Add det curve (#258)

lib/scholar/metrics/classification.ex

@@ -1486,4 +1486,70 @@ defmodule Scholar.Metrics.Classification do
       )
     end
   end
+
+  @doc """
+  Compute error rates for different probability thresholds (DET).
+
+  Note: This metric is used for evaluation of ranking and error tradeoffs of
+  a binary classification task.
+
+  ## Examples
+
+      iex> y_true = Nx.tensor([0, 0, 1, 1])
+      iex> y_score = Nx.tensor([0.1, 0.4, 0.35, 0.8])
+      iex> distinct_value_indices = Scholar.Metrics.Classification.distinct_value_indices(y_score)
+      iex> {fpr, fnr, thresholds} = Scholar.Metrics.Classification.det_curve(y_true, y_score, distinct_value_indices)
+      iex> fpr
+      #Nx.Tensor<
+        f32[4]
+        [1.0, 0.5, 0.5, 0.0]
+      >
+      iex> fnr
+      #Nx.Tensor<
+        f32[4]
+        [0.0, 0.0, 0.5, 0.5]
+      >
+      iex> thresholds
+      #Nx.Tensor<
+        f32[4]
+        [0.10000000149011612, 0.3499999940395355, 0.4000000059604645, 0.800000011920929]
+      >
+
+      iex> y_true = Nx.tensor([0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1])
+      iex> y_score = Nx.tensor([0.1, 0.1, 0.2, 0.2, 0.3, 0.3, 0.4, 0.4, 0.5, 0.5, 0.6, 0.7, 0.7, 0.8, 0.9])
+      iex> distinct_value_indices = Scholar.Metrics.Classification.distinct_value_indices(y_score)
+      iex> {fpr, fnr, thresholds} = Scholar.Metrics.Classification.det_curve(y_true, y_score, distinct_value_indices)
+      iex> fpr
+      #Nx.Tensor<
+        f32[9]
+        [1.0, 0.6666666865348816, 0.6666666865348816, 0.6666666865348816, 0.3333333432674408, 0.3333333432674408, 0.1666666716337204, 0.1666666716337204, 0.0]
+      >
+      iex> fnr
+      #Nx.Tensor<
+        f32[9]
+        [0.0, 0.0, 0.2222222238779068, 0.4444444477558136, 0.4444444477558136, 0.6666666865348816, 0.6666666865348816, 0.8888888955116272, 0.8888888955116272]
+      >
+      iex> thresholds
+      #Nx.Tensor<
+        f32[9]
+        [0.10000000149011612, 0.20000000298023224, 0.30000001192092896, 0.4000000059604645, 0.5, 0.6000000238418579, 0.699999988079071, 0.800000011920929, 0.8999999761581421]
+      >
+  """
+  defn det_curve(y_true, y_score, distinct_value_indices, weights \\ 1.0) do
+    num_samples = Nx.axis_size(y_true, 0)
+
+    weights = validate_weights(weights, num_samples, type: to_float_type(y_true))
+
+    check_shape(y_true, y_score)
+
+    {fps, tps, thresholds} =
+      binary_clf_curve(y_true, y_score, distinct_value_indices, weights)
+
+    positive_count = tps[[-1]]
+    negative_count = fps[[-1]]
+
+    fns = positive_count - tps
+
+    {Nx.reverse(fps) / negative_count, Nx.reverse(fns) / positive_count, Nx.reverse(thresholds)}
+  end
 end