]
->
-```
-
-```elixir
-{corr_size, _} = Nx.shape(correlation)
-correlation_list = Nx.to_flat_list(correlation)
-column_names = DF.names(df_data)
-
-corr_to_plot =
-  DF.new(
-    x: List.flatten(List.duplicate(column_names, corr_size)),
-    y: List.flatten(for name <- column_names, do: List.duplicate(name, corr_size)),
-    corr_val: Enum.map(correlation_list, fn x -> Float.round(x, 2) end)
-  )
-
-Vl.new(
-  title: [
-    text: "Correlation Matrix for California Housing",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(corr_to_plot)
-|> Vl.config(axis: [grid: false, tickband: :extent])
-|> Vl.layers([
-  Vl.new()
-  |> Vl.mark(:rect)
-  |> Vl.encode_field(:x, "x", type: :nominal, title: "", sort: false)
-  |> Vl.encode_field(:y, "y", type: :nominal, title: "", sort: false)
-  |> Vl.encode_field(:color, "corr_val", type: :quantitative, scale: [scheme: :inferno]),
-  Vl.new()
-  |> Vl.mark(:text)
-  |> Vl.encode_field(:x, "x", type: :nominal, title: "")
-  |> Vl.encode_field(:y, "y", type: :nominal, title: "")
-  |> Vl.encode_field(:text, "corr_val", type: :quantitative)
-  |> Vl.encode_field(:color, "corr_val",
-    type: :quantitative,
-    condition: [
-      [test: "datum['corr_val'] < 0", value: :white],
-      [test: "datum['corr_val'] >= 0", value: :black]
-    ]
-  )
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"corr_val":1.0,"x":"fixed acidity","y":"fixed acidity"},{"corr_val":-0.02,"x":"volatile acidity","y":"fixed acidity"},{"corr_val":0.29,"x":"citric acid","y":"fixed acidity"},{"corr_val":0.09,"x":"residual sugar","y":"fixed acidity"},{"corr_val":0.02,"x":"chlorides","y":"fixed acidity"},{"corr_val":-0.05,"x":"free sulfur dioxide","y":"fixed acidity"},{"corr_val":0.09,"x":"total sulfur dioxide","y":"fixed acidity"},{"corr_val":0.27,"x":"density","y":"fixed acidity"},{"corr_val":-0.43,"x":"pH","y":"fixed acidity"},{"corr_val":-0.02,"x":"sulphates","y":"fixed acidity"},{"corr_val":-0.12,"x":"alcohol","y":"fixed acidity"},{"corr_val":-0.11,"x":"quality","y":"fixed acidity"},{"corr_val":-0.02,"x":"fixed acidity","y":"volatile acidity"},{"corr_val":1.0,"x":"volatile acidity","y":"volatile acidity"},{"corr_val":-0.15,"x":"citric acid","y":"volatile acidity"},{"corr_val":0.06,"x":"residual sugar","y":"volatile acidity"},{"corr_val":0.07,"x":"chlorides","y":"volatile acidity"},{"corr_val":-0.1,"x":"free sulfur dioxide","y":"volatile acidity"},{"corr_val":0.09,"x":"total sulfur dioxide","y":"volatile acidity"},{"corr_val":0.03,"x":"density","y":"volatile acidity"},{"corr_val":-0.03,"x":"pH","y":"volatile acidity"},{"corr_val":-0.04,"x":"sulphates","y":"volatile acidity"},{"corr_val":0.07,"x":"alcohol","y":"volatile acidity"},{"corr_val":-0.19,"x":"quality","y":"volatile acidity"},{"corr_val":0.29,"x":"fixed acidity","y":"citric acid"},{"corr_val":-0.15,"x":"volatile acidity","y":"citric acid"},{"corr_val":1.0,"x":"citric acid","y":"citric acid"},{"corr_val":0.09,"x":"residual sugar","y":"citric acid"},{"corr_val":0.11,"x":"chlorides","y":"citric acid"},{"corr_val":0.09,"x":"free sulfur dioxide","y":"citric acid"},{"corr_val":0.12,"x":"total sulfur dioxide","y":"citric acid"},{"corr_val":0.15,"x":"density","y":"citric acid"},{"corr_val":-0.16,"x":"pH","y":"citric acid"},{"corr_val":0.06,"x":"sulphates","y":"citric acid"},{"corr_val":-0.08,"x":"alcohol","y":"citric acid"},{"corr_val":-0.01,"x":"quality","y":"citric acid"},{"corr_val":0.09,"x":"fixed acidity","y":"residual sugar"},{"corr_val":0.06,"x":"volatile acidity","y":"residual sugar"},{"corr_val":0.09,"x":"citric acid","y":"residual sugar"},{"corr_val":1.0,"x":"residual sugar","y":"residual sugar"},{"corr_val":0.09,"x":"chlorides","y":"residual sugar"},{"corr_val":0.3,"x":"free sulfur dioxide","y":"residual sugar"},{"corr_val":0.4,"x":"total sulfur dioxide","y":"residual sugar"},{"corr_val":0.84,"x":"density","y":"residual sugar"},{"corr_val":-0.19,"x":"pH","y":"residual sugar"},{"corr_val":-0.03,"x":"sulphates","y":"residual sugar"},{"corr_val":-0.45,"x":"alcohol","y":"residual sugar"},{"corr_val":-0.1,"x":"quality","y":"residual sugar"},{"corr_val":0.02,"x":"fixed acidity","y":"chlorides"},{"corr_val":0.07,"x":"volatile acidity","y":"chlorides"},{"corr_val":0.11,"x":"citric acid","y":"chlorides"},{"corr_val":0.09,"x":"residual sugar","y":"chlorides"},{"corr_val":1.0,"x":"chlorides","y":"chlorides"},{"corr_val":0.1,"x":"free sulfur dioxide","y":"chlorides"},{"corr_val":0.2,"x":"total sulfur dioxide","y":"chlorides"},{"corr_val":0.26,"x":"density","y":"chlorides"},{"corr_val":-0.09,"x":"pH","y":"chlorides"},{"corr_val":0.02,"x":"sulphates","y":"chlorides"},{"corr_val":-0.36,"x":"alcohol","y":"chlorides"},{"corr_val":-0.21,"x":"quality","y":"chlorides"},{"corr_val":-0.05,"x":"fixed acidity","y":"free sulfur dioxide"},{"corr_val":-0.1,"x":"volatile acidity","y":"free sulfur dioxide"},{"corr_val":0.09,"x":"citric acid","y":"free sulfur dioxide"},{"corr_val":0.3,"x":"residual sugar","y":"free sulfur dioxide"},{"corr_val":0.1,"x":"chlorides","y":"free sulfur dioxide"},{"corr_val":1.0,"x":"free sulfur dioxide","y":"free sulfur dioxide"},{"corr_val":0.62,"x":"total sulfur dioxide","y":"free sulfur dioxide"},{"corr_val":0.29,"x":"density","y":"free sulfur dioxide"},{"corr_val":0.0,"x":"pH","y":"free sulfur dioxide"},{"corr_val":0.06,"x":"sulphates","y":"free sulfur dioxide"},{"corr_val":-0.25,"x":"alcohol","y":"free sulfur dioxide"},{"corr_val":0.01,"x":"quality","y":"free sulfur dioxide"},{"corr_val":0.09,"x":"fixed acidity","y":"total sulfur dioxide"},{"corr_val":0.09,"x":"volatile acidity","y":"total sulfur dioxide"},{"corr_val":0.12,"x":"citric acid","y":"total sulfur dioxide"},{"corr_val":0.4,"x":"residual sugar","y":"total sulfur dioxide"},{"corr_val":0.2,"x":"chlorides","y":"total sulfur dioxide"},{"corr_val":0.62,"x":"free sulfur dioxide","y":"total sulfur dioxide"},{"corr_val":1.0,"x":"total sulfur dioxide","y":"total sulfur dioxide"},{"corr_val":0.53,"x":"density","y":"total sulfur dioxide"},{"corr_val":0.0,"x":"pH","y":"total sulfur dioxide"},{"corr_val":0.13,"x":"sulphates","y":"total sulfur dioxide"},{"corr_val":-0.45,"x":"alcohol","y":"total sulfur dioxide"},{"corr_val":-0.17,"x":"quality","y":"total sulfur dioxide"},{"corr_val":0.27,"x":"fixed acidity","y":"density"},{"corr_val":0.03,"x":"volatile acidity","y":"density"},{"corr_val":0.15,"x":"citric acid","y":"density"},{"corr_val":0.84,"x":"residual sugar","y":"density"},{"corr_val":0.26,"x":"chlorides","y":"density"},{"corr_val":0.29,"x":"free sulfur dioxide","y":"density"},{"corr_val":0.53,"x":"total sulfur dioxide","y":"density"},{"corr_val":1.0,"x":"density","y":"density"},{"corr_val":-0.09,"x":"pH","y":"density"},{"corr_val":0.07,"x":"sulphates","y":"density"},{"corr_val":-0.78,"x":"alcohol","y":"density"},{"corr_val":-0.31,"x":"quality","y":"density"},{"corr_val":-0.43,"x":"fixed acidity","y":"pH"},{"corr_val":-0.03,"x":"volatile acidity","y":"pH"},{"corr_val":-0.16,"x":"citric acid","y":"pH"},{"corr_val":-0.19,"x":"residual sugar","y":"pH"},{"corr_val":-0.09,"x":"chlorides","y":"pH"},{"corr_val":0.0,"x":"free sulfur dioxide","y":"pH"},{"corr_val":0.0,"x":"total sulfur dioxide","y":"pH"},{"corr_val":-0.09,"x":"density","y":"pH"},{"corr_val":1.0,"x":"pH","y":"pH"},{"corr_val":0.16,"x":"sulphates","y":"pH"},{"corr_val":0.12,"x":"alcohol","y":"pH"},{"corr_val":0.1,"x":"quality","y":"pH"},{"corr_val":-0.02,"x":"fixed acidity","y":"sulphates"},{"corr_val":-0.04,"x":"volatile acidity","y":"sulphates"},{"corr_val":0.06,"x":"citric acid","y":"sulphates"},{"corr_val":-0.03,"x":"residual sugar","y":"sulphates"},{"corr_val":0.02,"x":"chlorides","y":"sulphates"},{"corr_val":0.06,"x":"free sulfur dioxide","y":"sulphates"},{"corr_val":0.13,"x":"total sulfur dioxide","y":"sulphates"},{"corr_val":0.07,"x":"density","y":"sulphates"},{"corr_val":0.16,"x":"pH","y":"sulphates"},{"corr_val":1.0,"x":"sulphates","y":"sulphates"},{"corr_val":-0.02,"x":"alcohol","y":"sulphates"},{"corr_val":0.05,"x":"quality","y":"sulphates"},{"corr_val":-0.12,"x":"fixed acidity","y":"alcohol"},{"corr_val":0.07,"x":"volatile acidity","y":"alcohol"},{"corr_val":-0.08,"x":"citric acid","y":"alcohol"},{"corr_val":-0.45,"x":"residual sugar","y":"alcohol"},{"corr_val":-0.36,"x":"chlorides","y":"alcohol"},{"corr_val":-0.25,"x":"free sulfur dioxide","y":"alcohol"},{"corr_val":-0.45,"x":"total sulfur dioxide","y":"alcohol"},{"corr_val":-0.78,"x":"density","y":"alcohol"},{"corr_val":0.12,"x":"pH","y":"alcohol"},{"corr_val":-0.02,"x":"sulphates","y":"alcohol"},{"corr_val":1.0,"x":"alcohol","y":"alcohol"},{"corr_val":0.44,"x":"quality","y":"alcohol"},{"corr_val":-0.11,"x":"fixed acidity","y":"quality"},{"corr_val":-0.19,"x":"volatile acidity","y":"quality"},{"corr_val":-0.01,"x":"citric acid","y":"quality"},{"corr_val":-0.1,"x":"residual sugar","y":"quality"},{"corr_val":-0.21,"x":"chlorides","y":"quality"},{"corr_val":0.01,"x":"free sulfur dioxide","y":"quality"},{"corr_val":-0.17,"x":"total sulfur dioxide","y":"quality"},{"corr_val":-0.31,"x":"density","y":"quality"},{"corr_val":0.1,"x":"pH","y":"quality"},{"corr_val":0.05,"x":"sulphates","y":"quality"},{"corr_val":0.44,"x":"alcohol","y":"quality"},{"corr_val":1.0,"x":"quality","y":"quality"}]},"height":630,"layer":[{"encoding":{"color":{"field":"corr_val","scale":{"scheme":"viridis"},"type":"quantitative"},"x":{"field":"x","type":"nominal"},"y":{"field":"y","type":"nominal"}},"mark":"rect"},{"encoding":{"text":{"field":"corr_val","type":"quantitative"},"x":{"field":"x","type":"nominal"},"y":{"field":"y","type":"nominal"}},"mark":"text"}],"title":{"offset":20,"text":"Correlation Matrix for California Housing"},"width":630}
-```
-
-We can observe from the correlation heatmap that there is no strong correlation between the quality of wine and any single feature. However, we can see that there are two strong correlations: density is proportional to the amount of residual sugar and inversely proportional to the amount of alcohol.
-
-Given that citric acid, free sulfur dioxide, and sulphates are not strongly correlated with the quality of wine or any other features, we can drop them from the dataset to simplify our analysis.
-
-Before dropping the features, it is important to consider their potential impact on the final prediction. Even if they are not strongly correlated with the target variable (quality), they may still provide useful information for the KNN algorithm. It is recommended to experiment with different feature subsets to find the optimal combination for the given task. You can try running the notebook again without dropping these features.
-
-```elixir
-tensor_data =
-  DF.discard(df_data, ["citric acid", "free sulfur dioxide", "sulphates"]) |> Nx.stack(axis: 1)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64[4898][9]
-  EXLA.Backend<host:0, 0.3730900597.862060556.254521>
-  [
-    [7.0, 0.27, 20.7, 0.045, 170.0, 1.001, 3.0, 8.8, 6.0],
-    [6.3, 0.3, 1.6, 0.049, 132.0, 0.994, 3.3, 9.5, 6.0],
-    [8.1, 0.28, 6.9, 0.05, 97.0, 0.9951, 3.26, 10.1, 6.0],
-    [7.2, 0.23, 8.5, 0.058, 186.0, 0.9956, 3.19, 9.9, 6.0],
-    [7.2, 0.23, 8.5, 0.058, 186.0, 0.9956, 3.19, 9.9, 6.0],
-    [8.1, 0.28, 6.9, 0.05, 97.0, ...],
-    ...
-  ]
->
-```
-
-The next step will be splitting the dataset into features and labels. To make the classification task easier, we will convert the labels into three categories: "poor," "medium," and "excellent". Additionally, we will normalize the features using the standard scaler.
-
-```elixir
-x = tensor_data[[.., 0..-2//1]]
-y = tensor_data[[.., -1]]
-
-# convert quality into labels quality: (0, 4) poor => 0, (5, 6) medium => 1, (7, 10) excelent => 2
-
-poor_and_better_mask = Nx.greater(y, 4)
-medium_and_better_mask = Nx.greater(y, 6)
-
-y = Nx.select(poor_and_better_mask, Nx.select(medium_and_better_mask, 2, 1), 0)
-x = Scholar.Preprocessing.standard_scale(x)
-
-{x, y}
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-{#Nx.Tensor<
-   f64[4898][8]
-   EXLA.Backend<host:0, 0.3730900597.862060556.254557>
-   [
-     [-0.29385297541380284, -0.4368649169854585, -0.0027291121847267076, -0.44164614831586296, 3.1698834995014824, -0.4213312276408997, -0.37885264350988346, -0.2556031247705665],
-     [-0.30872791733061694, -0.43622741947473787, -0.40860252734351166, -0.4415611486477669, 2.3623866525887167, -0.4214799770600679, -0.3724776684026774, -0.24072818285375244],
-     [-0.27047806668738067, -0.43665241781521824, -0.29597796711620483, -0.4415398987307429, 1.6186395567480112, -0.42145660215134145, -0.37332766508363824, -0.22797823263934036],
-     [-0.2896029920089988, -0.4377149136664193, -0.2619780998777726, -0.44136989939455074, 3.509882171885805, -0.42144597719282945, -0.3748151592753196, -0.23222821604414437],
-     [-0.2896029920089988, -0.4377149136664193, -0.2619780998777726, -0.44136989939455074, 3.509882171885805, -0.42144597719282945, -0.3748151592753196, -0.23222821604414437],
-     [-0.27047806668738067, -0.43665241781521824, -0.29597796711620483, -0.4415398987307429, 1.6186395567480112, -0.42145660215134145, -0.37332766508363824, -0.22797823263934036],
-     [-0.310852909033019, ...],
-     ...
-   ]
- >,
- #Nx.Tensor<
-   s64[4898]
-   EXLA.Backend<host:0, 0.3730900597.862060556.254534>
-   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, ...]
- >}
-```
-
-After performing EDA on our wine dataset, we can now train our KNN model and make predictions. However, the question arises as to what value of neighbors should we choose for the KNN model. To answer this question, we will use *K-Fold Cross-Validation* (specifically, Nested Cross-Validation). K-Fold is a procedure performed on the training dataset where we split the data into k smaller subsets (folds). For each tested parameter value, we run k separate trainings and testings, where one fold is the validation (test) dataset, and the other k-1 folds are the training dataset. To make this process clear, there is a GIF below that explains it visually.
-
-| ![KFold](https://upload.wikimedia.org/wikipedia/commons/4/4b/KfoldCV.gif)                                                                                    |
-| :----------------------------------------------------------------------------------------------------------------------------------------------------------: |
-| Figure 3: Illustration of KFold Cross-Validation when n = 12 observations and k = 3. After data is shuffled, a total of 3 models will be trained and tested. |
-
-```elixir
-defmodule Comb do
-  def combinations([]), do: [[]]
-
-  def combinations([{name, values} | opts]) do
-    for subcombination <- combinations(opts), value <- values do
-      [{name, value} | subcombination]
-    end
-  end
-end
-
-Comb.combinations(task: [:classification], num_classes: [3], num_neighbors: Enum.to_list(1..30))
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-[
-  [task: :classification, num_classes: 3, num_neighbors: 1],
-  [task: :classification, num_classes: 3, num_neighbors: 2],
-  [task: :classification, num_classes: 3, num_neighbors: 3],
-  [task: :classification, num_classes: 3, num_neighbors: 4],
-  [task: :classification, num_classes: 3, num_neighbors: 5],
-  [task: :classification, num_classes: 3, num_neighbors: 6],
-  [task: :classification, num_classes: 3, num_neighbors: 7],
-  [task: :classification, num_classes: 3, num_neighbors: 8],
-  [task: :classification, num_classes: 3, num_neighbors: 9],
-  [task: :classification, num_classes: 3, num_neighbors: 10],
-  [task: :classification, num_classes: 3, num_neighbors: 11],
-  [task: :classification, num_classes: 3, num_neighbors: 12],
-  [task: :classification, num_classes: 3, num_neighbors: 13],
-  [task: :classification, num_classes: 3, num_neighbors: 14],
-  [task: :classification, num_classes: 3, num_neighbors: 15],
-  [task: :classification, num_classes: 3, num_neighbors: 16],
-  [task: :classification, num_classes: 3, num_neighbors: 17],
-  [task: :classification, num_classes: 3, num_neighbors: 18],
-  [task: :classification, num_classes: 3, num_neighbors: 19],
-  [task: :classification, num_classes: 3, num_neighbors: 20],
-  [task: :classification, num_classes: 3, num_neighbors: 21],
-  [task: :classification, num_classes: 3, num_neighbors: 22],
-  [task: :classification, num_classes: 3, num_neighbors: 23],
-  [task: :classification, num_classes: 3, num_neighbors: 24],
-  [task: :classification, num_classes: 3, num_neighbors: 25],
-  [task: :classification, num_classes: 3, num_neighbors: 26],
-  [task: :classification, num_classes: 3, num_neighbors: 27],
-  [task: :classification, num_classes: 3, num_neighbors: 28],
-  [task: :classification, num_classes: 3, num_neighbors: 29],
-  [task: :classification, num_classes: 3, num_neighbors: 30]
-]
-```
-
-The code implementing KFold cross-validation is located at the beginning of the notebook.
-
-```elixir
-min_num_neighbors = 1
-param_space_size = 30
-
-# K in KFold
-k = 10
-train_size = 4000
-
-{indices, _new_key} = Nx.Random.shuffle(key, Nx.iota(Nx.shape(y)))
-x = Nx.take(x, indices)
-y = Nx.take(y, indices)
-{train_data, test_data} = Nx.split(x, train_size)
-{train_labels, test_labels} = Nx.split(y, train_size)
-
-folding_fun = fn x -> Scholar.ModelSelection.k_fold_split(x, k) end
-
-scoring_fun = fn x, y, opts ->
-  {x_train, x_test} = x
-  {y_train, y_test} = y
-
-  model =
-    KNN.fit(x_train, y_train,
-      num_classes: opts[:num_classes],
-      num_neighbors: opts[:num_neighbors],
-      task: opts[:task]
-    )
-
-  prediction = KNN.predict(model, x_test)
-
-  accuracy = Classification.accuracy(y_test, prediction)
-  [accuracy]
-end
-
-res =
-  Scholar.ModelSelection.grid_search(train_data, train_labels, folding_fun, scoring_fun,
-    task: [:classification],
-    num_classes: [3],
-    num_neighbors: Enum.to_list(min_num_neighbors..param_space_size)
-  )
-
-res = for(sub_res <- res, do: sub_res[:score]) |> Nx.concatenate() |> Nx.as_type(:f64)
-
-results =
-  DF.new(accuracy: res, num_neighbors: Nx.add(Nx.iota({param_space_size}), min_num_neighbors))
-```
-
-To potentially improve our KNN model's performance, we can try setting the weights parameter to `:distance` and use weighted version of grid search. Next, we can visualize the results of KFold using a plot.
-
-```elixir
-Vl.new(
-  title: [
-    text: "Accuracy vs Number of Neighbors",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(results)
-|> Vl.mark(:line, color: :gray, stroke_dash: [5, 5], point: true)
-|> Vl.encode_field(:x, "num_neighbors", type: :quantitative, scale: [domain: [1, 31]])
-|> Vl.encode_field(:y, "accuracy", type: :quantitative, scale: [domain: [0.7, 0.85]])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"accuracy":0.7682499885559082,"num_neighbors":1},{"accuracy":0.734250009059906,"num_neighbors":2},{"accuracy":0.7425000071525574,"num_neighbors":3},{"accuracy":0.7512499690055847,"num_neighbors":4},{"accuracy":0.7512499690055847,"num_neighbors":5},{"accuracy":0.749750018119812,"num_neighbors":6},{"accuracy":0.7477499842643738,"num_neighbors":7},{"accuracy":0.7487500309944153,"num_neighbors":8},{"accuracy":0.7487500309944153,"num_neighbors":9},{"accuracy":0.749250054359436,"num_neighbors":10},{"accuracy":0.7489999532699585,"num_neighbors":11},{"accuracy":0.7477499842643738,"num_neighbors":12},{"accuracy":0.7475000023841858,"num_neighbors":13},{"accuracy":0.7419999837875366,"num_neighbors":14},{"accuracy":0.7487500309944153,"num_neighbors":15},{"accuracy":0.747249960899353,"num_neighbors":16},{"accuracy":0.7505000233650208,"num_neighbors":17},{"accuracy":0.7475000023841858,"num_neighbors":18},{"accuracy":0.7475000023841858,"num_neighbors":19},{"accuracy":0.7477499842643738,"num_neighbors":20},{"accuracy":0.7480000257492065,"num_neighbors":21},{"accuracy":0.7477499842643738,"num_neighbors":22},{"accuracy":0.7459999918937683,"num_neighbors":23},{"accuracy":0.7442499995231628,"num_neighbors":24},{"accuracy":0.7442499995231628,"num_neighbors":25},{"accuracy":0.7437499761581421,"num_neighbors":26},{"accuracy":0.7434999942779541,"num_neighbors":27},{"accuracy":0.7464999556541443,"num_neighbors":28},{"accuracy":0.7430000305175781,"num_neighbors":29},{"accuracy":0.747249960899353,"num_neighbors":30}]},"encoding":{"x":{"field":"num_neighbors","scale":{"domain":[1,31]},"type":"quantitative"},"y":{"field":"accuracy","scale":{"domain":[0.7,0.8]},"type":"quantitative"}},"height":630,"mark":{"color":"gray","point":true,"strokeDash":[5,5],"type":"line"},"title":{"offset":20,"text":"Accuracy vs Number of Neighbors"},"width":630}
-```
-
-```elixir
-best_neighbors = Nx.add(Nx.argmax(res), min_num_neighbors) |> Nx.to_number()
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-1
-```
-
-Ok, let's test our best model on test data.
-
-```elixir
-best_model = KNN.fit(train_data, train_labels, num_neighbors: best_neighbors, num_classes: 3)
-
-final_prediction = KNN.predict(best_model, test_data)
-Classification.accuracy(test_labels, final_prediction)
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f32
-  EXLA.Backend<host:0, 0.3730900597.862322700.16513>
-  0.7672605514526367
->
-```
-
-Pretty well, now let's move on to a regression task using KNN.
-
-<!-- livebook:{"branch_parent_index":1} -->
-
-## Regression
-
-KNNs can also be used in regression tasks. We will explore this on a dataset about Airfoil Self-Noise. Here's a brief description of the dataset:
-
-**Data Set Information**:
-
-The NASA data set comprises different size NACA 0012 airfoils at various wind tunnel speeds and angles of attack. The span of the airfoil and the observer position were the same in all of the experiments.
-
-**Attribute Information**:
-
-This problem has the following inputs:
-
-1. Frequency, in Hertzs.
-2. Angle of attack, in degrees.
-3. Chord length, in meters.
-4. Free-stream velocity, in meters per second.
-5. Suction side displacement thickness, in meters.
-
-The only output is:
-
-1. Scaled sound pressure level, in decibels.
-
-Dua, D. and Graff, C. (2019). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.
-
-```elixir
-dataset =
-  Req.get!(
-    "https://archive.ics.uci.edu/ml/machine-learning-databases/00291/airfoil_self_noise.dat"
-  ).body
-
-column_names = [
-  "frequency",
-  "angle_of_attack",
-  "chord_length",
-  "free_stream_velocity",
-  "suction_side_displacement_thickness",
-  "scaled_sound_pressure_level"
-]
-
-dataset_df = DF.load_csv!(dataset, header: false, delimiter: "\t") |> DF.rename(column_names)
-labels = DF.select(dataset_df, "scaled_sound_pressure_level")
-data = DF.discard(dataset_df, "scaled_sound_pressure_level")
-```
-
-Below are the KDE plots of the dataset's features. We will analyze them in the next step.
-
-```elixir
-Vl.new(
-  title: [
-    text: "KDE plots of Features",
-    anchor: :middle,
-    offset: 20
-  ]
-)
-|> Vl.data_from_values(data)
-|> Vl.concat(
-  [
-    Vl.new()
-    |> Vl.concat(
-      [
-        Vl.new(
-          title: [
-            text: "KDE plot of Frequency feature",
-            offset: 20
-          ],
-          width: 350,
-          height: 300
-        )
-        |> Vl.transform(density: "frequency")
-        |> Vl.mark(:area, color: "lightblue")
-        |> Vl.encode_field(:x, "value", type: :quantitative, title: "Frequency (Hz)")
-        |> Vl.encode_field(:y, "density", type: :quantitative),
-        Vl.new(
-          title: [
-            text: "KDE plot of Angle of Attack feature",
-            offset: 20
-          ],
-          width: 350,
-          height: 300
-        )
-        |> Vl.transform(density: "angle_of_attack")
-        |> Vl.mark(:area, color: "lightgreen")
-        |> Vl.encode_field(:x, "value", type: :quantitative, title: "Angle of attack")
-        |> Vl.encode_field(:y, "density", type: :quantitative),
-        Vl.new(
-          title: [
-            text: "KDE plot of Chord length feature",
-            offset: 20
-          ],
-          width: 350,
-          height: 300
-        )
-        |> Vl.transform(density: "chord_length")
-        |> Vl.mark(:area, color: "pink")
-        |> Vl.encode_field(:x, "value", type: :quantitative, title: "Chord length")
-        |> Vl.encode_field(:y, "density", type: :quantitative)
-      ],
-      :vertical
-    ),
-    Vl.new()
-    |> Vl.concat(
-      [
-        Vl.new(
-          title: [
-            text: "KDE plot of Free Stream Velocity feature",
-            offset: 20
-          ],
-          width: 350,
-          height: 300
-        )
-        |> Vl.data_from_values(data)
-        |> Vl.transform(density: "free_stream_velocity")
-        |> Vl.mark(:area, color: "purple")
-        |> Vl.encode_field(:x, "value", type: :quantitative, title: "Free-stream velocity")
-        |> Vl.encode_field(:y, "density", type: :quantitative),
-        Vl.new(
-          title: [
-            text: ["KDE plot of Suction Side Displacement", "Thickness feature"],
-            offset: 20
-          ],
-          width: 350,
-          height: 300
-        )
-        |> Vl.data_from_values(data)
-        |> Vl.transform(density: "suction_side_displacement_thickness")
-        |> Vl.mark(:area, color: "red")
-        |> Vl.encode_field(:x, "value",
-          type: :quantitative,
-          title: "Suction Side Displacement Thickness"
-        )
-        |> Vl.encode_field(:y, "density", type: :quantitative)
-      ],
-      :vertical
-    )
-  ],
-  :horizontal
-)
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
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500,"suction_side_displacement_thickness":0.0418756},{"angle_of_attack":12.3,"chord_length":0.1016,"free_stream_velocity":31.7,"frequency":3150,"suction_side_displacement_thickness":0.0418756},{"angle_of_attack":12.3,"chord_length":0.1016,"free_stream_velocity":31.7,"frequency":4000,"suction_side_displacement_thickness":0.0418756},{"angle_of_attack":12.3,"chord_length":0.1016,"free_stream_velocity":31.7,"frequency":5000,"suction_side_displacement_thickness":0.0418756},{"angle_of_attack":12.3,"chord_length":0.1016,"free_stream_velocity":31.7,"frequency":6300,"suction_side_displacement_thickness":0.0418756},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":200,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":250,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":315,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":400,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":500,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":630,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":800,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":1000,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":1250,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":1600,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":2000,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":2500,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":3150,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency":4000,"suction_side_displacement_thickness":0.0437259},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":200,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":250,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":315,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":400,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":500,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":630,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":800,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":1000,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":1250,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":1600,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":2000,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":2500,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":3150,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":4000,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":5000,"suction_side_displacement_thickness":0.0528487},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency":6300,"suction_side_displacement_thickness":0.0528487}]},"encoding":{"x":{"field":"value","title":"Suction Side Displacement Thickness","type":"quantitative"},"y":{"field":"density","type":"quantitative"}},"height":300,"mark":{"color":"red","type":"area"},"title":{"offset":20,"text":["KDE plot of Suction Side Displacement","Thickness feature"]},"transform":[{"density":"suction_side_displacement_thickness"}],"width":350}]}],"title":{"anchor":"middle","offset":20,"text":"KDE plots of Features"}}
-```
-
-The Suction Side Displacement Thickness and Frequency features have asymmetric distributions with many observations having small values. To make these distributions less skewed, we will use the logarithms of these two features.
-
-```elixir
-data =
-  DF.mutate(data,
-    frequency_log: log(frequency),
-    suction_side_displacement_thickness_log: log(suction_side_displacement_thickness)
-  )
-
-data = DF.discard(data, ["frequency", "suction_side_displacement_thickness"])
-```
-
-Scale data and convert them to tensors.
-
-```elixir
-x = Nx.stack(data, axis: 1) |> Scholar.Preprocessing.standard_scale()
-y = Nx.stack(labels, axis: 1) |> Nx.squeeze(axes: [1])
-{x, y}
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-{#Nx.Tensor<
-   f64[1503][5]
-   EXLA.Backend<host:0, 0.3730900597.862322700.16607>
-   [
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.24959453243691035, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.2391306895323175, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.22866684662772468, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.21709086757891163, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.2066270246743188, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.19616318176972597, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.18532568847301975, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.17412335981632007, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.1636595169117272, -0.8410438169469526],
-     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.15282202361502104, ...],
-     ...
-   ]
- >,
- #Nx.Tensor<
-   f64[1503]
-   EXLA.Backend<host:0, 0.3730900597.862322700.16611>
-   [126.201, 125.201, 125.951, 127.591, 127.461, 125.571, 125.201, 123.061, 121.301, 119.541, 117.151, 115.391, 112.241, 108.721, 126.416, 127.696, 128.086, 126.966, 126.086, 126.986, 126.616, 124.106, 123.236, 121.106, 119.606, 117.976, 116.476, 113.076, 111.076, 118.129, 119.319, 122.779, 124.809, 126.959, 128.629, 129.099, 127.899, 125.499, 124.049, 123.689, 121.399, 120.319, 119.229, 117.789, 116.229, 114.779, 112.139, 109.619, ...]
- >}
-```
-
-In this section, we will apply a similar KFold procedure as in the classification section to find the best value for the `:num_neighbors` parameter in the KNN regression model.
-
-```elixir
-min_num_neighbors = 1
-param_space_size = 30
-
-# K in KFold
-k = 10
-train_size = 1100
-
-{indices, _new_key} = Nx.Random.shuffle(key, Nx.iota(Nx.shape(y)))
-x_shuffled = Nx.take(x, indices)
-y_shuffled = Nx.take(y, indices)
-{train_data, test_data} = Nx.split(x_shuffled, train_size)
-{train_labels, test_labels} = Nx.split(y_shuffled, train_size)
-
-folding_fun = fn x -> Scholar.ModelSelection.k_fold_split(x, k) end
-
-scoring_fun = fn x, y, opts ->
-  {x_train, x_test} = x
-  {y_train, y_test} = y
-
-  model =
-    KNN.fit(x_train, y_train,
-      num_classes: opts[:num_classes],
-      num_neighbors: opts[:num_neighbors],
-      task: opts[:task]
-    )
-
-  prediction = KNN.predict(model, x_test)
-
-  rmse = Regression.mean_square_error(y_test, prediction) |> Nx.sqrt()
-  [rmse]
-end
-
-res =
-  Scholar.ModelSelection.grid_search(train_data, train_labels, folding_fun, scoring_fun,
-    task: [:regression],
-    # dummy, for regression it doesn't matter
-    num_classes: [3],
-    num_neighbors: Enum.to_list(min_num_neighbors..param_space_size)
-  )
-
-res = for(sub_res <- res, do: sub_res[:score]) |> Nx.concatenate() |> Nx.as_type(:f64)
-
-results = DF.new(RMSE: res, num_neighbors: Nx.add(Nx.iota({param_space_size}), min_num_neighbors))
-```
-
-```elixir
-Vl.new(
-  title: [
-    text: "RMSE vs. Number of Neighbors",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(results)
-|> Vl.mark(:line, color: :gray, stroke_dash: [5, 5], point: true)
-|> Vl.encode_field(:x, "num_neighbors", type: :quantitative, scale: [domain: [1, 31]])
-|> Vl.encode_field(:y, "RMSE", type: :quantitative, scale: [domain: [2.6, 6.0]])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"RMSE":2.954160435119645,"num_neighbors":1},{"RMSE":2.705136057088256,"num_neighbors":2},{"RMSE":2.9964430952256733,"num_neighbors":3},{"RMSE":3.2905484274001795,"num_neighbors":4},{"RMSE":3.4905466912822405,"num_neighbors":5},{"RMSE":3.6884594409820104,"num_neighbors":6},{"RMSE":3.8750230152441363,"num_neighbors":7},{"RMSE":4.047035866627379,"num_neighbors":8},{"RMSE":4.189331570582891,"num_neighbors":9},{"RMSE":4.324340953175694,"num_neighbors":10},{"RMSE":4.439531671658643,"num_neighbors":11},{"RMSE":4.571325241080606,"num_neighbors":12},{"RMSE":4.672862066067107,"num_neighbors":13},{"RMSE":4.787292392293998,"num_neighbors":14},{"RMSE":4.879060063659762,"num_neighbors":15},{"RMSE":4.978485008641893,"num_neighbors":16},{"RMSE":5.065103101842437,"num_neighbors":17},{"RMSE":5.160077780567819,"num_neighbors":18},{"RMSE":5.23622641273977,"num_neighbors":19},{"RMSE":5.284432293863683,"num_neighbors":20},{"RMSE":5.3405242911271005,"num_neighbors":21},{"RMSE":5.3922427790028795,"num_neighbors":22},{"RMSE":5.44295673910584,"num_neighbors":23},{"RMSE":5.47931644940631,"num_neighbors":24},{"RMSE":5.523618789257428,"num_neighbors":25},{"RMSE":5.567065728104048,"num_neighbors":26},{"RMSE":5.602044586338607,"num_neighbors":27},{"RMSE":5.641831179764594,"num_neighbors":28},{"RMSE":5.675274254551784,"num_neighbors":29},{"RMSE":5.708321768081241,"num_neighbors":30}]},"encoding":{"x":{"field":"num_neighbors","scale":{"domain":[1,31]},"type":"quantitative"},"y":{"field":"RMSE","scale":{"domain":[2.6,6.0]},"type":"quantitative"}},"height":630,"mark":{"color":"gray","point":true,"strokeDash":[5,5],"type":"line"},"title":{"offset":20,"text":"RMSE vs. Number of Neighbors"},"width":630}
-```
-
-```elixir
-best_neighbors = Nx.add(Nx.argmin(res), min_num_neighbors) |> Nx.to_number()
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-2
-```
-
-The best value is 2. Now try this value to a final prediction.
-
-```elixir
-best_model =
-  KNN.fit(train_data, train_labels,
-    num_neighbors: best_neighbors,
-    num_classes: 3,
-    task: :regression
-  )
-
-final_prediction = KNN.predict(best_model, test_data)
-Regression.mean_square_error(test_labels, final_prediction) |> Nx.sqrt()
-```
-
-<!-- livebook:{"output":true} -->
-
-```
-#Nx.Tensor<
-  f64
-  EXLA.Backend<host:0, 0.3730900597.862322700.26551>
-  2.2414312639566227
->
-```
-
-### Outliers prediction
-
-<!-- livebook:{"break_markdown":true} -->
-
-KNNs can be used for outlier detection. In this task, we will also use the Airfoil Self-Noise dataset. We will calculate for each sample a mean value of distances to the three closest points from dataset.
-
-```elixir
-model = KNN.fit(x, y, num_neighbors: 3, task: :regression)
-{num_samples, _} = Nx.shape(x)
-{distances, indices} = KNN.k_neighbors(model, x)
-
-mean_distances = Nx.mean(distances, axes: [1], keep_axes: true)
-
-samples_mean_distances =
-  Nx.concatenate([mean_distances, Nx.iota({num_samples, 1})], axis: 1)
-  |> DF.new()
-  |> DF.rename(["mean_distances", "index"])
-```
-
-Now, plot the mean values of distances.
-
-```elixir
-Vl.new(
-  title: [
-    text: "Plot to check anomalies",
-    offset: 20
-  ],
-  width: 800,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(samples_mean_distances)
-  |> Vl.mark(:line, color: :jet)
-  |> Vl.encode_field(:x, "index", type: :quantitative, scale: [domain: [0, 1510]])
-  |> Vl.encode_field(:y, "mean_distances",
-    type: :quantitative,
-    title: "Mean distance to clusters",
-    scale: [domain: [0.0065, 0.012]]
-  ),
-  Vl.new()
-  |> Vl.data_from_values(DF.new(y: [0.009]))
-  |> Vl.mark(:rule, color: :red, stroke_dash: [5, 5])
-  |> Vl.encode_field(:y, "y", type: :quantitative, title: "")
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"index":0.0,"mean_distances":0.010463842904592837},{"index":1.0,"mean_distances":0.006975895269728555},{"index":2.0,"mean_distances":0.00708550244172234},{"index":3.0,"mean_distances":0.007085502441722349},{"index":4.0,"mean_distances":0.006975895269728555},{"index":5.0,"mean_distances":0.00708550244172234},{"index":6.0,"mean_distances":0.007210052572426806},{"index":7.0,"mean_distances":0.007085502441722358},{"index":8.0,"mean_distances":0.007085502441722358},{"index":9.0,"mean_distances":0.007210052572426788},{"index":10.0,"mean_distances":0.007085502441722358},{"index":11.0,"mean_distances":0.006975895269728555},{"index":12.0,"mean_distances":0.00708550244172233},{"index":13.0,"mean_distances":0.007456214489795751},{"index":14.0,"mean_distances":0.007112422456047339},{"index":15.0,"mean_distances":0.007112422456047339},{"index":16.0,"mean_distances":0.0069878723253428724},{"index":17.0,"mean_distances":0.006975895269728555},{"index":18.0,"mean_distances":0.006987872325342863},{"index":19.0,"mean_distances":0.0069878723253428724},{"index":20.0,"mean_distances":0.006975895269728555},{"index":21.0,"mean_distances":0.006987872325342863},{"index":22.0,"mean_distances":0.007112422456047329},{"index":23.0,"mean_distances":0.006987872325342881},{"index":24.0,"mean_distances":0.006987872325342881},{"index":25.0,"mean_distances":0.007112422456047311},{"index":26.0,"mean_distances":0.007222057187097518},{"index":27.0,"mean_distances":0.006975895269728555},{"index":28.0,"mean_distances":0.010463842904592818},{"index":29.0,"mean_distances":0.010588393035297313},{"index":30.0,"mean_distances":0.007100445400433031},{"index":31.0,"mean_distances":0.006981435020399144},{"index":32.0,"mean_distances":0.006856884889694677},{"index":33.0,"mean_distances":0.006856884889694677},{"index":34.0,"mean_distances":0.006981435020399144},{"index":35.0,"mean_distances":0.006856884889694677},{"index":36.0,"mean_distances":0.006856884889694668},{"index":37.0,"mean_distances":0.006856884889694668},{"index":38.0,"mean_distances":0.006856884889694677},{"index":39.0,"mean_distances":0.006856884889694668},{"index":40.0,"mean_distances":0.006856884889694668},{"index":41.0,"mean_distances":0.006981435020399135},{"index":42.0,"mean_distances":0.006856884889694687},{"index":43.0,"mean_distances":0.006856884889694687},{"index":44.0,"mean_distances":0.006981435020399117},{"index":45.0,"mean_distances":0.007222057187097518},{"index":46.0,"mean_distances":0.006975895269728555},{"index":47.0,"mean_distances":0.010463842904592818},{"index":48.0,"mean_distances":0.010588393035297313},{"index":49.0,"mean_distances":0.007100445400433031},{"index":50.0,"mean_distances":0.006895525269163041},{"index":51.0,"mean_distances":0.006770975138458574},{"index":52.0,"mean_distances":0.006770975138458574},{"index":53.0,"mean_distances":0.006895525269163041},{"index":54.0,"mean_distances":0.006770975138458574},{"index":55.0,"mean_distances":0.006770975138458565},{"index":56.0,"mean_distances":0.006770975138458565},{"index":57.0,"mean_distances":0.006770975138458574},{"index":58.0,"mean_distances":0.006770975138458565},{"index":59.0,"mean_distances":0.006770975138458565},{"index":60.0,"mean_distances":0.006895525269163032},{"index":61.0,"mean_distances":0.006770975138458583},{"index":62.0,"mean_distances":0.006770975138458583},{"index":63.0,"mean_distances":0.0068955252691630135},{"index":64.0,"mean_distances":0.007222057187097518},{"index":65.0,"mean_distances":0.010710004821961808},{"index":66.0,"mean_distances":0.010463842904592837},{"index":67.0,"mean_distances":0.006975895269728555},{"index":68.0,"mean_distances":0.007346607317801956},{"index":69.0,"mean_distances":0.007346607317801966},{"index":70.0,"mean_distances":0.006975895269728555},{"index":71.0,"mean_distances":0.007100445400433013},{"index":72.0,"mean_distances":0.007346607317801966},{"index":73.0,"mean_distances":0.007222057187097518},{"index":74.0,"mean_distances":0.007100445400433013},{"index":75.0,"mean_distances":0.007346607317801947},{"index":76.0,"mean_distances":0.007222057187097518},{"index":77.0,"mean_distances":0.006975895269728555},{"index":78.0,"mean_distances":0.007346607317801947},{"index":79.0,"mean_distances":0.01120526700073963},{"index":80.0,"mean_distances":0.010956166739330697},{"index":81.0,"mean_distances":0.00722205718709749},{"index":82.0,"mean_distances":0.007100445400433031},{"index":83.0,"mean_distances":0.007346607317801966},{"index":84.0,"mean_distances":0.0072220571870974986},{"index":85.0,"mean_distances":0.006975895269728555},{"index":86.0,"mean_distances":0.007346607317801956},{"index":87.0,"mean_distances":0.007346607317801966},{"index":88.0,"mean_distances":0.006975895269728555},{"index":89.0,"mean_distances":0.007100445400433013},{"index":90.0,"mean_distances":0.007346607317801966},{"index":91.0,"mean_distances":0.007222057187097518},{"index":92.0,"mean_distances":0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distance to clusters","type":"quantitative"}},"mark":{"color":"jet","type":"line"}},{"data":{"values":[{"y":0.009}]},"encoding":{"y":{"field":"y","type":"quantitative"}},"mark":{"color":"red","strokeDash":[5,5],"type":"rule"}}],"title":{"offset":20,"text":"Plot to check anomalies"},"width":800}
-```
-
-We can assume, that samples with average distance bigger than 0.0105 can be treated as outliers.
-
-```elixir
-data = DF.put(data, :is_outlier, Nx.greater(mean_distances, 0.0105))
-```
-
-```elixir
-Vl.new(
-  title: [
-    text: "Logarithm of Frequency vs Logarithm of Suction Side Displacement Thickness",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(data)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.param("brush", select: :interval)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "frequency_log", type: :quantitative, scale: [domain: [4.5, 10.5]])
-  |> Vl.encode_field(:y, "suction_side_displacement_thickness_log",
-    type: :quantitative,
-    scale: [domain: [-8.0, -2.5]]
-  )
-  |> Vl.encode(:color,
-    condition: [param: "brush", field: "is_outlier", type: :nominal],
-    value: :gray
-  ),
-  Vl.new()
-  |> Vl.transform(filter: [param: "brush", field: "is_outlier", equal: true])
-  |> Vl.mark(:text)
-  |> Vl.encode(:x, value: 11)
-  |> Vl.encode(:y, value: -3.5)
-  |> Vl.encode_field(:text, "filter",
-    type: :quantitative,
-    aggregate: :count
-  )
-])
-```
-
-<!-- livebook:{"output":true} -->
-
-```vega-lite
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":0.1016,"free_stream_velocity":71.3,"frequency_log":8.055157731819678,"is_outlier":false,"suction_side_displacement_thickness_log":-3.129814675098908},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":71.3,"frequency_log":8.294049640102028,"is_outlier":true,"suction_side_displacement_thickness_log":-3.129814675098908},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":5.298317366548036,"is_outlier":true,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":5.521460917862246,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":5.752572638825633,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":5.991464547107982,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":6.214608098422191,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":6.4457198193855785,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":6.684611727667927,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":6.907755278982137,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":7.1308988302963465,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":7.3777589082278725,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":7.600902459542082,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":7.824046010856292,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":8.055157731819678,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":8.294049640102028,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":8.517193191416238,"is_outlier":false,"suction_side_displacement_thickness_log":-2.940322164887062},{"angle_of_attack":15.6,"chord_length":0.1016,"free_stream_velocity":39.6,"frequency_log":8.748304912379623,"is_outlier":true,"suction_side_displacement_thickness_log":-2.940322164887062}]},"height":630,"layer":[{"encoding":{"color":{"condition":{"field":"is_outlier","param":"brush","type":"nominal"},"value":"gray"},"x":{"field":"frequency_log","scale":{"domain":[4.5,10.5]},"type":"quantitative"},"y":{"field":"suction_side_displacement_thickness_log","scale":{"domain":[-8.0,-2.5]},"type":"quantitative"}},"mark":"circle","params":[{"name":"brush","select":"interval"}]},{"encoding":{"text":{"aggregate":"count","field":"filter","type":"quantitative"},"x":{"value":11},"y":{"value":-3.5}},"mark":"text","transform":[{"filter":{"equal":true,"field":"is_outlier","param":"brush"}}]}],"title":{"offset":20,"text":"Logarithm of Frequency vs Logarithm of Suction Side Displacement Thickness"},"width":630}
-```
+<!-- livebook:{"persist_outputs":true} -->
+
+# K-Nearest Neighbors
+
+```elixir
+Mix.install([
+  {:scholar, "~> 0.2.0"},
+  {:explorer, "~> 0.6.1"},
+  {:exla, "~> 0.6.0"},
+  {:nx, "~> 0.6.0", override: true},
+  {:req, "~> 0.3.9"},
+  {:kino_vega_lite, "~> 0.1.9"},
+  {:kino, "~> 0.10.0"},
+  {:scidata, "~> 0.1.10"},
+  {:kino_explorer, "~> 0.1.7"},
+  {:tucan, "~> 0.2.1"}
+])
+```
+
+## Setup
+
+We will extensively use VegaLite, Explorer, and Scholar throughout this guide, so let's define some aliases:
+
+```elixir
+require Explorer.DataFrame, as: DF
+require Explorer.Series, as: S
+require Explorer.Query, as: Q
+alias Scholar.Neighbors.KNearestNeighbors, as: KNN
+alias Scholar.Metrics.Classification
+alias Scholar.Metrics.Regression
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+Scholar.Metrics.Regression
+```
+
+And let's configure `EXLA.Backend` as our default across the notebook and all branched sections:
+
+```elixir
+Nx.global_default_backend(EXLA.Backend)
+seed = 42
+key = Nx.Random.key(42)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+
+02:33:33.173 [info] TfrtCpuClient created.
+
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  u32[2]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254101>
+  [0, 42]
+>
+```
+
+## Introduction
+
+This notebook will cover the three primary applications of K-Nearest Neighbors: classification, regression, and
+anomaly detection.
+
+<!-- livebook:{"branch_parent_index":1} -->
+
+## Classification
+
+The process of classification using KNN is relatively straightforward. We start by working with a dataset where each sample is assigned a label. To predict the label of a new sample, we compute the distance between it and all the other samples in the dataset. Next, we select only the $k$ closest samples based on the distance metric, where $k$ is a user-defined parameter. We then examine the labels of these $k$ samples and choose the label that appears most frequently. This label is assigned as the predicted label for the new sample.
+
+Let's first grasp how kNN works visually with a small example.
+
+```elixir
+data =
+  DF.new(
+    x: [-1, 0.2, -0.5, -2.1, -2.3, -2.2, 0.1, 0.3, 0.4, 0.7, 1.3],
+    y: [-0.1, 0.4, 0.5, 0.4, 1.1, -1.0, -0.1, 0.2, 1.5, 1.6, 0.9],
+    label: [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
+  )
+
+point_to_predict = DF.new(x: [0.0], y: [0.0])
+
+k_eq_3 = DF.new(x: [0.45], y: [0.45], name: ["k = 3"])
+k_eq_5 = DF.new(x: [0.72], y: [0.72], name: ["k = 5"])
+
+radius = fn x, y -> :math.sqrt(x ** 2 + y ** 2) end
+
+Tucan.layers([
+  Tucan.scatter(data, "x", "y",
+    point_size: 200,
+    filled: true,
+    shape_by: "label",
+    color_by: "label"
+  )
+  |> Tucan.Scale.set_color_scheme(:plasma),
+  Tucan.scatter(point_to_predict, "x", "y",
+    point_size: 400,
+    point_color: "green",
+    point_shape: "triangle-up",
+    filled: true
+  ),
+  Tucan.circle(Tucan.new(), {0, 0}, radius.(0.2, 0.4), line_color: "brown", stroke_width: 2),
+  Tucan.circle(Tucan.new(), {0, 0}, radius.(-1, 0.1), line_color: "blue", stroke_width: 2),
+  Tucan.annotate(Tucan.new(), 0.42, 0.42, "k = 3", color: "brown", size: 20),
+  Tucan.annotate(Tucan.new(), 0.81, 0.81, "k = 5", color: "blue", size: 20)
+])
+|> Tucan.Scale.set_xy_domain(-2.4, 1.7)
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot showing KNN prediction process", offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"label":0,"x":-1.0,"y":-0.1},{"label":0,"x":0.2,"y":0.4},{"label":0,"x":-0.5,"y":0.5},{"label":0,"x":-2.1,"y":0.4},{"label":0,"x":-2.3,"y":1.1},{"label":0,"x":-2.2,"y":-1.0},{"label":1,"x":0.1,"y":-0.1},{"label":1,"x":0.3,"y":0.2},{"label":1,"x":0.4,"y":1.5},{"label":1,"x":0.7,"y":1.6},{"label":1,"x":1.3,"y":0.9}]},"encoding":{"color":{"field":"label","scale":{"reverse":false,"scheme":"plasma"},"type":"nominal"},"shape":{"field":"label","type":"nominal"},"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7],"zero":false},"type":"quantitative"}},"mark":{"fillOpacity":1,"filled":true,"size":200,"type":"point"}},{"data":{"values":[{"x":0.0,"y":0.0}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7],"zero":false},"type":"quantitative"}},"mark":{"color":"green","fillOpacity":1,"filled":true,"shape":"triangle-up","size":400,"type":"point"}},{"data":{"sequence":{"as":"theta","start":0,"step":0.1,"stop":361}},"encoding":{"order":{"field":"theta"},"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7]},"type":"quantitative"}},"mark":{"color":"brown","strokeWidth":2,"type":"line"},"transform":[{"as":"x","calculate":"0 + cos(datum.theta*PI/180) * 0.447213595499958"},{"as":"y","calculate":"0 + sin(datum.theta*PI/180) * 0.447213595499958"}]},{"data":{"sequence":{"as":"theta","start":0,"step":0.1,"stop":361}},"encoding":{"order":{"field":"theta"},"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7]},"type":"quantitative"}},"mark":{"color":"blue","strokeWidth":2,"type":"line"},"transform":[{"as":"x","calculate":"0 + cos(datum.theta*PI/180) * 1.004987562112089"},{"as":"y","calculate":"0 + sin(datum.theta*PI/180) * 1.004987562112089"}]},{"data":{"values":[{"x":0.42,"y":0.42}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7]},"type":"quantitative"}},"mark":{"color":"brown","size":20,"text":"k = 3","type":"text"}},{"data":{"values":[{"x":0.81,"y":0.81}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.4,1.7]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[-2.4,1.7]},"type":"quantitative"}},"mark":{"color":"blue","size":20,"text":"k = 5","type":"text"}}],"title":{"offset":20,"text":"Scatterplot showing KNN prediction process"},"width":630}
+```
+
+Note that the final prediction may vary depending on the value of $k$. For example, with $k = 3$, we would predict the green triangle as an orange square (1), whereas with $k = 5$, the purple circle (0) would be the final prediction.
+
+Let's now test this using Scholar code. First, we will define our data.
+
+```elixir
+x = Nx.stack(DF.discard(data, "label"), axis: 1)
+labels = Nx.stack(DF.select(data, "label"), axis: 1) |> Nx.squeeze(axes: [1])
+x_pred = Nx.stack(point_to_predict, axis: 1)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64[1][2]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254170>
+  [
+    [0.0, 0.0]
+  ]
+>
+```
+
+Let's now try with $k = 3$.
+
+```elixir
+model = KNN.fit(x, labels, num_classes: 2, num_neighbors: 3)
+KNN.predict(model, x_pred)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  s64[1]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254247>
+  [1]
+>
+```
+
+And $k = 5$.
+
+```elixir
+model = KNN.fit(x, labels, num_classes: 2, num_neighbors: 5)
+KNN.predict(model, x_pred)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  s64[1]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254320>
+  [0]
+>
+```
+
+As we can see, the predictions match our intuition from analyzing the plot.
+
+Now, let's try KNN on a more complicated dataset: the Wine dataset. Our task will be to classify the quality of the wine. Before we load the dataset into `Explorer.DataFrame` for more efficient exploration, let's check some more detailed information about the dataset.
+
+```elixir
+info =
+  Req.get!(
+    "https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality.names"
+  ).body
+
+Kino.Markdown.new(info)
+```
+
+```elixir
+data =
+  Req.get!(
+    "https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv"
+  ).body
+
+df_data = DF.load_csv!(data, delimiter: ";", dtypes: %{"total sulfur dioxide": :float})
+tensor_data = Nx.stack(df_data, axis: 1)
+df_data
+```
+
+As we can see, there are no null values in the dataset. Now, let's check the size of the dataset.
+
+```elixir
+DF.shape(df_data)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+{4898, 12}
+```
+
+Let's check some statistical properties of the dataset. We will start with *skewness*, which measures the asymmetry of the probability distribution of a random variable about its mean. To better understand this concept, please take a look at the picture below.
+
+| ![Skewness](https://upload.wikimedia.org/wikipedia/commons/c/cc/Relationship_between_mean_and_median_under_different_skewness.png) |
+| :--------------------------------------------------------------------------------------------------------------------------------: |
+| Figure 1: A general relationship of mean and median under differently skewed unimodal distribution                                 |
+
+Now, let's check the skewness of our dataset using Scholar.Stats.skew function.
+
+```elixir
+Scholar.Stats.skew(tensor_data)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64[12]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254424>
+  [0.6475530855160632, 1.5764965159574844, 1.2815277799152376, 1.0767638711454446, 5.0217921696710315, 1.4063140718346212, 0.3905901775815236, 0.9774735389046988, 0.45764233925379794, 0.9768943947733456, 0.4871927332763434, 0.15574868141362447]
+>
+```
+
+As we can see, all features have positive skewness, which means that their distributions are more similar to the left plot in the picture above.
+
+Moving on to another statistical function, let's discuss *kurtosis*. Kurtosis measures how much data is located in the tails of distributions. If the kurtosis is greater than 0, the distribution is said to be "platykurtic", indicating that it has more extreme values than a univariate normal distribution. Similarly, a "leptokurtic" distribution has positive kurtosis and less extreme values, while a "mesokurtic" distribution has the same kurtosis as a normal distribution. Let's check the kurtosis of our dataset.
+
+| ![Skewness](https://vitalflux.com/wp-content/uploads/2023/01/fourth-moment-kurtosis-640x334.png) |
+| :----------------------------------------------------------------------------------------------: |
+| Figure 2: Plot showing Platykurtic, Mesokurtic and Leptokurtic distributions                     |
+
+```elixir
+Scholar.Stats.kurtosis(tensor_data)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64[12]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254451>
+  [2.168736944824719, 5.08520490451785, 6.167374226819426, 3.4650542966046363, 37.52503905008619, 11.453415905047144, 0.5700448984658735, 9.78258726703508, 0.5290085383907339, 1.5880812942840778, -0.6989373013774784, 0.21508011570192975]
+>
+```
+
+Almost all features have positive kurtosis (they are leptokurtic). `alcohol` has negative excess kurtosis, which means it is platykurtic. Below there is Kernel Density Estimate (KDE) to check how exactly this tail look like.
+
+```elixir
+# Increase the sample size (or use 1.0 to plot all data)
+sample = DF.sample(df_data, 0.5, seed: seed)
+
+Tucan.hconcat([
+  Tucan.density(sample, "alcohol", only: ["alcohol"], area_color: "lightblue")
+  |> Tucan.Axes.set_x_title("% of alcohol")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of alcohol feature", offset: 20),
+  Tucan.density(sample, "pH", only: ["pH"], area_color: "lightgreen")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of pH feature", offset: 20)
+])
+|> Tucan.set_title("KDE plots of Features", anchor: :middle, offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","hconcat":[{"data":{"values":[{"alcohol":8.9},{"alcohol":9.5},{"alcohol":10.1},{"alcohol":10.6},{"alcohol":9.9},{"alcohol":10.1},{"alcohol":9.6},{"alcohol":9.2},{"alcohol":12.2},{"alcohol":10.5},{"alcohol":9.2},{"alcohol":9.7},{"alcohol":9.2},{"alcohol":10.8},{"alcohol":9.8},{"alcohol":10.6},{"alcohol":11.7},{"alcohol":11.4},{"alcohol":11.3},{"alcohol":9.9},{"alcohol":12.8},{"alcohol":11.0},{"alcohol":10.3},{"alcohol":11.6},{"alcohol":10.1},{"alcohol":10.4},{"alcohol":10.0},{"alcohol":10.5},{"alcohol":11.6},{"alcohol":12.3},{"alcohol":10.0},{"alcohol":10.2},{"alcohol":10.5},{"alcohol":9.0},{"alcohol":10.4},{"alcohol":9.6},{"alcohol":10.0},{"alcohol":11.2},{"alcohol":10.0},{"alcohol":12.4},{"alcohol":9.4},{"alcohol":10.0},{"alcohol":9.8},{"alcohol":9.5},{"alcohol":9.5},{"alcohol":10.0},{"alcohol":10.1},{"alcohol":9.8},{"alcohol":9.8},{"alcohol":11.8},{"alcohol":11.7},{"alcohol":9.6},{"alcohol":10.4},{"alcohol":10.9},{"alcohol":9.1},{"alcohol":11.0},{"alcohol":11.4},{"alcohol":8.9},{"alcohol":13.1},{"alcohol":9.9},{"alcohol":8.6},{"alcohol":8.9},{"alcohol":11.5},{"alcohol":10.6},{"alcohol":10.15},{"alcohol":9.3},{"alcohol":12.6},{"alcohol":9.8},{"alcohol":10.7},{"alcohol":9.5},{"alcohol":9.0},{"alcohol":9.5},{"alcohol":10.0},{"alcohol":9.1},{"alcohol":10.7},{"alcohol":9.5},{"alcohol":9.1},{"alcohol":10.4},{"alcohol":9.3},{"alcohol":9.0},{"alcohol":11.6},{"alcohol":9.2},{"alcohol":12.6},{"alcohol":9.5},{"alcohol":8.7},{"alcohol":8.7},{"alcohol":12.0},{"alcohol":11.1},{"alcohol":11.0},{"alcohol":11.5},{"alcohol":9.6},{"alcohol":9.0},{"alcohol":12.6},{"alcohol":9.9},{"alcohol":12.2},{"alcohol":12.1},{"alcohol":11.3},{"alcohol":11.4},{"alcohol":11.7},{"alcohol":10.0},{"alcohol":10.0},{"alcohol":11.5},{"alcohol":9.8},{"alcohol":8.8},{"alcohol":9.1},{"alcohol":9.2},{"alcohol":12.9},{"alcohol":12.5},{"alcohol":11.0},{"alcohol":9.2},{"alcohol":8.8},{"alcohol":8.9},{"alcohol":9.2},{"alcohol":9.1},{"alcohol":13.4},{"alcohol":13.4},{"alcohol":11.3},{"alcohol":11.8},{"alcohol":9.2},{"alcohol":9.2},{"alcohol":13.6},{"alcohol":10.7},{"alcohol":10.9},{"alcohol":9.1},{"alcohol":9.8},{"alcohol":11.0},{"alcohol":10.5},{"alcohol":9.7},{"alcohol":10.9},{"alcohol":9.4},{"alcohol":9.8},{"alcohol":9.7},{"alcohol":9.0},{"alcohol":9.2},{"alcohol":11.9},{"alcohol":9.6},{"alcohol":13.1},{"alcohol":8.7},{"alcohol":9.4},{"alcohol":12.6},{"alcohol":10.2},{"alcohol":8.7},{"alcohol":10.8},{"alcohol":13.5},{"alcohol":9.1},{"alcohol":11.9},{"alcohol":10.1},{"alcohol":10.9},{"alcohol":12.0},{"alcohol":12.0},{"alcohol":11.5},{"alcohol":9.9},{"alcohol":9.4},{"alcohol":12.4},{"alcohol":11.2},{"alcohol":8.9},{"alcohol":10.2},{"alcohol":11.1},{"alcohol":12.1},{"alcohol":12.1},{"alcohol":12.4},{"alcohol":9.1},{"alcohol":10.6},{"alcohol":9.5},{"alcohol":10.3},{"alcohol":9.7},{"alcohol":9.3},{"alcohol":12.6},{"alcohol":12.7},{"alcohol":11.5},{"alcohol":12.7},{"alcohol":11.0},{"alcohol":10.8},{"alcohol":11.5},{"alcohol":10.5333333333333},{"alcohol":11.4},{"alcohol":11.2},{"alcohol":9.4},{"alcohol":9.1},{"alcohol":12.4},{"alcohol":9.3},{"alcohol":10.4},{"alcohol":8.7},{"alcohol":12.4},{"alcohol":13.2},{"alcohol":11.9},{"alcohol":11.4},{"alcohol":12.2},{"alcohol":12.7},{"alcohol":8.9},{"alcohol":10.4},{"alcohol":8.7},{"alcohol":11.4},{"alcohol":9.0},{"alcohol":12.3},{"alcohol":9.7},{"alcohol":11.0},{"alcohol":11.5},{"alcohol":8.8},{"alcohol":8.9},{"alcohol":11.3},{"alcohol":8.8},{"alcohol":9.6},{"alcohol":12.0},{"alcohol":9.1},{"alcohol":8.8},{"alcohol":9.2},{"alcohol":11.7},{"alcohol":10.2},{"alcohol":9.5},{"alcohol":11.2},{"alcohol":9.9},{"alcohol":9.2},{"alcohol":9.2},{"alcohol":11.1},{"alcohol":11.5},{"alcohol":10.6},{"alcohol":9.4},{"alcohol":9.4},{"alcohol":12.5},{"alcohol":11.0},{"alcohol":9.1},{"alcohol":11.1},{"alcohol":9.5},{"alcohol":10.4},{"alcohol":9.1},{"alcohol":9.7},{"alcohol":10.2},{"alcohol":9.5},{"alcohol":11.2},{"alcohol":8.9},{"alcohol":13.0},{"alcohol":9.5},{"alcohol":10.7},{"alcohol":9.2},{"alcohol":12.0},{"alcohol":9.0},{"alcohol":9.4},{"alcohol":10.2},{"alcohol":13.5},{"alcohol":8.7},{"alcohol":12.6},{"alcohol":11.4},{"alcohol":9.7},{"alcohol":8.7},{"alcohol":13.6},{"alcohol":10.0},{"alcohol":10.9},{"alcohol":10.9},{"alcohol":10.8},{"alcohol":10.0},{"alcohol":9.8},{"alcohol":12.7},{"alcohol":9.4},{"alcohol":9.3},{"alcohol":8.9},{"alcohol":11.1},{"alcohol":8.0},{"alcohol":10.5},{"alcohol":11.4},{"alcohol":9.0},{"alcohol":8.9},{"alcohol":10.2},{"alcohol":11.3},{"alcohol":10.6},{"alcohol":13.1},{"alcohol":9.2},{"alcohol":9.7},{"alcohol":9.7},{"alcohol":9.7},{"alcohol":11.6},{"alcohol":11.3},{"alcohol":9.3},{"alcohol":11.8},{"alcohol":9.5},{"alcohol":10.5},{"alcohol":9.8},{"alcohol":9.1},{"alcohol":10.9333333333333},{"alcohol":12.4},{"alcohol":12.6},{"alcohol":12.3},{"alcohol":10.5},{"alcohol":11.1},{"alcohol":8.8},{"alcohol":11.0},{"alcohol":12.0},{"alcohol":9.5},{"alcohol":11.1},{"alcohol":12.4},{"alcohol":9.0},{"alcohol":9.0},{"alcohol":9.1},{"alcohol":9.8},{"alcohol":1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H":3.16},{"pH":3.17},{"pH":3.34},{"pH":3.1},{"pH":3.26},{"pH":3.12},{"pH":3.19},{"pH":3.46},{"pH":3.38},{"pH":3.1},{"pH":3.36},{"pH":3.19},{"pH":3.27},{"pH":3.18},{"pH":3.63},{"pH":3.19},{"pH":3.02},{"pH":2.99},{"pH":3.34},{"pH":3.12},{"pH":3.0},{"pH":3.14},{"pH":3.3},{"pH":3.38},{"pH":3.12},{"pH":3.3},{"pH":3.14},{"pH":3.32},{"pH":3.43},{"pH":3.2},{"pH":3.05},{"pH":3.2},{"pH":3.39},{"pH":3.27},{"pH":3.19},{"pH":3.22},{"pH":3.31},{"pH":3.15},{"pH":3.13},{"pH":3.27},{"pH":3.05},{"pH":3.37},{"pH":3.22},{"pH":2.97},{"pH":3.25},{"pH":3.32},{"pH":3.5},{"pH":3.07},{"pH":3.19},{"pH":3.11},{"pH":3.15},{"pH":3.18},{"pH":3.1},{"pH":3.4},{"pH":3.39},{"pH":3.4},{"pH":3.18},{"pH":3.15},{"pH":3.05},{"pH":3.22},{"pH":3.12},{"pH":3.27},{"pH":3.11},{"pH":3.27},{"pH":3.12},{"pH":3.06},{"pH":3.05},{"pH":3.2},{"pH":3.16},{"pH":3.3},{"pH":3.47},{"pH":3.37},{"pH":3.22},{"pH":3.01},{"pH":2.96},{"pH":2.93},{"pH":3.18},{"pH":3.12},{"pH":3.36},{"pH":3.14},{"pH":3.14},{"pH":3.1},{"pH":3.23},{"pH":3.34},{"pH":3.14},{"pH":3.14},{"pH":3.23},{"pH":3.21},{"pH":3.15},{"pH":3.22},{"pH":3.4},{"pH":3.16},{"pH":2.97},{"pH":3.22},{"pH":3.29},{"pH":3.08},{"pH":3.08},{"pH":3.11},{"pH":3.27},{"pH":2.92},{"pH":3.31},{"pH":3.04},{"pH":3.1},{"pH":2.92},{"pH":3.23},{"pH":3.11},{"pH":3.1},{"pH":3.08},{"pH":3.16},{"pH":3.24},{"pH":3.1},{"pH":3.23},{"pH":3.08},{"pH":3.21},{"pH":3.0},{"pH":3.31},{"pH":3.0},{"pH":3.15},{"pH":3.19},{"pH":3.08},{"pH":3.18},{"pH":2.9},{"pH":3.32},{"pH":3.52},{"pH":3.16},{"pH":3.13},{"pH":3.15},{"pH":3.11},{"pH":3.14},{"pH":3.28},{"pH":3.12},{"pH":3.13},{"pH":3.06},{"pH":3.09},{"pH":3.06},{"pH":3.03},{"pH":3.08},{"pH":3.06},{"pH":3.19},{"pH":2.96},{"pH":2.92},{"pH":3.07},{"pH":3.17},{"pH":3.35},{"pH":3.17},{"pH":2.92},{"pH":3.16},{"pH":3.13},{"pH":3.36},{"pH":3.13},{"pH":3.17},{"pH":3.1},{"pH":3.25},{"pH":3.04},{"pH":3.21},{"pH":3.08},{"pH":3.1},{"pH":3.19},{"pH":3.28},{"pH":3.23},{"pH":3.08},{"pH":3.54},{"pH":3.16},{"pH":3.23},{"pH":3.14},{"pH":3.24},{"pH":2.97},{"pH":3.11},{"pH":3.32},{"pH":3.02},{"pH":3.24},{"pH":3.12},{"pH":3.06},{"pH":3.11},{"pH":3.52},{"pH":3.11},{"pH":3.08},{"pH":2.99},{"pH":3.47},{"pH":3.07},{"pH":3.29},{"pH":3.19},{"pH":3.17},{"pH":3.35},{"pH":3.2},{"pH":3.74},{"pH":3.2},{"pH":3.17},{"pH":3.17},{"pH":3.08},{"pH":3.27},{"pH":2.98},{"pH":3.14},{"pH":3.23},{"pH":3.06},{"pH":3.06},{"pH":3.19},{"pH":3.17},{"pH":3.06},{"pH":3.17},{"pH":3.17},{"pH":3.29},{"pH":3.34},{"pH":3.18},{"pH":3.38},{"pH":3.11},{"pH":3.28},{"pH":3.1},{"pH":3.34},{"pH":3.38},{"pH":3.34},{"pH":3.32},{"pH":3.21},{"pH":3.14},{"pH":3.24},{"pH":3.33},{"pH":3.06},{"pH":3.28},{"pH":3.11},{"pH":3.14},{"pH":2.88},{"pH":3.34},{"pH":3.0},{"pH":3.0},{"pH":3.19},{"pH":3.2},{"pH":3.25},{"pH":3.32},{"pH":3.17},{"pH":3.19},{"pH":3.1},{"pH":3.79},{"pH":3.08},{"pH":3.18},{"pH":3.22},{"pH":3.13},{"pH":3.11},{"pH":3.31},{"pH":3.11},{"pH":3.06},{"pH":3.25},{"pH":3.26},{"pH":3.18},{"pH":3.24},{"pH":3.24},{"pH":3.18},{"pH":3.29},{"pH":3.2},{"pH":3.48},{"pH":3.07},{"pH":2.98},{"pH":3.2},{"pH":3.1},{"pH":3.4},{"pH":3.04},{"pH":3.11},{"pH":3.18},{"pH":3.0},{"pH":2.95},{"pH":3.06},{"pH":3.47},{"pH":2.9},{"pH":2.96},{"pH":3.15},{"pH":3.06},{"pH":3.25},{"pH":3.3},{"pH":3.2},{"pH":3.05},{"pH":3.03},{"pH":3.17},{"pH":3.3},{"pH":3.15},{"pH":3.42},{"pH":3.15},{"pH":3.19},{"pH":3.12},{"pH":3.22},{"pH":3.25},{"pH":3.68},{"pH":3.19},{"pH":3.21},{"pH":3.25},{"pH":3.05},{"pH":3.37},{"pH":3.38},{"pH":3.14},{"pH":3.05},{"pH":3.09},{"pH":3.49},{"pH":3.06},{"pH":3.5},{"pH":3.24},{"pH":3.06},{"pH":2.88},{"pH":3.25},{"pH":3.29},{"pH":3.23},{"pH":3.06},{"pH":3.38},{"pH":3.43},{"pH":3.11},{"pH":3.25},{"pH":3.25},{"pH":3.45},{"pH":3.16},{"pH":3.27},{"pH":3.17},{"pH":3.15},{"pH":3.24},{"pH":3.13},{"pH":3.1},{"pH":3.12},{"pH":3.2},{"pH":3.04},{"pH":3.24},{"pH":3.17},{"pH":3.34},{"pH":3.1},{"pH":2.96},{"pH":3.38},{"pH":3.05},{"pH":3.47},{"pH":3.35},{"pH":3.27},{"pH":3.3},{"pH":3.22},{"pH":3.15},{"pH":3.16},{"pH":2.98},{"pH":3.05},{"pH":3.13},{"pH":3.56},{"pH":3.36},{"pH":3.56},{"pH":3.36},{"pH":3.23},{"pH":3.14},{"pH":3.28},{"pH":3.39},{"pH":3.22},{"pH":3.28},{"pH":3.21},{"pH":3.11},{"pH":3.27},{"pH":3.17},{"pH":3.01},{"pH":3.14},{"pH":3.18},{"pH":3.48},{"pH":3.14},{"pH":3.03},{"pH":3.0},{"pH":3.15},{"pH":3.0},{"pH":3.06},{"pH":3.38},{"pH":3.14},{"pH":3.53}]},"encoding":{"x":{"axis":{"title":"pH"},"field":"value","scale":{"zero":false},"type":"quantitative"},"y":{"field":"density","type":"quantitative"}},"height":300,"mark":{"color":"lightgreen","fillOpacity":1,"orient":"vertical","type":"area"},"title":{"offset":20,"text":"KDE plot of pH feature"},"transform":[{"counts":false,"cumulative":false,"density":"pH","maxsteps":200,"minsteps":25}],"width":350}],"title":{"anchor":"middle","offset":20,"text":"KDE plots of Features"}}
+```
+
+The previous analysis indicates that the alcohol feature has more extreme values than pH. Now, we will create a correlation heatmap to investigate the relationships between the features in the dataset.
+
+```elixir
+correlation = Scholar.Covariance.correlation_matrix(tensor_data, biased: true)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64[12][12]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254489>
+  [
+    [1.0, -0.022697290146647113, 0.2891806976936754, 0.08902070136217163, 0.023085643656347757, -0.049395859081173187, 0.09106975615864087, 0.2653310138391866, -0.42585829099138195, -0.017142985021137338, -0.12088112319453302, -0.11366283071301796],
+    [-0.022697290146647113, 1.0000000000000007, -0.14947181064857518, 0.06428606009099526, 0.07051157147938472, -0.09701193927796008, 0.0892605035517784, 0.02711384546243434, -0.03191536827348892, -0.03572814690581474, 0.06771794277504414, -0.19472296892113428],
+    [0.2891806976936754, -0.14947181064857518, 1.0000000000000009, 0.09421162429049387, 0.11436444838681839, 0.09407722101469612, 0.12113079766441823, 0.14950257057002272, -0.16374821140062368, 0.06233094028523288, -0.07572873005717942, -0.009209090883975417],
+    [0.08902070136217163, 0.06428606009099526, 0.09421162429049387, 1.0000000000000002, 0.0886845359412256, 0.299098353693518, 0.40143931115992487, 0.8389664549045833, -0.19413345399025597, -0.026664365853858334, -0.45063122203172884, -0.09757682889469321],
+    [0.023085643656347757, 0.07051157147938472, ...],
+    ...
+  ]
+>
+```
+
+```elixir
+{corr_size, _} = Nx.shape(correlation)
+correlation_list = Nx.to_flat_list(correlation)
+column_names = DF.names(df_data)
+
+corr_to_plot =
+  DF.new(
+    x: List.flatten(List.duplicate(column_names, corr_size)),
+    y: List.flatten(for name <- column_names, do: List.duplicate(name, corr_size)),
+    corr_val: Enum.map(correlation_list, fn x -> Float.round(x, 2) end)
+  )
+
+Tucan.heatmap(corr_to_plot, "x", "y", "corr_val", annotate: true, text_color: [{nil, 0, "white"}])
+|> Tucan.Scale.set_color_scheme(:inferno)
+|> Tucan.Axes.set_title(:color, "Correlation")
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Correlation Matrix for California Housing", offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","__tucan__":{"multilayer":true},"data":{"values":[{"corr_val":1.0,"x":"fixed acidity","y":"fixed acidity"},{"corr_val":-0.02,"x":"volatile acidity","y":"fixed acidity"},{"corr_val":0.29,"x":"citric acid","y":"fixed acidity"},{"corr_val":0.09,"x":"residual sugar","y":"fixed acidity"},{"corr_val":0.02,"x":"chlorides","y":"fixed acidity"},{"corr_val":-0.05,"x":"free sulfur dioxide","y":"fixed acidity"},{"corr_val":0.09,"x":"total sulfur dioxide","y":"fixed acidity"},{"corr_val":0.27,"x":"density","y":"fixed acidity"},{"corr_val":-0.43,"x":"pH","y":"fixed acidity"},{"corr_val":-0.02,"x":"sulphates","y":"fixed acidity"},{"corr_val":-0.12,"x":"alcohol","y":"fixed acidity"},{"corr_val":-0.11,"x":"quality","y":"fixed acidity"},{"corr_val":-0.02,"x":"fixed acidity","y":"volatile acidity"},{"corr_val":1.0,"x":"volatile acidity","y":"volatile acidity"},{"corr_val":-0.15,"x":"citric acid","y":"volatile acidity"},{"corr_val":0.06,"x":"residual sugar","y":"volatile acidity"},{"corr_val":0.07,"x":"chlorides","y":"volatile acidity"},{"corr_val":-0.1,"x":"free sulfur dioxide","y":"volatile acidity"},{"corr_val":0.09,"x":"total sulfur dioxide","y":"volatile acidity"},{"corr_val":0.03,"x":"density","y":"volatile acidity"},{"corr_val":-0.03,"x":"pH","y":"volatile acidity"},{"corr_val":-0.04,"x":"sulphates","y":"volatile acidity"},{"corr_val":0.07,"x":"alcohol","y":"volatile acidity"},{"corr_val":-0.19,"x":"quality","y":"volatile acidity"},{"corr_val":0.29,"x":"fixed acidity","y":"citric acid"},{"corr_val":-0.15,"x":"volatile acidity","y":"citric acid"},{"corr_val":1.0,"x":"citric acid","y":"citric acid"},{"corr_val":0.09,"x":"residual sugar","y":"citric acid"},{"corr_val":0.11,"x":"chlorides","y":"citric acid"},{"corr_val":0.09,"x":"free sulfur dioxide","y":"citric acid"},{"corr_val":0.12,"x":"total sulfur dioxide","y":"citric acid"},{"corr_val":0.15,"x":"density","y":"citric acid"},{"corr_val":-0.16,"x":"pH","y":"citric acid"},{"corr_val":0.06,"x":"sulphates","y":"citric acid"},{"corr_val":-0.08,"x":"alcohol","y":"citric acid"},{"corr_val":-0.01,"x":"quality","y":"citric acid"},{"corr_val":0.09,"x":"fixed acidity","y":"residual sugar"},{"corr_val":0.06,"x":"volatile acidity","y":"residual sugar"},{"corr_val":0.09,"x":"citric acid","y":"residual sugar"},{"corr_val":1.0,"x":"residual sugar","y":"residual sugar"},{"corr_val":0.09,"x":"chlorides","y":"residual sugar"},{"corr_val":0.3,"x":"free sulfur dioxide","y":"residual sugar"},{"corr_val":0.4,"x":"total sulfur dioxide","y":"residual sugar"},{"corr_val":0.84,"x":"density","y":"residual sugar"},{"corr_val":-0.19,"x":"pH","y":"residual sugar"},{"corr_val":-0.03,"x":"sulphates","y":"residual sugar"},{"corr_val":-0.45,"x":"alcohol","y":"residual sugar"},{"corr_val":-0.1,"x":"quality","y":"residual sugar"},{"corr_val":0.02,"x":"fixed acidity","y":"chlorides"},{"corr_val":0.07,"x":"volatile acidity","y":"chlorides"},{"corr_val":0.11,"x":"citric acid","y":"chlorides"},{"corr_val":0.09,"x":"residual sugar","y":"chlorides"},{"corr_val":1.0,"x":"chlorides","y":"chlorides"},{"corr_val":0.1,"x":"free sulfur dioxide","y":"chlorides"},{"corr_val":0.2,"x":"total sulfur dioxide","y":"chlorides"},{"corr_val":0.26,"x":"density","y":"chlorides"},{"corr_val":-0.09,"x":"pH","y":"chlorides"},{"corr_val":0.02,"x":"sulphates","y":"chlorides"},{"corr_val":-0.36,"x":"alcohol","y":"chlorides"},{"corr_val":-0.21,"x":"quality","y":"chlorides"},{"corr_val":-0.05,"x":"fixed acidity","y":"free sulfur dioxide"},{"corr_val":-0.1,"x":"volatile acidity","y":"free sulfur dioxide"},{"corr_val":0.09,"x":"citric acid","y":"free sulfur dioxide"},{"corr_val":0.3,"x":"residual sugar","y":"free sulfur dioxide"},{"corr_val":0.1,"x":"chlorides","y":"free sulfur dioxide"},{"corr_val":1.0,"x":"free sulfur dioxide","y":"free sulfur dioxide"},{"corr_val":0.62,"x":"total sulfur dioxide","y":"free sulfur dioxide"},{"corr_val":0.29,"x":"density","y":"free sulfur dioxide"},{"corr_val":0.0,"x":"pH","y":"free sulfur dioxide"},{"corr_val":0.06,"x":"sulphates","y":"free sulfur dioxide"},{"corr_val":-0.25,"x":"alcohol","y":"free sulfur dioxide"},{"corr_val":0.01,"x":"quality","y":"free sulfur dioxide"},{"corr_val":0.09,"x":"fixed acidity","y":"total sulfur dioxide"},{"corr_val":0.09,"x":"volatile acidity","y":"total sulfur dioxide"},{"corr_val":0.12,"x":"citric acid","y":"total sulfur dioxide"},{"corr_val":0.4,"x":"residual sugar","y":"total sulfur dioxide"},{"corr_val":0.2,"x":"chlorides","y":"total sulfur dioxide"},{"corr_val":0.62,"x":"free sulfur dioxide","y":"total sulfur dioxide"},{"corr_val":1.0,"x":"total sulfur dioxide","y":"total sulfur dioxide"},{"corr_val":0.53,"x":"density","y":"total sulfur dioxide"},{"corr_val":0.0,"x":"pH","y":"total sulfur dioxide"},{"corr_val":0.13,"x":"sulphates","y":"total sulfur dioxide"},{"corr_val":-0.45,"x":"alcohol","y":"total sulfur dioxide"},{"corr_val":-0.17,"x":"quality","y":"total sulfur dioxide"},{"corr_val":0.27,"x":"fixed acidity","y":"density"},{"corr_val":0.03,"x":"volatile acidity","y":"density"},{"corr_val":0.15,"x":"citric acid","y":"density"},{"corr_val":0.84,"x":"residual sugar","y":"density"},{"corr_val":0.26,"x":"chlorides","y":"density"},{"corr_val":0.29,"x":"free sulfur dioxide","y":"density"},{"corr_val":0.53,"x":"total sulfur dioxide","y":"density"},{"corr_val":1.0,"x":"density","y":"density"},{"corr_val":-0.09,"x":"pH","y":"density"},{"corr_val":0.07,"x":"sulphates","y":"density"},{"corr_val":-0.78,"x":"alcohol","y":"density"},{"corr_val":-0.31,"x":"quality","y":"density"},{"corr_val":-0.43,"x":"fixed acidity","y":"pH"},{"corr_val":-0.03,"x":"volatile acidity","y":"pH"},{"corr_val":-0.16,"x":"citric acid","y":"pH"},{"corr_val":-0.19,"x":"residual sugar","y":"pH"},{"corr_val":-0.09,"x":"chlorides","y":"pH"},{"corr_val":0.0,"x":"free sulfur dioxide","y":"pH"},{"corr_val":0.0,"x":"total sulfur dioxide","y":"pH"},{"corr_val":-0.09,"x":"density","y":"pH"},{"corr_val":1.0,"x":"pH","y":"pH"},{"corr_val":0.16,"x":"sulphates","y":"pH"},{"corr_val":0.12,"x":"alcohol","y":"pH"},{"corr_val":0.1,"x":"quality","y":"pH"},{"corr_val":-0.02,"x":"fixed acidity","y":"sulphates"},{"corr_val":-0.04,"x":"volatile acidity","y":"sulphates"},{"corr_val":0.06,"x":"citric acid","y":"sulphates"},{"corr_val":-0.03,"x":"residual sugar","y":"sulphates"},{"corr_val":0.02,"x":"chlorides","y":"sulphates"},{"corr_val":0.06,"x":"free sulfur dioxide","y":"sulphates"},{"corr_val":0.13,"x":"total sulfur dioxide","y":"sulphates"},{"corr_val":0.07,"x":"density","y":"sulphates"},{"corr_val":0.16,"x":"pH","y":"sulphates"},{"corr_val":1.0,"x":"sulphates","y":"sulphates"},{"corr_val":-0.02,"x":"alcohol","y":"sulphates"},{"corr_val":0.05,"x":"quality","y":"sulphates"},{"corr_val":-0.12,"x":"fixed acidity","y":"alcohol"},{"corr_val":0.07,"x":"volatile acidity","y":"alcohol"},{"corr_val":-0.08,"x":"citric acid","y":"alcohol"},{"corr_val":-0.45,"x":"residual sugar","y":"alcohol"},{"corr_val":-0.36,"x":"chlorides","y":"alcohol"},{"corr_val":-0.25,"x":"free sulfur dioxide","y":"alcohol"},{"corr_val":-0.45,"x":"total sulfur dioxide","y":"alcohol"},{"corr_val":-0.78,"x":"density","y":"alcohol"},{"corr_val":0.12,"x":"pH","y":"alcohol"},{"corr_val":-0.02,"x":"sulphates","y":"alcohol"},{"corr_val":1.0,"x":"alcohol","y":"alcohol"},{"corr_val":0.44,"x":"quality","y":"alcohol"},{"corr_val":-0.11,"x":"fixed acidity","y":"quality"},{"corr_val":-0.19,"x":"volatile acidity","y":"quality"},{"corr_val":-0.01,"x":"citric acid","y":"quality"},{"corr_val":-0.1,"x":"residual sugar","y":"quality"},{"corr_val":-0.21,"x":"chlorides","y":"quality"},{"corr_val":0.01,"x":"free sulfur dioxide","y":"quality"},{"corr_val":-0.17,"x":"total sulfur dioxide","y":"quality"},{"corr_val":-0.31,"x":"density","y":"quality"},{"corr_val":0.1,"x":"pH","y":"quality"},{"corr_val":0.05,"x":"sulphates","y":"quality"},{"corr_val":0.44,"x":"alcohol","y":"quality"},{"corr_val":1.0,"x":"quality","y":"quality"}]},"height":630,"layer":[{"encoding":{"color":{"aggregate":"mean","axis":{"title":"Correlation"},"field":"corr_val","scale":{"reverse":false,"scheme":"inferno"},"type":"quantitative"},"x":{"field":"x","type":"nominal"},"y":{"field":"y","type":"nominal"}},"mark":{"fillOpacity":1,"type":"rect"}},{"encoding":{"color":{"aggregate":"mean","axis":{"title":"Correlation"},"condition":[{"test":"datum['mean_corr_val'] < 0","value":"white"},{"test":"true","value":"black"}],"field":"corr_val","scale":{"reverse":false,"scheme":"inferno"},"type":"quantitative"},"text":{"aggregate":"mean","field":"corr_val","type":"quantitative"},"x":{"field":"x","type":"nominal"},"y":{"field":"y","type":"nominal"}},"mark":"text"}],"title":{"offset":20,"text":"Correlation Matrix for California Housing"},"width":630}
