05_linear_1d_classification_cross_entropy.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#### `Cross-entropy` loss function"
      ],
      "metadata": {
        "id": "cDvAqa90yD5B"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Recall the setup\n",
        "\n",
        "* Input $x$\n",
        "* Linear regression $y_{\\text{pred}}=ax+b$\n",
        "* Convert to probability $h(y_{\\text{pred}})=\\frac{1}{1+e^{-y_{\\text{pred}}}}$"
      ],
      "metadata": {
        "id": "Mh-rPFJFtVnY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cross-entropy loss for `one sample` is\n",
        "\n",
        "$$J=-y_{\\text{act}}\\log(h(y_{\\text{pred}}))-(1-y_{\\text{act}})\\log(1-h(y_{\\text{pred}}))$$\n",
        "\n",
        "where $y_{\\text{act}}$ is either 1 or 0"
      ],
      "metadata": {
        "id": "mXGuIszXtqBV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### `Intuition`"
      ],
      "metadata": {
        "id": "Y56xWDshyKxK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cross-entropy makes cost high if wrong and confident predictions are made, and makes cost low if correct and confident predictions are made"
      ],
      "metadata": {
        "id": "-uT0SR6GBxeT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.style.use('dark_background')\n",
        "np.set_printoptions(formatter={'float': '{: 0.4f}'.format})"
      ],
      "metadata": {
        "id": "6FXz0yonyx5n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_values = np.linspace(0.01, 4, 400)\n",
        "y_values = -np.log(x_values)\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "plt.plot(x_values, y_values, color='c')\n",
        "plt.xlabel('x')\n",
        "plt.title('$y=-\\log(x)$')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "VchiDQD1yxWG",
        "outputId": "86b70eed-77d4-400f-ac24-83ad61dfcd4b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Derivation of `gradient` w.r.t. parameters"
      ],
      "metadata": {
        "id": "WHc3ry13B2gz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(1) differentiate $J$ w.r.t. $h(y_{\\text{pred}})$\n",
        "\n",
        "$$\\frac{dJ}{dh(y_{\\text{pred}})}=-\\frac{y_\\text{act}}{h(y_{\\text{pred}})}+\\frac{1-y_{\\text{act}}}{1-h(y_{\\text{pred}})}$$"
      ],
      "metadata": {
        "id": "SYZSWEhEukug"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(2) differentiate $J$ w.r.t. $y_{\\text{pred}}$ using chain rule\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{dJ}{dy_{\\text{pred}}}&=\\frac{dJ}{dh(y_{\\text{pred}})}\\cdot \\frac{dh(y_{\\text{pred}})}{dy_{\\text{pred}}}\\\\\n",
        "&=\\left(-\\frac{y_\\text{act}}{h(y_{\\text{pred}})}+\\frac{1-y_{\\text{act}}}{1-h(y_{\\text{pred}})}\\right)\\cdot -h(y_{\\text{pred}})^2\\cdot \\left(1-\\frac{1}{h(y_{\\text{pred}})}\\right)\\\\\n",
        "&=\\left(-\\frac{y_\\text{act}}{h(y_{\\text{pred}})}+\\frac{1-y_{\\text{act}}}{1-h(y_{\\text{pred}})}\\right)\\cdot h(y_{\\text{pred}})\\cdot \\left(1-h(y_{\\text{pred}})\\right)\\\\\n",
        "&=-y_\\text{act}\\cdot \\left(1-h(y_\\text{pred})\\right)+(1-y_{\\text{act}})\\cdot h(y_{\\text{pred}})\\\\\n",
        "&=\\boxed{h(y_{\\text{pred}})-y_{\\text{act}}}\n",
        "\\end{align*}$$"
      ],
      "metadata": {
        "id": "og7ABZB7wBD_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "(3) differentiate $J$ w.r.t. $a$ using chain rule\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{dJ}{da}&=\\frac{dJ}{dy_{\\text{pred}}}\\cdot \\frac{dy_{\\text{pred}}}{da}\\\\\n",
        "&=\\boxed{\\left(h(y_{\\text{pred}})-y_{\\text{act}}\\right)\\cdot x}\n",
        "\\end{align*}$$\n",
        "\n",
        "Similarly\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\frac{dJ}{db}&=\\frac{dJ}{dy_{\\text{pred}}}\\cdot \\frac{dy_{\\text{pred}}}{db}\\\\\n",
        "&=\\boxed{\\left(h(y_{\\text{pred}})-y_{\\text{act}}\\right)\\cdot 1}\n",
        "\\end{align*}$$"
      ],
      "metadata": {
        "id": "_XFjAz030itj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Putting everything into `Python`"
      ],
      "metadata": {
        "id": "bMnzBuRECJMI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "# Generate data for class 0 (centered around 2)\n",
        "mean_class0 = 2\n",
        "std_class0 = 0.5\n",
        "num_points = 20\n",
        "class0_data = np.random.normal(mean_class0, std_class0, num_points)  # shape (20,)\n",
        "\n",
        "# Generate data for class 1 (centered around 5)\n",
        "mean_class1 = 5\n",
        "std_class1 = 0.5\n",
        "class1_data = np.random.normal(mean_class1, std_class1, num_points)  # shape (20,)\n",
        "\n",
        "# Combine data\n",
        "x = np.concatenate([class0_data, class1_data])  # shape (40,)\n",
        "y = np.array([0] * num_points + [1] * num_points)  # shape (40,)\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "plt.scatter(class0_data, np.zeros(num_points), color='red', label='Class 0', alpha=0.6, edgecolors='w')\n",
        "plt.scatter(class1_data, np.zeros(num_points), color='blue', label='Class 1', alpha=0.6, edgecolors='w')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.title('Data points')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "id": "OoKS6tEBv2Ip",
        "outputId": "bc59cc75-d634-4373-910b-c17b570d60b5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Initial guess\n",
        "a = 0\n",
        "b = 0\n",
        "learning_rate = 0.05\n",
        "num_iterations = 10000\n",
        "\n",
        "# Sigmoid function\n",
        "def sigmoid(z):\n",
        "    return 1 / (1 + np.exp(-z))\n",
        "\n",
        "# Store loss values\n",
        "loss_values = []\n",
        "\n",
        "# