camp_logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a target=\"_blank\" href=\"https://colab.research.google.com/github/cyneuro/ML_camp/blob/main/camp_logistic_regression.ipynb\">\n",
    "  <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/>\n",
    "</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JEjkWxhclJB3"
   },
   "source": [
    "# LOGISTIC REGRESSION"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vwHcnvKITLRI"
   },
   "source": [
    "[Video: Logistic Regression](https://youtu.be/yIYKR4sgzI8?si=8fXB3GGjcA6dfzzG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "17eWGsR-RWe9"
   },
   "source": [
    "## Classification\n",
    "\n",
    "In linear regression, the computer uses a line to *fit* the data. In logistic regression, the computer uses a line to *split* the data into two **classes**.\n",
    "\n",
    "The goal of logistic regression is to define a line so that data in one class falls on one side of the line and data in the other class falls on the other side. In the image below, the blue line splits the two black and red classes. This means that the model believes that any point that falls *above* the line is part of the black class, and any point that falls *below* the line is part of the red class.\n",
    "\n",
    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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IdmRh4F7ZcrV"
   },
   "source": [
    "Logistic regression is used for classification problems, which means that the target variable can be of one of $K$ distinct classes. Here we discuss binary logistic regression, so that $y_i$ can be either $0$ or $1$.\n",
    "\n",
    "For example, let's look at the data below.\n",
    "\n",
    "<table width=25%>\n",
    "  <tr>\n",
    "    <th colspan=2>$X$</th>\n",
    "    <th>$y$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <th>$x_1$</th>\n",
    "    <th>$x_2$</th>\n",
    "    <th>$y_i$</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$-2$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$-1$</td>\n",
    "    <td align=center>$3$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$-1$</td>\n",
    "    <td align=center>$-1$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$2$</td>\n",
    "    <td align=center>$-2$</td>\n",
    "    <td align=center>$0$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$2$</td>\n",
    "    <td align=center>$1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td align=center>$3$</td>\n",
    "    <td align=center>$-1$</td>\n",
    "    <td align=center>$1$</td>\n",
    "  </tr>\n",
    "</table>\n",
    "\n",
    "As you see in the table, $X$ represents *all* of the ($x_1$, $x_2$) pairs in the dataset.\n",
    "<br>\n",
    "Each input feature vector $X_i$ (($x_1$, $x_2$) pair) is assigned a class $y_i$ ($0$ or $1$).\n",
    "<br>\n",
    "The model's goal is to learn how to classify a data point as $0$ or $1$ based on its features. Here, the features are just 2D coordinates, but in larger problems there may be dozens of features like weight, height, temperature, or any other metric you can think of.\n",
    "<br></br>\n",
    "Let's take a look at this data on a graph (Class $0$ = blue, Class $1$ = red):\n",
    "\n",
    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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7Lz_RgjnmQu7"
   },
   "source": [
    "## Activity 1 - Frame the problem *(You solve)*\n",
    "\n",
    "Consider the 2D logistic regression problem shown above. How might we frame the problem to define a line that splits the two classes optimally?\n",
    "<br>\n",
    "What is loss in this problem and how would we minimize it?\n",
    "<br></br>\n",
    "Write down your thoughts before moving forward."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q2QX4B4hnt-D"
   },
   "source": [
    "## The model\n",
    "\n",
    "Logistic regression can be visually represented as follows. Below we look at each component of the model.\n",
    "\n",
    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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zlFdCO1L91RH"
   },
   "source": [
    "### Weights and bias\n",
    "\n",
    "Logistic regression uses **weights** and **bias** to adjust its computation to produce more accurate outputs. These are the line's parameters like slope and the intercept that are adjusted during training.\n",
    "\n",
    "Recall, in linear regression the estimated output is defined as $\\hat{y_i}=mx_i + b$. Here, $m$ is the *weight* because it multiplies the input $x_i$, while $b$ is the *bias* which is simply added on.\n",
    "\n",
    "### Weighted Sum\n",
    "\n",
    "When the inputs ($x_0, x_1, x_2, x_3...x_n$) are taken in, the perceptron calculates $z$, the **weighted sum*** The weighted sum is the dot product of the weights and inputs plus the bias\n",
    "\n",
    "$$\n",
    "z=\\theta_0x_0 + \\theta_1x_1 + \\theta_2x_2 + ... + \\theta_nx_n\n",
    "$$\n",
    "\n",
    "To understand what $z$ means better, let us look back at the 2D example with red and blue circles.\n",
    "\n",
    "In this problem, there are two features, $x_1$ and $x_2$. A line in the 2D plane can be defined by:\n",
    "$$x_2=mx_1+b$$\n",
    "\n",
    "Move all variables to one side:\n",
    "$$x_2-mx_1-b=0$$\n",
    "<br>\n",
    "Now, we can change $m$ and $b$ to $\\theta$ notation for the weights and biases.\n",
    "\n",
    "$$\\theta_2x_2+\\theta_1x_1+\\theta_0=0$$\n",
    "$$...$$\n",
    "$$\\theta_2x_2+\\theta_1x_1+\\theta_0=z$$\n",
    "\n",
    "So, what does this weighted sum mean? Just like linear regression, it defines a line given some parameters ($\\theta_i$).\n",
    "<br>\n",
    "If a data point ($x_1, x_2$) from the dataset lies on the line, $z=0$.\n",
    "<br>\n",
    "If a data point lies *above* the line, $z>0$.\n",
    "<br>\n",
    "If a data point lies *below* the line, $z<0$.\n",
    "<br>\n",
    "\n",
    "**Whether a data point's $z$ value is negative or nonnegative determines the model's classification of that point.**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IjU72v1aABe0"
   },
   "source": [
    "### Activity 2 - Calculate weighted sum *(You solve)*\n",
    "\n",
    "Pick random numbers for $\\theta_0$, $\\theta_1$, and $\\theta_2$.\n",
    "<br>\n",
    "Plot the line using the $z$ equation:\n",
    "$$\\theta_2x_2+\\theta_1x_1+\\theta_0=0$$\n",
    "<br>\n",
    "Choose $(x_1, x_2)$ coordinates that lie above, on, and below the line and calculate their $z$ value.\n",
    "<br>\n",
    "Do your calculations make sense according to the purpose of the weighted sum?\n",
    "<br></br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "id": "LV_MO1M2ALnt"
   },
   "outputs": [],
   "source": [
    "#@title Run this code once you have finished the activity\n",
    "\n",
    "from numpy.random import randn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "np.random.seed()\n",
    "\n",
    "# Randomly initialize weights and bias\n",
    "theta_0 = np.random.uniform(1, 2)\n",
    "theta_1 = np.random.uniform(1, 2)\n",
    "theta_2 = np.random.uniform(1, 2)\n",
    "\n",
    "# Generate x1 values\n",
    "x1 = np.linspace(-10, 10, 400)\n",
    "\n",
    "# Calculate x2 values\n",
    "# θ0 + θ1x1 + θ2x2 = 0\n",
    "# θ2x2 = -θ1x1 - θ0\n",
    "# x2 = (-θ1x1 - θ0)/θ2\n",
    "x2 = (-theta_1 * x1 - theta_0) / theta_2\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Plot the decision boundary\n",
    "ax.plot(x1, x2, 'tab:blue', label='Decision Boundary')\n",
    "\n",
    "# Generate random coordinates for points above, on and below the line\n",
    "points_above = np.random.uniform(low=-10, high=10, size=(5, 1))\n",
    "points_above = np.column_stack((points_above, ((-theta_1 * points_above - theta_0) / theta_2) + np.random.uniform(3,5, size=(5,1))))\n",
    "\n",
    "points_on = np.random.uniform(low=-10, high=10, size=(5, 1))\n",
    "points_on = np.column_stack((points_on, (-theta_1 * points_on - theta_0) / theta_2))\n",
    "\n",
    "points_below = np.random.uniform(low=-10, high=10, size=(5, 1))\n",
    "points_below = np.column_stack((points_below, ((-theta_1 * points_below - theta_0) / theta_2) - np.random.uniform(3,5, size=(5,1))))\n",
    "\n",
    "# Plot the points\n",
    "ax.scatter(*points_above.T, label='Above')\n",
    "ax.scatter(*points_on.T, label='On')\n",
    "ax.scatter(*points_below.T, label='Below')\n",
    "\n",
    "# Calculate and print z values\n",
    "for label, points in [('Above', points_above), ('On', points_on), ('Below', points_below)]:\n",
    "    z_values = theta_0 + theta_1 * points[:, 0] + theta_2 * points[:, 1]\n",
    "    print(f'Z-values for points {label} the line: {z_values}')\n",
    "\n",
    "# Set plot limits and labels\n",
    "ax.set_xlim([-10, 10])\n",
    "ax.set_ylim([-10, 10])\n",
    "ax.set_xlabel('x1')\n",
    "ax.set_ylabel('x2')\n",
    "ax.grid()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l6cKUUuY__Ne"
   },
   "source": [
    "### Sigmoid Function\n",
    "\n",
    "The weighted sum ($z$) determines the assignment of a data point to one of two classes – this is known as hard classification. However, on real problems, we are often interested in probability of the point beloning to each class, so that we can make the classification decision ourselves – this is known as soft classification. Logistic regression supports soft classification by using the **sigmoid function** to map the weighted sum to the interval between $0$ and $1$.\n",
    "\n",
    "$$\\sigma(z)=\\frac{1}{1+e^{-z}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 452
    },
    "id": "DY9GjpcsogMP",
    "outputId": "35ef6e1d-a1aa-4d2c-9c98-e56a38549aec"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def sigmoid(x):\n",
    "  return 1/(1 + np.exp(-x))\n",
    "\n",
    "x = np.linspace(-5, 5)\n",
    "y = sigmoid(x)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_title('Sigmoid Function (σ(x))')\n",
    "\n",
    "ax.plot(x, y);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Jrpv9Hhk_5Sv"
   },
   "source": [
    "If $z$ is a large *negative* number, $e^{-z}$ becomes a very large *positive* number, making the output close to $0$.\n",
    "If $z$ is a large *positive* number, $e^{-z}$ becomes very close to $0$, making the output close to $1$.\n",
    "If $z=0$, the $\\sigma(z)=0.5$.\n",
    "<br></br>\n",
    "In essence, the more *positive* $z$ is, the closer $\\sigma(z)$ is to $1$. The more *negative* $z$ is, the closer $\\sigma(z)$ is to $0$.\n",
    "\n",
    "Now we can choose a threshold on $\\sigma(z)$ to assign a data point to one of the classes. For example,\n",
    "\n",
    "If $\\sigma(z) \\ge 0.5$, the data point is classified as a $1$. If $\\sigma(z)<0.5$, the data point is classified as a $0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l5XbrZeuSedb"
   },
   "source": [
    "### Loss function for logistic regression\n",
    "\n",
    "The loss function typically used for logistic regression is known as **cross entropy**:\n",
    "$$\n",
    "L(\\theta) = -\\frac{1}{N}\\sum_{i=1}^N y_i \\log \\hat{p}(y_i) + (1-y_i)\\log(1 - \\hat{p}(y_i))\n",
    "$$\n",
    "\n",
    "– as it properly interprets the sigmoid output as a *probability*.\n",
    "\n",
    "To train and optimize the logistic regression model, the weights and biases ($\\theta$) must be updated in the direction that minimizes loss with ***gradient descent***, just as in linear regression.\n",