+```
+
+We can observe from the correlation heatmap that there is no strong correlation between the quality of wine and any single feature. However, we can see that there are two strong correlations: density is proportional to the amount of residual sugar and inversely proportional to the amount of alcohol.
+
+Given that citric acid, free sulfur dioxide, and sulphates are not strongly correlated with the quality of wine or any other features, we can drop them from the dataset to simplify our analysis.
+
+Before dropping the features, it is important to consider their potential impact on the final prediction. Even if they are not strongly correlated with the target variable (quality), they may still provide useful information for the KNN algorithm. It is recommended to experiment with different feature subsets to find the optimal combination for the given task. You can try running the notebook again without dropping these features.
+
+```elixir
+tensor_data =
+  DF.discard(df_data, ["citric acid", "free sulfur dioxide", "sulphates"]) |> Nx.stack(axis: 1)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64[4898][9]
+  EXLA.Backend<host:0, 0.3730900597.862060556.254521>
+  [
+    [7.0, 0.27, 20.7, 0.045, 170.0, 1.001, 3.0, 8.8, 6.0],
+    [6.3, 0.3, 1.6, 0.049, 132.0, 0.994, 3.3, 9.5, 6.0],
+    [8.1, 0.28, 6.9, 0.05, 97.0, 0.9951, 3.26, 10.1, 6.0],
+    [7.2, 0.23, 8.5, 0.058, 186.0, 0.9956, 3.19, 9.9, 6.0],
+    [7.2, 0.23, 8.5, 0.058, 186.0, 0.9956, 3.19, 9.9, 6.0],
+    [8.1, 0.28, 6.9, 0.05, 97.0, ...],
+    ...
+  ]
+>
+```
+
+The next step will be splitting the dataset into features and labels. To make the classification task easier, we will convert the labels into three categories: "poor," "medium," and "excellent". Additionally, we will normalize the features using the standard scaler.
+
+```elixir
+x = tensor_data[[.., 0..-2//1]]
+y = tensor_data[[.., -1]]
+
+# convert quality into labels quality: (0, 4) poor => 0, (5, 6) medium => 1, (7, 10) excelent => 2
+
+poor_and_better_mask = Nx.greater(y, 4)
+medium_and_better_mask = Nx.greater(y, 6)
+
+y = Nx.select(poor_and_better_mask, Nx.select(medium_and_better_mask, 2, 1), 0)
+x = Scholar.Preprocessing.standard_scale(x)
+
+{x, y}
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+{#Nx.Tensor<
+   f64[4898][8]
+   EXLA.Backend<host:0, 0.3730900597.862060556.254557>
+   [
+     [-0.29385297541380284, -0.4368649169854585, -0.0027291121847267076, -0.44164614831586296, 3.1698834995014824, -0.4213312276408997, -0.37885264350988346, -0.2556031247705665],
+     [-0.30872791733061694, -0.43622741947473787, -0.40860252734351166, -0.4415611486477669, 2.3623866525887167, -0.4214799770600679, -0.3724776684026774, -0.24072818285375244],
+     [-0.27047806668738067, -0.43665241781521824, -0.29597796711620483, -0.4415398987307429, 1.6186395567480112, -0.42145660215134145, -0.37332766508363824, -0.22797823263934036],
+     [-0.2896029920089988, -0.4377149136664193, -0.2619780998777726, -0.44136989939455074, 3.509882171885805, -0.42144597719282945, -0.3748151592753196, -0.23222821604414437],
+     [-0.2896029920089988, -0.4377149136664193, -0.2619780998777726, -0.44136989939455074, 3.509882171885805, -0.42144597719282945, -0.3748151592753196, -0.23222821604414437],
+     [-0.27047806668738067, -0.43665241781521824, -0.29597796711620483, -0.4415398987307429, 1.6186395567480112, -0.42145660215134145, -0.37332766508363824, -0.22797823263934036],
+     [-0.310852909033019, ...],
+     ...
+   ]
+ >,
+ #Nx.Tensor<
+   s64[4898]
+   EXLA.Backend<host:0, 0.3730900597.862060556.254534>
+   [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, ...]
+ >}
+```
+
+After performing EDA on our wine dataset, we can now train our KNN model and make predictions. However, the question arises as to what value of neighbors should we choose for the KNN model. To answer this question, we will use *K-Fold Cross-Validation* (specifically, Nested Cross-Validation). K-Fold is a procedure performed on the training dataset where we split the data into k smaller subsets (folds). For each tested parameter value, we run k separate trainings and testings, where one fold is the validation (test) dataset, and the other k-1 folds are the training dataset. To make this process clear, there is a GIF below that explains it visually.
+
+| ![KFold](https://upload.wikimedia.org/wikipedia/commons/4/4b/KfoldCV.gif)                                                                                    |
+| :----------------------------------------------------------------------------------------------------------------------------------------------------------: |
+| Figure 3: Illustration of KFold Cross-Validation when n = 12 observations and k = 3. After data is shuffled, a total of 3 models will be trained and tested. |
+
+```elixir
+defmodule Comb do
+  def combinations([]), do: [[]]
+
+  def combinations([{name, values} | opts]) do
+    for subcombination <- combinations(opts), value <- values do
+      [{name, value} | subcombination]
+    end
+  end
+end
+
+Comb.combinations(task: [:classification], num_classes: [3], num_neighbors: Enum.to_list(1..30))
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+[
+  [task: :classification, num_classes: 3, num_neighbors: 1],
+  [task: :classification, num_classes: 3, num_neighbors: 2],
+  [task: :classification, num_classes: 3, num_neighbors: 3],
+  [task: :classification, num_classes: 3, num_neighbors: 4],
+  [task: :classification, num_classes: 3, num_neighbors: 5],
+  [task: :classification, num_classes: 3, num_neighbors: 6],
+  [task: :classification, num_classes: 3, num_neighbors: 7],
+  [task: :classification, num_classes: 3, num_neighbors: 8],
+  [task: :classification, num_classes: 3, num_neighbors: 9],
+  [task: :classification, num_classes: 3, num_neighbors: 10],
+  [task: :classification, num_classes: 3, num_neighbors: 11],
+  [task: :classification, num_classes: 3, num_neighbors: 12],
+  [task: :classification, num_classes: 3, num_neighbors: 13],
+  [task: :classification, num_classes: 3, num_neighbors: 14],
+  [task: :classification, num_classes: 3, num_neighbors: 15],
+  [task: :classification, num_classes: 3, num_neighbors: 16],
+  [task: :classification, num_classes: 3, num_neighbors: 17],
+  [task: :classification, num_classes: 3, num_neighbors: 18],
+  [task: :classification, num_classes: 3, num_neighbors: 19],
+  [task: :classification, num_classes: 3, num_neighbors: 20],
+  [task: :classification, num_classes: 3, num_neighbors: 21],
+  [task: :classification, num_classes: 3, num_neighbors: 22],
+  [task: :classification, num_classes: 3, num_neighbors: 23],
+  [task: :classification, num_classes: 3, num_neighbors: 24],
+  [task: :classification, num_classes: 3, num_neighbors: 25],
+  [task: :classification, num_classes: 3, num_neighbors: 26],
+  [task: :classification, num_classes: 3, num_neighbors: 27],
+  [task: :classification, num_classes: 3, num_neighbors: 28],
+  [task: :classification, num_classes: 3, num_neighbors: 29],
+  [task: :classification, num_classes: 3, num_neighbors: 30]
+]
+```
+
+The code implementing KFold cross-validation is located at the beginning of the notebook.
+
+```elixir
+min_num_neighbors = 1
+param_space_size = 30
+
+# K in KFold
+k = 10
+train_size = 4000
+
+{indices, _new_key} = Nx.Random.shuffle(key, Nx.iota(Nx.shape(y)))
+x = Nx.take(x, indices)
+y = Nx.take(y, indices)
+{train_data, test_data} = Nx.split(x, train_size)
+{train_labels, test_labels} = Nx.split(y, train_size)
+
+folding_fun = fn x -> Scholar.ModelSelection.k_fold_split(x, k) end
+
+scoring_fun = fn x, y, opts ->
+  {x_train, x_test} = x
+  {y_train, y_test} = y
+
+  model =
+    KNN.fit(x_train, y_train,
+      num_classes: opts[:num_classes],
+      num_neighbors: opts[:num_neighbors],
+      task: opts[:task]
+    )
+
+  prediction = KNN.predict(model, x_test)
+
+  accuracy = Classification.accuracy(y_test, prediction)
+  [accuracy]
+end
+
+res =
+  Scholar.ModelSelection.grid_search(train_data, train_labels, folding_fun, scoring_fun,
+    task: [:classification],
+    num_classes: [3],
+    num_neighbors: Enum.to_list(min_num_neighbors..param_space_size)
+  )
+
+res = for(sub_res <- res, do: sub_res[:score]) |> Nx.concatenate() |> Nx.as_type(:f64)
+
+results =
+  DF.new(accuracy: res, num_neighbors: Nx.add(Nx.iota({param_space_size}), min_num_neighbors))
+```
+
+To potentially improve our KNN model's performance, we can try setting the weights parameter to `:distance` and use weighted version of grid search. Next, we can visualize the results of KFold using a plot.
+
+```elixir
+Tucan.lineplot(results, "num_neighbors", "accuracy",
+  line_color: "gray",
+  points: true,
+  stroke_dash: [5, 5]
+)
+|> Tucan.Scale.set_x_domain(1, 31)
+|> Tucan.Scale.set_y_domain(0.7, 0.85)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Accuracy vs Number of Neighbors", offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"accuracy":0.7682499885559082,"num_neighbors":1},{"accuracy":0.7342499494552612,"num_neighbors":2},{"accuracy":0.7425000071525574,"num_neighbors":3},{"accuracy":0.7512500286102295,"num_neighbors":4},{"accuracy":0.7512499690055847,"num_neighbors":5},{"accuracy":0.7497500777244568,"num_neighbors":6},{"accuracy":0.7477500438690186,"num_neighbors":7},{"accuracy":0.7487500309944153,"num_neighbors":8},{"accuracy":0.7487499713897705,"num_neighbors":9},{"accuracy":0.749250054359436,"num_neighbors":10},{"accuracy":0.749000072479248,"num_neighbors":11},{"accuracy":0.7477499842643738,"num_neighbors":12},{"accuracy":0.7475000023841858,"num_neighbors":13},{"accuracy":0.7419999837875366,"num_neighbors":14},{"accuracy":0.7487500309944153,"num_neighbors":15},{"accuracy":0.747249960899353,"num_neighbors":16},{"accuracy":0.7505000233650208,"num_neighbors":17},{"accuracy":0.747499942779541,"num_neighbors":18},{"accuracy":0.7475000023841858,"num_neighbors":19},{"accuracy":0.7477500438690186,"num_neighbors":20},{"accuracy":0.747999906539917,"num_neighbors":21},{"accuracy":0.7477499842643738,"num_neighbors":22},{"accuracy":0.7459999918937683,"num_neighbors":23},{"accuracy":0.7442499399185181,"num_neighbors":24},{"accuracy":0.7442500591278076,"num_neighbors":25},{"accuracy":0.7437500357627869,"num_neighbors":26},{"accuracy":0.7434999942779541,"num_neighbors":27},{"accuracy":0.7465000152587891,"num_neighbors":28},{"accuracy":0.7430000305175781,"num_neighbors":29},{"accuracy":0.7472500205039978,"num_neighbors":30}]},"encoding":{"x":{"field":"num_neighbors","scale":{"domain":[1,31]},"type":"quantitative"},"y":{"field":"accuracy","scale":{"domain":[0.7,0.85]},"type":"quantitative"}},"height":630,"mark":{"color":"gray","fillOpacity":1,"point":[],"strokeDash":[5,5],"type":"line"},"title":{"offset":20,"text":"Accuracy vs Number of Neighbors"},"width":630}
+```
+
+```elixir
+best_neighbors = Nx.add(Nx.argmax(res), min_num_neighbors) |> Nx.to_number()
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+1
+```
+
+Ok, let's test our best model on test data.
+
+```elixir
+best_model = KNN.fit(train_data, train_labels, num_neighbors: best_neighbors, num_classes: 3)
+
+final_prediction = KNN.predict(best_model, test_data)
+Classification.accuracy(test_labels, final_prediction)
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f32
+  EXLA.Backend<host:0, 0.3730900597.862322700.16513>
+  0.7672605514526367
+>
+```
+
+Pretty well, now let's move on to a regression task using KNN.
+
+<!-- livebook:{"branch_parent_index":1} -->
+
+## Regression
+
+KNNs can also be used in regression tasks. We will explore this on a dataset about Airfoil Self-Noise. Here's a brief description of the dataset:
+
+**Data Set Information**:
+
+The NASA data set comprises different size NACA 0012 airfoils at various wind tunnel speeds and angles of attack. The span of the airfoil and the observer position were the same in all of the experiments.
+
+**Attribute Information**:
+
+This problem has the following inputs:
+
+1. Frequency, in Hertzs.
+2. Angle of attack, in degrees.
+3. Chord length, in meters.
+4. Free-stream velocity, in meters per second.
+5. Suction side displacement thickness, in meters.
+
+The only output is:
+
+1. Scaled sound pressure level, in decibels.
+
+Dua, D. and Graff, C. (2019). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.
+
+```elixir
+dataset =
+  Req.get!(
+    "https://archive.ics.uci.edu/ml/machine-learning-databases/00291/airfoil_self_noise.dat"
+  ).body
+
+column_names = [
+  "frequency",
+  "angle_of_attack",
+  "chord_length",
+  "free_stream_velocity",
+  "suction_side_displacement_thickness",
+  "scaled_sound_pressure_level"
+]
+
+dataset_df = DF.load_csv!(dataset, header: false, delimiter: "\t") |> DF.rename(column_names)
+labels = DF.select(dataset_df, "scaled_sound_pressure_level")
+data = DF.discard(dataset_df, "scaled_sound_pressure_level")
+```
+
+Below are the KDE plots of the dataset's features. We will analyze them in the next step.
+
+```elixir
+Tucan.new(data, columns: 2)
+|> Tucan.concat([
+  Tucan.density(Tucan.new(), "frequency", area_color: "lightblue")
+  |> Tucan.Axes.set_x_title("Frequency (Hz)")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of Frequency feature", offset: 20),
+  Tucan.density(Tucan.new(), "free_stream_velocity", area_color: "purple")
+  |> Tucan.Axes.set_x_title("Angle of attack")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of Angle of Attack feature", offset: 20),
+  Tucan.density(Tucan.new(), "angle_of_attack", area_color: "lightgreen")
+  |> Tucan.Axes.set_x_title("Angle of attack")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of Angle of Attack feature", offset: 20),
+  Tucan.density(Tucan.new(), "suction_side_displacement_thickness", area_color: "red")
+  |> Tucan.Axes.set_x_title("Suction Side Displacement Thickness")
+  |> Tucan.set_size(350, 300)
+  |> Tucan.set_title("KDE plot of Suction Side Displacement\nThickness feature", offset: 20)
+])
+|> Tucan.set_title("KDE plots of Features", anchor: :middle, offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
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plots of Features"}}
+```
+
+The Suction Side Displacement Thickness and Frequency features have asymmetric distributions with many observations having small values. To make these distributions less skewed, we will use the logarithms of these two features.
+
+```elixir
+data =
+  DF.mutate(data,
+    frequency_log: log(frequency),
+    suction_side_displacement_thickness_log: log(suction_side_displacement_thickness)
+  )
+
+data = DF.discard(data, ["frequency", "suction_side_displacement_thickness"])
+```
+
+Scale data and convert them to tensors.
+
+```elixir
+x = Nx.stack(data, axis: 1) |> Scholar.Preprocessing.standard_scale()
+y = Nx.stack(labels, axis: 1) |> Nx.squeeze(axes: [1])
+{x, y}
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+{#Nx.Tensor<
+   f64[1503][5]
+   EXLA.Backend<host:0, 0.3730900597.862322700.16607>
+   [
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.24959453243691035, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.2391306895323175, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.22866684662772468, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.21709086757891163, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.2066270246743188, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.19616318176972597, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.18532568847301975, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.17412335981632007, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.1636595169117272, -0.8410438169469526],
+     [-0.5630552019680845, -0.5487622533323925, 2.780406864058286, -0.15282202361502104, ...],
+     ...
+   ]
+ >,
+ #Nx.Tensor<
+   f64[1503]
+   EXLA.Backend<host:0, 0.3730900597.862322700.16611>
+   [126.201, 125.201, 125.951, 127.591, 127.461, 125.571, 125.201, 123.061, 121.301, 119.541, 117.151, 115.391, 112.241, 108.721, 126.416, 127.696, 128.086, 126.966, 126.086, 126.986, 126.616, 124.106, 123.236, 121.106, 119.606, 117.976, 116.476, 113.076, 111.076, 118.129, 119.319, 122.779, 124.809, 126.959, 128.629, 129.099, 127.899, 125.499, 124.049, 123.689, 121.399, 120.319, 119.229, 117.789, 116.229, 114.779, 112.139, 109.619, ...]
+ >}
+```
+
+In this section, we will apply a similar KFold procedure as in the classification section to find the best value for the `:num_neighbors` parameter in the KNN regression model.
+
+```elixir
+min_num_neighbors = 1
+param_space_size = 30
+
+# K in KFold
+k = 10
+train_size = 1100
+
+{indices, _new_key} = Nx.Random.shuffle(key, Nx.iota(Nx.shape(y)))
+x_shuffled = Nx.take(x, indices)
+y_shuffled = Nx.take(y, indices)
+{train_data, test_data} = Nx.split(x_shuffled, train_size)
+{train_labels, test_labels} = Nx.split(y_shuffled, train_size)
+
+folding_fun = fn x -> Scholar.ModelSelection.k_fold_split(x, k) end
+
+scoring_fun = fn x, y, opts ->
+  {x_train, x_test} = x
+  {y_train, y_test} = y
+
+  model =
+    KNN.fit(x_train, y_train,
+      num_classes: opts[:num_classes],
+      num_neighbors: opts[:num_neighbors],
+      task: opts[:task]
+    )
+
+  prediction = KNN.predict(model, x_test)
+
+  rmse = Regression.mean_square_error(y_test, prediction) |> Nx.sqrt()
+  [rmse]
+end
+
+res =
+  Scholar.ModelSelection.grid_search(train_data, train_labels, folding_fun, scoring_fun,
+    task: [:regression],
+    # dummy, for regression it doesn't matter
+    num_classes: [3],
+    num_neighbors: Enum.to_list(min_num_neighbors..param_space_size)
+  )
+
+res = for(sub_res <- res, do: sub_res[:score]) |> Nx.concatenate() |> Nx.as_type(:f64)
+
+results = DF.new(RMSE: res, num_neighbors: Nx.add(Nx.iota({param_space_size}), min_num_neighbors))
+```
+
+```elixir
+Tucan.lineplot(results, "num_neighbors", "RMSE",
+  points: true,
+  stroke_dash: [5, 5],
+  line_color: "gray"
+)
+|> Tucan.Scale.set_x_domain(1, 31)
+|> Tucan.Scale.set_y_domain(2.6, 6.0)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("RMSE vs. Number of Neighbors", offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"RMSE":2.954160435119645,"num_neighbors":1},{"RMSE":2.705136057088256,"num_neighbors":2},{"RMSE":2.9964430952256738,"num_neighbors":3},{"RMSE":3.2895292240984704,"num_neighbors":4},{"RMSE":3.4905466912822405,"num_neighbors":5},{"RMSE":3.6884594409820095,"num_neighbors":6},{"RMSE":3.875131011976625,"num_neighbors":7},{"RMSE":4.046962310349941,"num_neighbors":8},{"RMSE":4.189331570582892,"num_neighbors":9},{"RMSE":4.324340953175694,"num_neighbors":10},{"RMSE":4.439134168936841,"num_neighbors":11},{"RMSE":4.571325241080605,"num_neighbors":12},{"RMSE":4.672719859268416,"num_neighbors":13},{"RMSE":4.787292392293998,"num_neighbors":14},{"RMSE":4.87906006365976,"num_neighbors":15},{"RMSE":4.978559443345275,"num_neighbors":16},{"RMSE":5.065103101842437,"num_neighbors":17},{"RMSE":5.160223634422015,"num_neighbors":18},{"RMSE":5.23665283726623,"num_neighbors":19},{"RMSE":5.284519365203477,"num_neighbors":20},{"RMSE":5.339524539430938,"num_neighbors":21},{"RMSE":5.39248480824124,"num_neighbors":22},{"RMSE":5.442956739105839,"num_neighbors":23},{"RMSE":5.479308758383082,"num_neighbors":24},{"RMSE":5.523703869999222,"num_neighbors":25},{"RMSE":5.566695428489409,"num_neighbors":26},{"RMSE":5.602044586338607,"num_neighbors":27},{"RMSE":5.6421550268197365,"num_neighbors":28},{"RMSE":5.675274254551783,"num_neighbors":29},{"RMSE":5.707381896414202,"num_neighbors":30}]},"encoding":{"x":{"field":"num_neighbors","scale":{"domain":[1,31]},"type":"quantitative"},"y":{"field":"RMSE","scale":{"domain":[2.6,6.0]},"type":"quantitative"}},"height":630,"mark":{"color":"gray","fillOpacity":1,"point":[],"strokeDash":[5,5],"type":"line"},"title":{"offset":20,"text":"RMSE vs. Number of Neighbors"},"width":630}
+```
+
+```elixir
+best_neighbors = Nx.add(Nx.argmin(res), min_num_neighbors) |> Nx.to_number()
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+2
+```
+
+The best value is 2. Now try this value to a final prediction.
+
+```elixir
+best_model =
+  KNN.fit(train_data, train_labels,
+    num_neighbors: best_neighbors,
+    num_classes: 3,
+    task: :regression
+  )
+
+final_prediction = KNN.predict(best_model, test_data)
+Regression.mean_square_error(test_labels, final_prediction) |> Nx.sqrt()
+```
+
+<!-- livebook:{"output":true} -->
+
+```
+#Nx.Tensor<
+  f64
+  EXLA.Backend<host:0, 0.3730900597.862322700.26551>
+  2.2414312639566227
+>
+```
+
+### Outliers prediction
+
+<!-- livebook:{"break_markdown":true} -->
+
+KNNs can be used for outlier detection. In this task, we will also use the Airfoil Self-Noise dataset. We will calculate for each sample a mean value of distances to the three closest points from dataset.
+
+```elixir
+model = KNN.fit(x, y, num_neighbors: 3, task: :regression)
+{num_samples, _} = Nx.shape(x)
+{distances, indices} = KNN.k_neighbors(model, x)
+
+mean_distances = Nx.mean(distances, axes: [1], keep_axes: true)
+
+samples_mean_distances =
+  Nx.concatenate([mean_distances, Nx.iota({num_samples, 1})], axis: 1)
+  |> DF.new()
+  |> DF.rename(["mean_distances", "index"])
+```
+
+Now, plot the mean values of distances.
+
+```elixir
+Tucan.lineplot(samples_mean_distances, "index", "mean_distances", line_color: "jet")
+|> Tucan.hruler(0.009, line_color: "red", stroke_dash: [5, 5])
+|> Tucan.Scale.set_x_domain(0, 1510)
+|> Tucan.Scale.set_y_domain(0.0065, 0.012)
+|> Tucan.set_size(800, 630)
+|> Tucan.set_title("Plot to check anomalies", offset: 20)
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
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to check anomalies"},"width":800}
+```
+
+We can assume, that samples with average distance bigger than 0.0105 can be treated as outliers.
+
+```elixir
+data = DF.put(data, :is_outlier, Nx.greater(mean_distances, 0.0105))
+```
+
+```elixir
+alias VegaLite, as: Vl
+
+Vl.new(
+  title: [
+    text: "Logarithm of Frequency vs Logarithm of Suction Side Displacement Thickness",
+    offset: 20
+  ],
+  width: 630,
+  height: 630
+)
+|> Vl.data_from_values(data)
+|> Vl.layers([
+  Vl.new()
+  |> Vl.param("brush", select: :interval)
+  |> Vl.mark(:circle)
+  |> Vl.encode_field(:x, "frequency_log", type: :quantitative, scale: [domain: [4.5, 10.5]])
+  |> Vl.encode_field(:y, "suction_side_displacement_thickness_log",
+    type: :quantitative,
+    scale: [domain: [-8.0, -2.5]]
+  )
+  |> Vl.encode(:color,
+    condition: [param: "brush", field: "is_outlier", type: :nominal],
+    value: :gray
+  ),
+  Vl.new()
+  |> Vl.transform(filter: [param: "brush", field: "is_outlier", equal: true])
+  |> Vl.mark(:text)
+  |> Vl.encode(:x, value: 11)
+  |> Vl.encode(:y, value: -3.5)
+  |> Vl.encode_field(:text, "filter",
+    type: :quantitative,
+    aggregate: :count
+  )
+])
+```
+
+<!-- livebook:{"output":true} -->
+
+```vega-lite
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of Frequency vs Logarithm of Suction Side Displacement Thickness"},"width":630}
+```
diff --git a/notebooks/linear_regression.livemd b/notebooks/linear_regression.livemd
index 20320ea0..dbfe1083 100644
--- a/notebooks/linear_regression.livemd
+++ b/notebooks/linear_regression.livemd
@@ -11,22 +11,16 @@ Mix.install([
   {:req, "~> 0.3.9"},
   {:kino_vega_lite, "~> 0.1.9"},
   {:kino, "~> 0.10.0"},
-  {:kino_explorer, "~> 0.1.7"}
+  {:kino_explorer, "~> 0.1.7"},
+  {:tucan, "~> 0.2.1"}
 ])
 ```
 
-<!-- livebook:{"output":true} -->
-
-```
-:ok
-```
-
 ## Introduction
 
 In the livebook, we will cover the typical use cases of linear regression on practical examples.
 
 ```elixir
-alias VegaLite, as: Vl
 require Explorer.DataFrame, as: DF
 require Explorer.Series, as: S
 alias Scholar.Linear.LinearRegression, as: LR
@@ -93,32 +87,17 @@ size = 100
 
 df = DF.new(x: x, y: y)
 
-Vl.new(
-  title: [
-    text: "Scatterplot of Generated Data",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(df)
-|> Vl.mark(:circle)
-|> Vl.encode_field(:x, "x",
-  type: :quantitative,
-  scale: [domain: [-0.05, 2.05]],
-  axis: [grid: false]
-)
-|> Vl.encode_field(:y, "y",
-  type: :quantitative,
-  scale: [domain: [2.5, 12]],
-  axis: [grid: false]
-)
+Tucan.scatter(df, "x", "y", width: 630, height: 630, filled: true)
+|> Tucan.Scale.set_x_domain(-0.05, 2.05)
+|> Tucan.Scale.set_y_domain(2.5, 12)
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12]},"type":"quantitative"}},"height":630,"mark":"circle","title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12],"zero":false},"type":"quantitative"}},"height":630,"mark":{"fillOpacity":1,"filled":true,"type":"point"},"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
 ```
 
 For a regression task, we will use the `Scholar.Linear.LinearRegression` module.
@@ -161,44 +140,21 @@ line = %{
   y: [x_1 * coefficients + intercept, x_2 * coefficients + intercept]
 }
 
-# Graph scales
-x_scale = [domain: [-0.05, 2.05]]
-y_scale = [domain: [2.5, 12]]
-
-Vl.new(
-  title: [
-    text: "Scatterplot of Generated Data",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(df)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: x_scale,
-    axis: [grid: false]
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: y_scale,
-    axis: [grid: false]
-  ),
-  Vl.new()
-  |> Vl.data_from_values(line)
-  |> Vl.mark(:line, color: :green)
-  |> Vl.encode_field(:x, "x", type: :quantitative, scale: x_scale)
-  |> Vl.encode_field(:y, "y", type: :quantitative, scale: y_scale)
+Tucan.layers([
+  Tucan.scatter(df, "x", "y", filled: true),
+  Tucan.lineplot(line, "x", "y", line_color: "green")
 ])
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.Scale.set_x_domain(-0.05, 2.05)
+|> Tucan.Scale.set_y_domain(2.5, 12)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12]},"type":"quantitative"}},"mark":"circle"},{"data":{"values":[{"x":0,"y":4.023067929858136},{"x":2,"y":9.938704547661537}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"green","type":"line"}}],"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12],"zero":false},"type":"quantitative"}},"mark":{"fillOpacity":1,"filled":true,"type":"point"}},{"data":{"values":[{"x":0,"y":4.023067929858136},{"x":2,"y":9.938704547661537}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12]},"type":"quantitative"}},"mark":{"color":"green","fillOpacity":1,"type":"line"}}],"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
 ```
 