    "<br></br>\n",
    "\n",
    "### Update Rule\n",
    "\n",
    "Parameters (weights and bias) are updated with the standard update rule, descending the loss' slope with respect to the parameters ($\\frac{∂L}{∂\\theta_i}$) at a specified learning rate ($\\alpha$).\n",
    "\n",
    "$$\\theta_i := \\theta_i - \\alpha\\times\\frac{∂L}{∂\\theta_i}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UfAOjybqX72M"
   },
   "source": [
    "### **Logistic Regression With sklearn**\n",
    "\n",
    "Using the machine learning library `sklearn`, we can solve the logistic regression problem from earlier with the blue and red circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 472
    },
    "id": "2mQVhLybYTgA",
    "outputId": "ae69370b-b242-4027-b637-57d24dbb74f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Data\n",
    "\n",
    "# Input features\n",
    "X = np.array(\n",
    "    [[-2, 1],\n",
    "     [-1, 3],\n",
    "     [-1, -1],\n",
    "     [2, -2],\n",
    "     [2, 1],\n",
    "     [3, -1]])\n",
    "\n",
    "# Target classes\n",
    "y = np.array([0, 1, 0, 0, 1, 1])\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Create a LogisticRegression model\n",
    "model = LogisticRegression()\n",
    "\n",
    "# Fit the model to the dataset\n",
    "model.fit(X, y)\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Plotting\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Separate data by class\n",
    "classes = {0: [], 1: []}\n",
    "data = zip(X, y)\n",
    "for x_i, y_i in zip(X, y):\n",
    "  classes[y_i].append(x_i)\n",
    "\n",
    "# Plot dataset\n",
    "ax.scatter(*np.asarray(classes[0]).T, color='tab:blue', s=100, label='Class 0')\n",
    "ax.scatter(*np.asarray(classes[1]).T, color='tab:red', s=100, label='Class 1')\n",
    "\n",
    "# Plot decision boundary\n",
    "# Get θ-values from the model\n",
    "theta_0 = model.intercept_[0]\n",
    "theta_1, theta_2 = model.coef_[0]\n",
    "\n",
    "x_in = np.linspace(-5, 5, 100)\n",
    "y_pred = (-theta_1 * x_in - theta_0) / theta_2\n",
    "\n",
    "ax.plot(x_in, y_pred, color='tab:green', label=f'Decision Boundary\\n({theta_0:.2f} + {theta_1:.2f}*x1 + {theta_2:.2f}*x2 = 0)')\n",
    "\n",
    "ax.grid()\n",
    "ax.set_title('Logistic Regression (sklearn)')\n",
    "ax.set_aspect(aspect='equal', adjustable='box')\n",
    "ax.set_xlim([-5,5])\n",
    "ax.set_ylim([-5,5])\n",
    "ax.set_xlabel('x1')\n",
    "ax.set_ylabel('x2')\n",
    "ax.legend(loc='lower left')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activity 3 – Classifying the Iris dataset *(You solve)*\n",
    "\n",
    "The Iris dataset is a dataset collected by Edgar Anderson in 1935 on four features (sepal length, sepal width, petal length, and petal width) of three species of Iris flowers (setosa, virginica, and versicolor). [Iris Dataset Information](http://www.lac.inpe.br/~rafael.santos/Docs/CAP394/WholeStory-Iris.html)\n",
    "\n",
    "The dataset consists of 50 samples per species, amounting to 150 samples total, each sample containing the values of the four features and their respective species classification.\n",
    "\n",
    "Though there are three classes (setosa, virginica, and versicolor), we can change the problem into binary classification (two classes) by splitting the data into *setosa* ($0$) and *not setosa* ($1$).\n",
    "\n",
    "**Solve this classification problem with logistic regression.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "# Data\n",
    "\n",
    "# Load the iris dataset\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "# Sepal Length, Sepal Width, Petal Length and Petal Width\n",
    "X = iris.data\n",
    "\n",
    "# Setosa (0), Versicolour (1), and Virginica (2)\n",
    "y = iris.target\n",
    "\n",