 Using `Scholar.Linear.LinearRegression.predict`, we can predict an expected value for a given input. However, we must remember that our prediction will be valid only if we consider linearly dependent data. Fortunately, our data set is perfect for this kind of prediction.
@@ -229,45 +185,22 @@ prediction = %{
   y: [y_prediction]
 }
 
-Vl.new(
-  title: [
-    text: "Scatterplot of Generated Data",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(df)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: x_scale,
-    axis: [grid: false]
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: y_scale,
-    axis: [grid: false]
-  ),
-  Vl.new()
-  |> Vl.data_from_values(line)
-  |> Vl.mark(:line, color: :green)
-  |> Vl.encode_field(:x, "x", type: :quantitative, scale: x_scale)
-  |> Vl.encode_field(:y, "y", type: :quantitative, scale: y_scale),
-  Vl.new()
-  |> Vl.data_from_values(prediction)
-  |> Vl.mark(:circle, color: :red, size: 80)
-  |> Vl.encode_field(:x, "x", type: :quantitative)
-  |> Vl.encode_field(:y, "y", type: :quantitative)
+Tucan.layers([
+  Tucan.scatter(df, "x", "y", filled: true),
+  Tucan.lineplot(line, "x", "y", line_color: "green"),
+  Tucan.scatter(prediction, "x", "y", point_color: "red", point_size: 80, filled: true)
 ])
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.Scale.set_x_domain(-0.05, 2.05)
+|> Tucan.Scale.set_y_domain(2.5, 12)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12]},"type":"quantitative"}},"mark":"circle"},{"data":{"values":[{"x":0,"y":4.023067929858136},{"x":2,"y":9.938704547661537}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"green","type":"line"}},{"data":{"values":[{"x":0.8299999833106995,"y":6.478057076882628}]},"encoding":{"x":{"field":"x","type":"quantitative"},"y":{"field":"y","type":"quantitative"}},"mark":{"color":"red","size":80,"type":"circle"}}],"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","height":630,"layer":[{"data":{"values":[{"x":1.9004864711486005,"y":9.588568089587561},{"x":1.4863498556419192,"y":8.128091393416636},{"x":1.7991174211376775,"y":9.789160149027026},{"x":0.12072062082750934,"y":3.9726630516564603},{"x":1.857364920863604,"y":9.25767072810677},{"x":0.3501109776898361,"y":5.016196041913261},{"x":1.0511571984036023,"y":7.0072175252613835},{"x":0.2684341945193349,"y":4.529725798132315},{"x":1.2610012264029522,"y":7.981418930695978},{"x":0.4076748594070785,"y":4.789392547766224},{"x":0.6277976898420019,"y":5.473504548640071},{"x":1.1925149126570633,"y":7.979905959554976},{"x":1.9099838593057608,"y":9.933633616185963},{"x":1.11272036330339,"y":7.576762743580341},{"x":1.802092739386969,"y":9.325967122317106},{"x":1.196864286097009,"y":7.638266926193305},{"x":0.03815120245380177,"y":4.518300718070865},{"x":0.6918418995897215,"y":5.594422797388837},{"x":0.04790910633931178,"y":4.622640731795469},{"x":1.0082350389606831,"y":6.573314789785342},{"x":1.3268160391024382,"y":8.167074289870962},{"x":1.116235950693984,"y":7.205542036877259},{"x":1.5635870611482732,"y":9.11314041027242},{"x":1.5325239230646464,"y":8.46042736714775},{"x":0.22518938365611207,"y":4.359911858835845},{"x":1.8818046241717257,"y":9.422655165383151},{"x":0.866399894741126,"y":6.273503204133702},{"x":1.7074705527133416,"y":9.1952114549056},{"x":0.7228909843461526,"y":6.399740242846538},{"x":0.8645396760222455,"y":6.921156361139643},{"x":1.8376110894013347,"y":9.599848131970901},{"x":1.442060988129032,"y":8.259326839274358},{"x":1.1443219627898706,"y":7.398380325540283},{"x":1.9442669979686977,"y":9.916636301589834},{"x":1.7051984640589528,"y":8.810676014365272},{"x":0.9316907243298531,"y":6.706793253908984},{"x":0.32105137135146666,"y":5.33310397346077},{"x":1.4251172135313435,"y":8.204359875917337},{"x":0.21636814613954103,"y":5.060604277707321},{"x":0.8400572418693812,"y":6.803452904281498},{"x":0.9280411984247863,"y":6.879738120117415},{"x":0.6748888124318428,"y":5.668202282091746},{"x":0.9269337184466582,"y":6.309717290697355},{"x":1.614491258449418,"y":8.584383516652984},{"x":1.7556955423296916,"y":8.88204901427903},{"x":0.742569049365005,"y":6.3831292487291265},{"x":0.04689839244109928,"y":4.047375477112247},{"x":1.3063798501777497,"y":7.7838559727772125},{"x":0.7399148832784985,"y":5.7390385507242065},{"x":0.609370240470565,"y":5.496753043300161},{"x":0.5288005556403474,"y":5.710591843063962},{"x":1.8613281986490335,"y":9.617393755825786},{"x":1.4934621266846162,"y":8.775190727806926},{"x":1.3841503724034614,"y":8.097058620455151},{"x":1.4411812067428929,"y":8.714222294939118},{"x":0.07275682745349732,"y":3.8582708188217256},{"x":1.6964330896073725,"y":9.558937877400908},{"x":0.9736420283819163,"y":6.666882792923979},{"x":1.5039805870455312,"y":8.704474518801195},{"x":0.2945974391450479,"y":4.7723887278383},{"x":0.1868592779917515,"y":4.731889701559963},{"x":1.335963209381183,"y":8.49731857456425},{"x":1.12438463727741,"y":7.846542179584407},{"x":0.9611253246535423,"y":7.302305818866566},{"x":0.944121396326294,"y":6.59392561989239},{"x":0.9160306018359226,"y":6.537631541250617},{"x":1.8140749900473794,"y":8.956656518284662},{"x":1.2494284448899267,"y":7.462139448629185},{"x":1.5981009200282497,"y":8.488717108113233},{"x":1.5216871497808855,"y":8.239844283942187},{"x":1.0141522485693928,"y":7.119631726438168},{"x":0.24505073662469545,"y":4.76994960528683},{"x":0.23453054126675754,"y":4.740933976429053},{"x":0.8375073700191651,"y":6.203902724203168},{"x":0.9555904929091139,"y":6.539672305648001},{"x":1.5116208882261697,"y":8.251922682601373},{"x":0.5430644133381208,"y":5.94392000741476},{"x":1.5396799405255837,"y":8.562605860505936},{"x":1.3288332597446675,"y":8.394908971950938},{"x":0.8098737558236753,"y":6.119922380724123},{"x":0.7300870101089743,"y":5.820357872554606},{"x":0.6003486177307833,"y":6.046316972091446},{"x":1.6984776836543856,"y":8.777896137233139},{"x":0.7881943630297616,"y":6.2074823217226704},{"x":0.8022304689606252,"y":6.421563438226328},{"x":0.9461487553849501,"y":7.224992163390045},{"x":1.1062159638629834,"y":7.778505164261029},{"x":0.5336394605277772,"y":5.208679631530884},{"x":0.4584282301025495,"y":5.523717683548369},{"x":0.274737610635972,"y":5.32305240175822},{"x":1.2533091829664782,"y":7.266026618765184},{"x":0.10113017428721793,"y":4.752841138832883},{"x":0.14571861443282952,"y":4.726179278830611},{"x":1.15906054645597,"y":7.915833252969062},{"x":0.27790158114728714,"y":5.013847161673044},{"x":1.239949192481978,"y":7.517406034765404},{"x":0.6661499949625322,"y":5.568160896538142},{"x":1.2693312956846792,"y":7.889092741514168},{"x":1.2086907347723854,"y":7.6883993210876},{"x":1.7333203144056522,"y":8.889281033197426}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12],"zero":false},"type":"quantitative"}},"mark":{"fillOpacity":1,"filled":true,"type":"point"}},{"data":{"values":[{"x":0,"y":4.023067929858136},{"x":2,"y":9.938704547661537}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12]},"type":"quantitative"}},"mark":{"color":"green","fillOpacity":1,"type":"line"}},{"data":{"values":[{"x":0.8299999833106995,"y":6.478057076882628}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-0.05,2.05],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,12],"zero":false},"type":"quantitative"}},"mark":{"color":"red","fillOpacity":1,"filled":true,"size":80,"type":"point"}}],"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
 ```
 
 As we expected, the red dot lies on the regression line.
@@ -332,36 +265,18 @@ Now let's plot the generated data:
 {x, y} = PolynomialData.data()
 df = DF.new(x: Nx.to_flat_list(x), y: Nx.to_flat_list(y))
 
-# Graph scales
-x_scale = [domain: [-2.05, 2.05]]
-y_scale = [domain: [2.5, 20]]
-
-Vl.new(
-  title: [
-    text: "Scatterplot of Generated Data",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.data_from_values(df)
-|> Vl.mark(:circle)
-|> Vl.encode_field(:x, "x",
-  type: :quantitative,
-  scale: x_scale,
-  axis: [grid: false]
-)
-|> Vl.encode_field(:y, "y",
-  type: :quantitative,
-  scale: y_scale,
-  axis: [grid: false]
-)
+Tucan.scatter(df, "x", "y", filled: true)
+|> Tucan.Scale.set_x_domain(-2.05, 2.05)
+|> Tucan.Scale.set_y_domain(2.5, 20)
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
-{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"x":-0.8965015411376953,"y":3.8109235763549805},{"x":0.021173477172851562,"y":5.0468549728393555},{"x":1.0788373947143555,"y":10.559005737304688},{"x":0.34316205978393555,"y":5.828140735626221},{"x":1.5906281471252441,"y":14.507883071899414},{"x":0.13052892684936523,"y":5.494438171386719},{"x":-0.017606735229492188,"y":5.139791965484619},{"x":-1.7063984870910645,"y":6.048481464385986},{"x":-0.8232769966125488,"y":4.1755475997924805},{"x":1.239438533782959,"y":11.804141998291016},{"x":-0.7493696212768555,"y":3.7624857425689697},{"x":1.5685210227966309,"y":15.080747604370117},{"x":1.2736377716064453,"y":11.830965042114258},{"x":0.28627920150756836,"y":6.291994571685791},{"x":-0.8452377319335938,"y":4.183845043182373},{"x":1.0702204704284668,"y":10.536632537841797},{"x":0.5425329208374023,"y":6.9816107749938965},{"x":0.8072428703308105,"y":8.398423194885254},{"x":0.06005859375,"y":5.642594337463379},{"x":-1.6828784942626953,"y":5.228835582733154},{"x":-1.6979928016662598,"y":5.282017707824707},{"x":-1.339439868927002,"y":4.808953762054443},{"x":-1.6378440856933594,"y":5.889084815979004},{"x":-0.9949426651000977,"y":4.288919448852539},{"x":-0.1635441780090332,"y":4.933962345123291},{"x":0.5056014060974121,"y":7.2391276359558105},{"x":-0.6962909698486328,"y":4.337333679199219},{"x":-0.011175155639648438,"y":5.329751968383789},{"x":1.9765315055847168,"y":18.869409561157227},{"x":-0.7610149383544922,"y":3.423267126083374},{"x":-1.946864128112793,"y":6.530677795410156},{"x":-0.021459579467773438,"y":5.185998916625977},{"x":0.5230484008789062,"y":7.557127475738525},{"x":1.1505427360534668,"y":11.130593299865723},{"x":0.33158349990844727,"y":6.636468887329102},{"x":1.9051923751831055,"y":18.391712188720703},{"x":0.7064709663391113,"y":8.222036361694336},{"x":0.832550048828125,"y":8.481558799743652},{"x":-1.5429472923278809,"y":4.780819892883301},{"x":1.910013198852539,"y":18.196731567382812},{"x":0.2634763717651367,"y":6.009212970733643},{"x":1.823348045349121,"y":17.614534378051758},{"x":-0.2560157775878906,"y":4.535557270050049},{"x":1.5738868713378906,"y":14.52468204498291},{"x":0.24407672882080078,"y":5.911610126495361},{"x":1.7351713180541992,"y":16.576759338378906},{"x":0.022307872772216797,"y":5.328531265258789},{"x":1.665010929107666,"y":15.157777786254883},{"x":-0.5437688827514648,"y":3.5709950923919678},{"x":1.312476634979248,"y":11.939286231994629},{"x":-1.4770846366882324,"y":4.936985492706299},{"x":1.6605911254882812,"y":15.417658805847168},{"x":1.7454309463500977,"y":15.889360427856445},{"x":-1.189291000366211,"y":4.214474678039551},{"x":-0.6745319366455078,"y":3.46466064453125},{"x":-1.3367595672607422,"y":4.8975324630737305},{"x":-0.0439295768737793,"y":5.127323627471924},{"x":-0.9130129814147949,"y":3.7275986671447754},{"x":1.0283713340759277,"y":10.355329513549805},{"x":-1.742908000946045,"y":6.096266746520996},{"x":1.6933608055114746,"y":16.230039596557617},{"x":-1.065746784210205,"y":3.970182418823242},{"x":0.9606437683105469,"y":9.539725303649902},{"x":0.04618549346923828,"y":4.721081733703613},{"x":-1.1336445808410645,"y":4.19744873046875},{"x":-1.0706229209899902,"y":3.8512279987335205},{"x":-1.884141445159912,"y":6.373000144958496},{"x":-0.14725208282470703,"y":4.171361923217773},{"x":1.1883292198181152,"y":11.732460021972656},{"x":0.1410541534423828,"y":5.41363525390625},{"x":1.3752241134643555,"y":12.717113494873047},{"x":-1.3611302375793457,"y":4.9649810791015625},{"x":0.08020591735839844,"y":5.477242946624756},{"x":1.7457842826843262,"y":16.750232696533203},{"x":-1.6559224128723145,"y":5.075651168823242},{"x":0.5720343589782715,"y":7.4426116943359375},{"x":-1.715710163116455,"y":6.0133891105651855},{"x":-1.6484870910644531,"y":5.388364791870117},{"x":-1.13641357421875,"y":4.0211639404296875},{"x":-1.8201804161071777,"y":5.7477922439575195},{"x":0.16124916076660156,"y":5.036750793457031},{"x":1.6229968070983887,"y":14.848661422729492},{"x":0.9078593254089355,"y":9.316896438598633},{"x":-1.973616123199463,"y":7.31505823135376},{"x":-1.08573579788208,"y":4.497128963470459},{"x":-1.9856038093566895,"y":7.066302299499512},{"x":1.0161328315734863,"y":9.7346830368042},{"x":1.637150764465332,"y":15.480567932128906},{"x":-0.8749380111694336,"y":3.704550266265869},{"x":0.5326972007751465,"y":7.397686958312988},{"x":-0.8989872932434082,"y":3.6920485496520996},{"x":1.6606526374816895,"y":15.98570442199707},{"x":1.3893942832946777,"y":13.498802185058594},{"x":-1.3748388290405273,"y":4.680605411529541},{"x":-0.22421789169311523,"y":4.457881927490234},{"x":-0.04375505447387695,"y":5.263555526733398},{"x":1.2894659042358398,"y":12.095159530639648},{"x":1.116281509399414,"y":10.542726516723633},{"x":1.725419044494629,"y":16.511856079101562},{"x":-1.203160285949707,"y":3.808946132659912}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.05,2.05]},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,20]},"type":"quantitative"}},"height":630,"mark":"circle","title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
+{"$schema":"https://vega.github.io/schema/vega-lite/v5.json","data":{"values":[{"x":-0.8965015411376953,"y":3.8109235763549805},{"x":0.021173477172851562,"y":5.0468549728393555},{"x":1.0788373947143555,"y":10.559005737304688},{"x":0.34316205978393555,"y":5.828140735626221},{"x":1.5906281471252441,"y":14.507883071899414},{"x":0.13052892684936523,"y":5.494438171386719},{"x":-0.017606735229492188,"y":5.139791965484619},{"x":-1.7063984870910645,"y":6.048481464385986},{"x":-0.8232769966125488,"y":4.1755475997924805},{"x":1.239438533782959,"y":11.804141998291016},{"x":-0.7493696212768555,"y":3.7624857425689697},{"x":1.5685210227966309,"y":15.080747604370117},{"x":1.2736377716064453,"y":11.830965042114258},{"x":0.28627920150756836,"y":6.291994571685791},{"x":-0.8452377319335938,"y":4.183845043182373},{"x":1.0702204704284668,"y":10.536632537841797},{"x":0.5425329208374023,"y":6.9816107749938965},{"x":0.8072428703308105,"y":8.398423194885254},{"x":0.06005859375,"y":5.642594337463379},{"x":-1.6828784942626953,"y":5.228835582733154},{"x":-1.6979928016662598,"y":5.282017707824707},{"x":-1.339439868927002,"y":4.808953762054443},{"x":-1.6378440856933594,"y":5.889084815979004},{"x":-0.9949426651000977,"y":4.288919448852539},{"x":-0.1635441780090332,"y":4.933962345123291},{"x":0.5056014060974121,"y":7.2391276359558105},{"x":-0.6962909698486328,"y":4.337333679199219},{"x":-0.011175155639648438,"y":5.329751968383789},{"x":1.9765315055847168,"y":18.869409561157227},{"x":-0.7610149383544922,"y":3.423267126083374},{"x":-1.946864128112793,"y":6.530677795410156},{"x":-0.021459579467773438,"y":5.185998916625977},{"x":0.5230484008789062,"y":7.557127475738525},{"x":1.1505427360534668,"y":11.130593299865723},{"x":0.33158349990844727,"y":6.636468887329102},{"x":1.9051923751831055,"y":18.391712188720703},{"x":0.7064709663391113,"y":8.222036361694336},{"x":0.832550048828125,"y":8.481558799743652},{"x":-1.5429472923278809,"y":4.780819892883301},{"x":1.910013198852539,"y":18.196731567382812},{"x":0.2634763717651367,"y":6.009212970733643},{"x":1.823348045349121,"y":17.614534378051758},{"x":-0.2560157775878906,"y":4.535557270050049},{"x":1.5738868713378906,"y":14.52468204498291},{"x":0.24407672882080078,"y":5.911610126495361},{"x":1.7351713180541992,"y":16.576759338378906},{"x":0.022307872772216797,"y":5.328531265258789},{"x":1.665010929107666,"y":15.157777786254883},{"x":-0.5437688827514648,"y":3.5709950923919678},{"x":1.312476634979248,"y":11.939286231994629},{"x":-1.4770846366882324,"y":4.936985492706299},{"x":1.6605911254882812,"y":15.417658805847168},{"x":1.7454309463500977,"y":15.889360427856445},{"x":-1.189291000366211,"y":4.214474678039551},{"x":-0.6745319366455078,"y":3.46466064453125},{"x":-1.3367595672607422,"y":4.8975324630737305},{"x":-0.0439295768737793,"y":5.127323627471924},{"x":-0.9130129814147949,"y":3.7275986671447754},{"x":1.0283713340759277,"y":10.355329513549805},{"x":-1.742908000946045,"y":6.096266746520996},{"x":1.6933608055114746,"y":16.230039596557617},{"x":-1.065746784210205,"y":3.970182418823242},{"x":0.9606437683105469,"y":9.539725303649902},{"x":0.04618549346923828,"y":4.721081733703613},{"x":-1.1336445808410645,"y":4.19744873046875},{"x":-1.0706229209899902,"y":3.8512279987335205},{"x":-1.884141445159912,"y":6.373000144958496},{"x":-0.14725208282470703,"y":4.171361923217773},{"x":1.1883292198181152,"y":11.732460021972656},{"x":0.1410541534423828,"y":5.41363525390625},{"x":1.3752241134643555,"y":12.717113494873047},{"x":-1.3611302375793457,"y":4.9649810791015625},{"x":0.08020591735839844,"y":5.477242946624756},{"x":1.7457842826843262,"y":16.750232696533203},{"x":-1.6559224128723145,"y":5.075651168823242},{"x":0.5720343589782715,"y":7.4426116943359375},{"x":-1.715710163116455,"y":6.0133891105651855},{"x":-1.6484870910644531,"y":5.388364791870117},{"x":-1.13641357421875,"y":4.0211639404296875},{"x":-1.8201804161071777,"y":5.7477922439575195},{"x":0.16124916076660156,"y":5.036750793457031},{"x":1.6229968070983887,"y":14.848661422729492},{"x":0.9078593254089355,"y":9.316896438598633},{"x":-1.973616123199463,"y":7.31505823135376},{"x":-1.08573579788208,"y":4.497128963470459},{"x":-1.9856038093566895,"y":7.066302299499512},{"x":1.0161328315734863,"y":9.7346830368042},{"x":1.637150764465332,"y":15.480567932128906},{"x":-0.8749380111694336,"y":3.704550266265869},{"x":0.5326972007751465,"y":7.397686958312988},{"x":-0.8989872932434082,"y":3.6920485496520996},{"x":1.6606526374816895,"y":15.98570442199707},{"x":1.3893942832946777,"y":13.498802185058594},{"x":-1.3748388290405273,"y":4.680605411529541},{"x":-0.22421789169311523,"y":4.457881927490234},{"x":-0.04375505447387695,"y":5.263555526733398},{"x":1.2894659042358398,"y":12.095159530639648},{"x":1.116281509399414,"y":10.542726516723633},{"x":1.725419044494629,"y":16.511856079101562},{"x":-1.203160285949707,"y":3.808946132659912}]},"encoding":{"x":{"axis":{"grid":false},"field":"x","scale":{"domain":[-2.05,2.05],"zero":false},"type":"quantitative"},"y":{"axis":{"grid":false},"field":"y","scale":{"domain":[2.5,20],"zero":false},"type":"quantitative"}},"height":630,"mark":{"fillOpacity":1,"filled":true,"type":"point"},"title":{"offset":20,"text":"Scatterplot of Generated Data"},"width":630}
 ```
 
 As is clear in the picture, the plotted data would most likely not be accurately estimated by a straight line like the ones linear regression estimates, so polynomial regression will better fit the data in this case. We do this with the `Scholar.Linear.PolynomialRegression` module. If you're familiar with the `Scholar.Linear.LinearRegression` module, the next steps will feel familiar.
@@ -404,58 +319,20 @@ df_results =
     y: y_values |> Nx.to_flat_list()
   )
 
-# Plot the predicted values
-Vl.new(
-  title: [
-    text: "Scatterplot of Predictions",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(df)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: x_scale,
-    axis: [grid: false]
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: y_scale,
-    axis: [grid: false]
-  ),
-  Vl.new()
-  |> Vl.data_from_values(df_results)
-  |> Vl.mark(:line, color: :green)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: x_scale
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: y_scale
-  ),
-  Vl.new()
-  |> Vl.data_from_values(df_linear_results)
-  |> Vl.mark(:line, color: :red)
-  |> Vl.encode_field(:x, "x",
-    type: :quantitative,
-    scale: x_scale
-  )
-  |> Vl.encode_field(:y, "y",
-    type: :quantitative,
-    scale: y_scale
-  )
+Tucan.layers([
+  Tucan.scatter(df, "x", "y", filled: true),
+  Tucan.lineplot(df_results, "x", "y", line_color: "green"),
+  Tucan.lineplot(df_linear_results, "x", "y", line_color: "red", clip: true)
 ])
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
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of Generated Data"},"width":630}
 ```
 
 Notice how the process is mostly the same for fitting a model and making a prediction. The one key difference comes in the coefficients, and how the input data is handled. The polynomial model returns a number of coefficients depending on the number of variables and the degree. This is why there are two coefficients but only one variable. In this example, with one variable and degree 2, we get two coefficients:
@@ -534,37 +411,23 @@ df_prediction =
     y: y_predictions
   )
 
-Vl.new(
-  title: [
-    text: "Plot of Generated Data and Predictions",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
-)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values(df)
-  |> Vl.mark(:circle)
-  |> Vl.encode_field(:x, "x", type: :quantitative, scale: x_scale, axis: [grid: false])
-  |> Vl.encode_field(:y, "y", type: :quantitative, scale: y_scale, axis: [grid: false]),
-  Vl.new()
-  |> Vl.data_from_values(df_results)
-  |> Vl.mark(:line, color: :green)
-  |> Vl.encode_field(:x, "x", type: :quantitative, scale: x_scale)
-  |> Vl.encode_field(:y, "y", type: :quantitative, scale: y_scale),
-  Vl.new()
-  |> Vl.data_from_values(df_prediction)
-  |> Vl.mark(:circle, color: :red, size: 80)
-  |> Vl.encode_field(:x, "x", type: :quantitative, scale: x_scale)
-  |> Vl.encode_field(:y, "y", type: :quantitative, scale: y_scale)
+x_scale = [domain: [-2.05, 2.05]]
+y_scale = [domain: [2.5, 20]]
+
+Tucan.layers([
+  Tucan.scatter(df, "x", "y", filled: true),
+  Tucan.lineplot(df_results, "x", "y", line_color: "green"),
+  Tucan.scatter(df_prediction, "x", "y", point_color: "red", point_size: 80, filled: true)
 ])
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Plot of Generated Data and Predictions", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
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of Generated Data and Predictions"},"width":630}
 ```
 
 Now we are ready to go into a more complex example!
@@ -609,30 +472,23 @@ Now, we will plot univariate histograms for each feature of the data set.
 # Increase the sample size (or use 1.0 to plot all data)
 sample = DF.sample(df, 0.2, seed: seed)
 
-Vl.new(
-  title: [
-    text: "Univariate Histograms of all features",
-    anchor: :middle
-  ],
-  width: 500,
-  height: 500,
-  columns: 3
-)
-|> Vl.data_from_values(sample)
-|> Vl.concat(
+histograms =
   for name <- List.delete(df.names, "ocean_proximity") do
-    Vl.new()
-    |> Vl.mark(:bar)
-    |> Vl.encode_field(:x, name, bin: [bin: true, maxbins: 50], axis: [ticks: false])
-    |> Vl.encode_field(:y, "value count", aggregate: :count)
+    Tucan.new()
+    |> Tucan.histogram(name, maxbins: 50, fill_opacity: 1.0)
+    |> Tucan.Axes.put_options(:x, ticks: false)
   end
-)
+
+Tucan.new(sample, columns: 3)
+|> Tucan.concat(histograms)
+|> Tucan.set_title("Univariate Histograms of all features", anchor: :middle)
+|> Tucan.set_size(500, 500)
 ```
 
 <!-- livebook:{"output":true} -->
 
 ```vega-lite
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OCEAN","population":834.0,"total_bedrooms":337.0,"total_rooms":1978.0},{"households":108.0,"housing_median_age":20.0,"latitude":37.76,"longitude":-120.9,"median_house_value":1.563e5,"median_income":2.2024,"ocean_proximity":"INLAND","population":304.0,"total_bedrooms":112.0,"total_rooms":570.0},{"households":387.0,"housing_median_age":44.0,"latitude":34.14,"longitude":-118.21,"median_house_value":1.865e5,"median_income":3.2222,"ocean_proximity":"<1H OCEAN","population":1105.0,"total_bedrooms":407.0,"total_rooms":1681.0},{"households":588.0,"housing_median_age":25.0,"latitude":34.14,"longitude":-118.21,"median_house_value":1.898e5,"median_income":2.2267,"ocean_proximity":"<1H OCEAN","population":1412.0,"total_bedrooms":628.0,"total_rooms":1908.0}]},"height":500,"title":{"anchor":"middle","text":"Univariate Histograms of all features"},"width":500}
 ```
 
 From histograms, we can spot that *median_income* and *median_house_values* have a similar distribution. Both of them are heavy-tailed with high skewness. We might speculate that those two features are strictly correlated. We will check that later on.
@@ -642,50 +498,28 @@ From histograms, we can spot that *median_income* and *median_house_values* have
 Now let's render the houses as a scatter plot using the latitude and longitude, overlayed on top of California's map. Let's also use color to encode the house prices and use the circle size to indicate the population of districts.
 