    "# To change this problem to binary classification (2 classes), let's\n",
    "# change the problem to classifying Setosa (0) and NOT Setosa (1) by changing all 2s to 1\n",
    "y = [1 if y_i == 2 else y_i for y_i in y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9_Iyf9nQvHsQ"
   },
   "source": [
    "# Additional Material – Logistic Regression With PyTorch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 472
    },
    "id": "owhDcSWvvLQG",
    "outputId": "8df437fe-7eaf-4d49-8139-1bdc19bdae03"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.optim as optim\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Data\n",
    "\n",
    "# Input features\n",
    "X = torch.tensor(\n",
    "    [[-2.0, 1.0],\n",
    "     [-1.0, 3.0],\n",
    "     [-1.0, -1.0],\n",
    "     [2.0, -2.0],\n",
    "     [2.0, 1.0],\n",
    "     [3.0, -1.0]])\n",
    "\n",
    "# Target classes\n",
    "y = torch.tensor([0.0, 1.0, 0.0, 0.0, 1.0, 1.0]).view(-1, 1)\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Define a LogisticRegression model\n",
    "class LogisticReg(torch.nn.Module):\n",
    "  def __init__(self):\n",
    "    super(LogisticReg, self).__init__()\n",
    "    self.linear = torch.nn.Linear(2,1)\n",
    "\n",
    "  def forward(self, X):\n",
    "    # Compute weighted sum\n",
    "    z = self.linear(X)\n",
    "    # Apply sigmoid function to obtain prediction\n",
    "    return torch.sigmoid(z)\n",
    "\n",
    "# Create a LogisticReg object\n",
    "model = LogisticReg()\n",
    "\n",
    "# Define a loss function (mean squared error) and optimizer (gradient descent)\n",
    "loss_function = torch.nn.MSELoss()\n",
    "optimizer = optim.SGD(model.parameters(), lr=0.05)\n",
    "\n",
    "# Fit the model\n",
    "for epoch in range(500):\n",
    "  # Feed inputs into model to get predictions\n",
    "  y_pred = model(X)\n",
    "\n",
    "  # Calculate loss\n",
    "  loss = loss_function(y_pred, y)\n",
    "\n",
    "  # Reset gradients to zero to prepare for calculations\n",
    "  optimizer.zero_grad()\n",
    "  # Calculate gradients\n",
    "  loss.backward()\n",
    "  # Update parameters\n",
    "  optimizer.step()\n",
    "\n",
    "#------------------------------------------------#\n",
    "\n",
    "# Plotting\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Convert from tensors to numpy arrays for plotting\n",
    "X_np = X.numpy()\n",
    "y_np = y.numpy().T[0]\n",
    "y_pred_np = model(X).detach().numpy()\n",
    "\n",
    "# Sort data by class\n",
    "classes = {0: [], 1: []}\n",
    "for x_i, y_i in zip(X_np, y_np):\n",
    "  classes[y_i].append(x_i)\n",
    "\n",
    "# Plot the X (x1, x2) data for each class\n",
    "ax.scatter(*np.array(classes[0]).T, color='tab:blue', s=100, label='Class 0')\n",
    "ax.scatter(*np.array(classes[1]).T, color='tab:red', s=100, label='Class 1')\n",
    "\n",
    "# Get weights and bias to find hypothesis line (decision boundary)\n",
    "theta_0 = model.linear.bias.data[0]\n",
    "theta_1 = model.linear.weight.data[0][0]\n",
    "theta_2 = model.linear.weight.data[0][1]\n",
    "\n",
    "# Generate coordinates of the decision boundary line\n",
    "x_boundary = np.linspace(-5, 5, 100)\n",
    "y_boundary = (-theta_1 * x_boundary - theta_0) / theta_2\n",
    "\n",
    "# Plot the decision boundary\n",
    "ax.plot(x_boundary, y_boundary, color='tab:green', label=f'Decision Boundary\\n({theta_0:.2f} + {theta_1:.2f}*x1 + {theta_2:.2f}*x2 = 0)')\n",
    "\n",
    "# Adjust the plot\n",
    "ax.set_title('Logistic Regression (PyTorch)')\n",
    "ax.set_xlabel('x1')\n",
    "ax.set_ylabel('x2')\n",
    "ax.set_xlim([-5,5])\n",
    "ax.set_ylim([-5,5])\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "ax.legend(loc='lower left')\n",
    "ax.grid()\n",
    "\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}