 ```elixir
-Vl.new(
-  title: [
-    text: "Scatterplot of Generated Data",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
+Tucan.scatter(df, "longitude", "latitude",
+  filled: true,
+  tooltip: true,
+  only: ~w(latitude longitude median_house_value population)
 )
-|> Vl.layers([
-  Vl.new()
-  |> Vl.data_from_values([
-    %{
-      url:
-        "https://raw.githubusercontent.com/ageron/handson-ml2/master/images/end_to_end_project/california.png"
-    }
-  ])
-  |> Vl.mark(:image,
-    width: 630,
-    aspect: false,
-    align: :right
-  )
-  |> Vl.encode_field(:url, "url", type: :nominal),
-  Vl.new()
-  |> Vl.data_from_values(df, only: ~w(latitude longitude median_house_value population))
-  |> Vl.mark(:circle, opacity: 0.4)
-  |> Vl.encode_field(:x, "longitude",
-    type: :quantitative,
-    axis: [grid: false],
-    scale: [domain: [-124.55, -113.80]]
-  )
-  |> Vl.encode_field(:y, "latitude",
-    type: :quantitative,
-    axis: [grid: false],
-    scale: [domain: [32.45, 42.05]]
-  )
-  |> Vl.encode_field(:color, "median_house_value", type: :quantitative, scale: [scheme: :viridis])
-  |> Vl.encode_field(:size, "population", type: :quantitative)
-])
+|> Tucan.color_by("median_house_value", type: :quantitative)
+|> Tucan.size_by("population")
+|> Tucan.Scale.set_x_domain(-124.55, -113.80)
+|> Tucan.Scale.set_y_domain(32.45, 42.05)
+|> Tucan.Grid.set_enabled(false)
+|> Tucan.Scale.set_color_scheme(:viridis)
+|> Tucan.background_image(
+  "https://raw.githubusercontent.com/ageron/handson-ml2/master/images/end_to_end_project/california.png"
+)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Scatterplot of Generated Data", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
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of Generated Data"},"width":630}
 ```
 
 From This plot, we can read that prices are substantially dependent on **geolocalization** and **population**. For geolocalization, we see, those areas closer to the ocean are more expensive. But it's not a strict rule since houses on the northern bay of California are much more affordable than in in-land Mid California. For the population, there are two dense areas with expensive housing: Los Angeles Bay (In South California) and San Francisco Bay (in Mid Califonia). They are metropolises with a lot of different tech companies, and business and cultural institutions, so, logically, housing in those places will be expensive.
@@ -942,40 +776,19 @@ corr_to_plot =
     corr_val: Enum.map(correlation_list, fn x -> Float.round(x, 2) end)
   )
 
-Vl.new(
-  title: [
-    text: "Correlation Matrix for California Housing",
-    offset: 20
-  ],
-  width: 630,
-  height: 630
+Tucan.heatmap(corr_to_plot, "x", "y", "corr_val",
+  annotate: true,
+  text_color: [{nil, 0, "white"}, {0, nil, "black"}]
 )
-|> Vl.data_from_values(corr_to_plot)
-|> Vl.layers([
-  Vl.new()
-  |> Vl.mark(:rect)
-  |> Vl.encode_field(:x, "x", type: :nominal, title: "", sort: false)
-  |> Vl.encode_field(:y, "y", type: :nominal, title: "", sort: false)
-  |> Vl.encode_field(:color, "corr_val", type: :quantitative, scale: [scheme: :viridis]),
-  Vl.new()
-  |> Vl.mark(:text)
-  |> Vl.encode_field(:x, "x", type: :nominal, title: "")
-  |> Vl.encode_field(:y, "y", type: :nominal, title: "")
-  |> Vl.encode_field(:text, "corr_val", type: :quantitative)
-  |> Vl.encode_field(:color, "corr_val",
-    type: :quantitative,
-    condition: [
-      [test: "datum['corr_val'] < 0", value: :white],
-      [test: "datum['corr_val'] >= 0", value: :black]
-    ]
-  )
-])
+|> Tucan.Scale.set_color_scheme(:viridis)
+|> Tucan.set_size(630, 630)
+|> Tucan.set_title("Correlation Matrix for California Housing", offset: 20)
 ```
 
 <!-- livebook:{"output":true} -->
 
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 ```
 
 We can spot that _median_house_value_ is strongly correlated with _median_income_. It's pretty straightforward, the more money you have, the more expensive house you can buy. Non-obvious is a negative correlation with _bedrooms_per_rooms_. But it also can be explained. Bedrooms are the most crucial rooms in the house. Firstly, you need to guarantee that you have a house with enough bedrooms. If this condition is satisfied, then you can focus on "additional rooms" like a chill room, cabinets and so on. So if you buy a house with more additional rooms, then you decrease the ratio.
diff --git a/test/scholar/cluster/affinity_propagation_test.exs b/test/scholar/cluster/affinity_propagation_test.exs
index 320e4ced..f63e4160 100644
--- a/test/scholar/cluster/affinity_propagation_test.exs
+++ b/test/scholar/cluster/affinity_propagation_test.exs
@@ -68,7 +68,7 @@ defmodule Scholar.Cluster.AffinityPropagationTest do
   end
 
   test "fit and compute_values" do
-    model = AffinityPropagation.fit(x(), key: key())
+    model = AffinityPropagation.fit(x(), key: key(), preference: :median)
 
     model = AffinityPropagation.prune(model)
 
@@ -94,14 +94,14 @@ defmodule Scholar.Cluster.AffinityPropagationTest do
   end
 
   test "predict with pruning" do
-    model = AffinityPropagation.fit(x(), key: key())
+    model = AffinityPropagation.fit(x(), key: key(), preference: :median)
     model = AffinityPropagation.prune(model)
     preds = AffinityPropagation.predict(model, x_test())
     assert preds == Nx.tensor([0, 2, 0, 5, 5, 5, 2, 2, 5, 2])
   end
 
   test "predict without pruning" do
-    model = AffinityPropagation.fit(x(), key: key())
+    model = AffinityPropagation.fit(x(), key: key(), preference: :median)
     preds = AffinityPropagation.predict(model, x_test())
     assert preds == Nx.tensor([2, 9, 2, 34, 34, 34, 9, 9, 34, 9])
   end
diff --git a/test/scholar/linear/isotonic_regression_test.exs b/test/scholar/linear/isotonic_regression_test.exs
index 4f21a7d3..a954a0bd 100644
--- a/test/scholar/linear/isotonic_regression_test.exs
+++ b/test/scholar/linear/isotonic_regression_test.exs
@@ -209,7 +209,7 @@ defmodule Scholar.Linear.IsotonicRegressionTest do
           [43.0, 44.0, 46.0, 47.0, 55.0, 56.0] ++
           [60.0, 61.0, 66.0, 67.0, 71.0, 72.0] ++
           [73.0, 76.0, 77.0, 80.0, 81.0, 87.0] ++
-          [88.0, 92.0, 93.0, 97.0, 98.0]
+          [88.0, 92.0, 93.0, 97.0, 98.0, 99.0]
       )
     )
   end
diff --git a/test/scholar/metrics/classification_test.exs b/test/scholar/metrics/classification_test.exs
index ed00802f..975abed0 100644
--- a/test/scholar/metrics/classification_test.exs
+++ b/test/scholar/metrics/classification_test.exs
@@ -14,4 +14,62 @@ defmodule Scholar.Metrics.ClassificationTest do
     assert_all_close(tpr, Nx.tensor([0.0, 0.5, 1.0, 1.0]))
     assert_all_close(thresholds, Nx.tensor([1.3, 0.3, 0.2, 0.1]))
   end
+
+  describe "fbeta_score" do
+    test "equals recall when beta is infinity" do
+      beta = Nx.tensor(:infinity)
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :u32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], type: :u32)
+      fbeta_scores = Classification.fbeta_score(y_true, y_pred, beta, num_classes: 2)
+
+      assert_all_close(fbeta_scores, Classification.recall(y_true, y_pred, num_classes: 2))
+    end
+
+    test "equals precision when beta is 0" do
+      beta = 0
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :u32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], type: :u32)
+      fbeta_scores = Classification.fbeta_score(y_true, y_pred, beta, num_classes: 2)
+
+      assert_all_close(fbeta_scores, Classification.precision(y_true, y_pred, num_classes: 2))
+    end
+  end
+
+  describe "mcc/2" do
+    test "returns 1 for perfect predictions" do
+      y_true = Nx.tensor([1, 0, 1, 0, 1])
+      y_pred = Nx.tensor([1, 0, 1, 0, 1])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([1.0], type: :f32)
+    end
+
+    test "returns -1 for completely wrong predictions" do
+      y_true = Nx.tensor([1, 0, 1, 0, 1])
+      y_pred = Nx.tensor([0, 1, 0, 1, 0])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([-1.0], type: :f32)
+    end
+
+    test "returns 0 when all predictions are positive" do
+      y_true = Nx.tensor([1, 0, 1, 0, 1])
+      y_pred = Nx.tensor([1, 1, 1, 1, 1])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([0.0], type: :f32)
+    end
+
+    test "returns 0 when all predictions are negative" do
+      y_true = Nx.tensor([1, 0, 1, 0, 1])
+      y_pred = Nx.tensor([0, 0, 0, 0, 0])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([0.0], type: :f32)
+    end
+
+    test "computes MCC for generic case" do
+      y_true = Nx.tensor([1, 0, 1, 0, 1])
+      y_pred = Nx.tensor([1, 0, 1, 1, 1])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([0.6123723983764648], type: :f32)
+    end
+
+    test "returns 0 when TP, TN, FP, and FN are all 0" do
+      y_true = Nx.tensor([0, 0, 0, 0, 0])
+      y_pred = Nx.tensor([0, 0, 0, 0, 0])
+      assert Classification.mcc(y_true, y_pred) == Nx.tensor([0.0], type: :f32)
+    end
+  end
 end
diff --git a/test/scholar/metrics/ranking_test.exs b/test/scholar/metrics/ranking_test.exs
new file mode 100644
index 00000000..a189ae52
--- /dev/null
+++ b/test/scholar/metrics/ranking_test.exs
@@ -0,0 +1,47 @@
+defmodule Scholar.Metrics.RankingTest do
+  use Scholar.Case, async: true
+  alias Scholar.Metrics.Ranking
+
+  describe "dcg/3" do
+    test "computes DCG when there are no ties" do
+      y_true = Nx.tensor([3, 2, 3, 0, 1, 2])
+      y_score = Nx.tensor([3.0, 2.2, 3.5, 0.5, 1.0, 2.1])
+
+      result = Ranking.dcg(y_true, y_score)
+
+      x = Nx.tensor([7.140995025634766])
+      assert x == Nx.broadcast(result, {1})
+    end
+
+    test "computes DCG with ties" do
+      y_true = Nx.tensor([3, 3, 3])
+      y_score = Nx.tensor([2.0, 2.0, 3.5])
+
+      result = Ranking.dcg(y_true, y_score)
+
+      x = Nx.tensor([6.3927892607143715])
+      assert x == Nx.broadcast(result, {1})
+    end
+
+    test "raises error when shapes mismatch" do
+      y_true = Nx.tensor([3, 2, 3])
+      y_score = Nx.tensor([3.0, 2.2, 3.5, 0.5])
+
+      assert_raise ArgumentError,
+                   "expected tensor to have shape {3}, got tensor with shape {4}",
+                   fn ->
+                     Ranking.dcg(y_true, y_score)
+                   end
+    end
+
+    test "computes DCG for top-k values" do
+      y_true = Nx.tensor([3, 2, 3, 0, 1, 2])
+      y_score = Nx.tensor([3.0, 2.2, 3.5, 0.5, 1.0, 2.1])
+
+      result = Ranking.dcg(y_true, y_score, k: 3)
+
+      x = Nx.tensor([5.892789363861084])
+      assert x == Nx.broadcast(result, {1})
+    end
+  end
+end
diff --git a/test/scholar/metrics/regression_test.exs b/test/scholar/metrics/regression_test.exs
index 68258382..2522da25 100644
--- a/test/scholar/metrics/regression_test.exs
+++ b/test/scholar/metrics/regression_test.exs
@@ -3,4 +3,67 @@ defmodule Scholar.Metrics.RegressionTest do
 
   alias Scholar.Metrics.Regression
   doctest Regression
+
+  describe "mean_tweedie_deviance!/3" do
+    test "raise when y_pred <= 0 and power < 0" do
+      power = -1
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :u32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 0], type: :u32)
+
+      assert_raise RuntimeError, ~r/mean Tweedie deviance/, fn ->
+        Regression.mean_tweedie_deviance!(y_true, y_pred, power)
+      end
+    end
+
+    test "raise when y_pred <= 0 and 1 <= power < 2" do
+      power = 1
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :u32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 0], type: :u32)
+
+      assert_raise RuntimeError, ~r/mean Tweedie deviance/, fn ->
+        Regression.mean_tweedie_deviance!(y_true, y_pred, power)
+      end
+    end
+
+    test "raise when y_pred <= 0 and power >= 2" do
+      power = 2
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :u32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 0], type: :u32)
+
+      assert_raise RuntimeError, ~r/mean Tweedie deviance/, fn ->
+        Regression.mean_tweedie_deviance!(y_true, y_pred, power)
+      end
+    end
+
+    test "raise when y_true < 0 and 1 <= power < 2" do
+      power = 1
+      y_true = Nx.tensor([-1, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :s32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], type: :s32)
+
+      assert_raise RuntimeError, ~r/mean Tweedie deviance/, fn ->
+        Regression.mean_tweedie_deviance!(y_true, y_pred, power)
+      end
+    end
+
+    test "raise when y_true <= 0 and power >= 2" do
+      power = 2
+      y_true = Nx.tensor([0, 0, 0, 0, 0, 1, 1, 1, 1, 1], type: :s32)
+      y_pred = Nx.tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1], type: :s32)
+
+      assert_raise RuntimeError, ~r/mean Tweedie deviance/, fn ->
+        Regression.mean_tweedie_deviance!(y_true, y_pred, power)
+      end
+    end
+  end
+
+  describe "d2_tweedie_score/3" do
+    test "equal R^2 when power is 0" do
+      y_true = Nx.tensor([1, 1, 1, 1, 1, 2, 2, 1, 3, 1], type: :u32)
+      y_pred = Nx.tensor([2, 2, 1, 1, 2, 2, 2, 1, 3, 1], type: :u32)
+      d2 = Regression.d2_tweedie_score(y_true, y_pred, 0)
+      r2 = Regression.r2_score(y_true, y_pred)
+
+      assert Nx.equal(d2, r2)
+    end
+  end
 end
diff --git a/test/scholar/neighbors/kd_tree_test.exs b/test/scholar/neighbors/kd_tree_test.exs
new file mode 100644
index 00000000..3df22fbe
--- /dev/null
+++ b/test/scholar/neighbors/kd_tree_test.exs
@@ -0,0 +1,72 @@
+defmodule Scholar.Neighbors.KDTreeTest do
+  use ExUnit.Case, async: true
+  doctest Scholar.Neighbors.KDTree
+
+  defp example do
+    Nx.tensor([
+      [10, 15],
+      [46, 63],
+      [68, 21],
+      [40, 33],
+      [25, 54],
+      [15, 43],
+      [44, 58],
+      [45, 40],
+      [62, 69],
+      [53, 67]
+    ])
+  end
+
+  describe "unbounded" do
+    test "sample" do
+      assert %Scholar.Neighbors.KDTree{levels: 4, indexes: indexes} =
+               Scholar.Neighbors.KDTree.unbounded(example(), compiler: EXLA)
+
+      assert Nx.to_flat_list(indexes) == [1, 5, 9, 3, 6, 2, 8, 0, 7, 4]
+    end
+
+    test "float" do
+      assert %Scholar.Neighbors.KDTree{levels: 4, indexes: indexes} =
+               Scholar.Neighbors.KDTree.unbounded(example() |> Nx.as_type(:f32),
+                 compiler: EXLA
+               )
+
+      assert Nx.to_flat_list(indexes) == [1, 5, 9, 3, 6, 2, 8, 0, 7, 4]
+    end
+
+    test "corner cases" do
+      assert %Scholar.Neighbors.KDTree{levels: 1, indexes: indexes} =
+               Scholar.Neighbors.KDTree.unbounded(Nx.iota({1, 2}), compiler: EXLA)
+
+      assert indexes == Nx.u32([0])
+
+      assert %Scholar.Neighbors.KDTree{levels: 2, indexes: indexes} =
+               Scholar.Neighbors.KDTree.unbounded(Nx.iota({2, 2}), compiler: EXLA)
+
+      assert indexes == Nx.u32([1, 0])
+    end
+  end
+
+  describe "bounded" do
+    test "iota" do
+      assert %Scholar.Neighbors.KDTree{levels: 3, indexes: indexes} =
+               Scholar.Neighbors.KDTree.bounded(Nx.iota({5, 2}), 10)
+
+      assert indexes == Nx.u32([3, 1, 4, 0, 2])
+    end
+
+    test "float" do
+      assert %Scholar.Neighbors.KDTree{levels: 4, indexes: indexes} =
+               Scholar.Neighbors.KDTree.bounded(example() |> Nx.as_type(:f32), 100)
+
+      assert Nx.to_flat_list(indexes) == [1, 5, 9, 3, 6, 2, 8, 0, 7, 4]
+    end
+
+    test "sample" do
+      assert %Scholar.Neighbors.KDTree{levels: 4, indexes: indexes} =
+               Scholar.Neighbors.KDTree.bounded(example(), 100)
+
+      assert Nx.to_flat_list(indexes) == [1, 5, 9, 3, 6, 2, 8, 0, 7, 4]
+    end
+  end
+end
diff --git a/test/test_helper.exs b/test/test_helper.exs
index e69de29b..5e96292b 100644
--- a/test/test_helper.exs
+++ b/test/test_helper.exs
@@ -0,0 +1 @@
+Application.ensure_all_started(:exla)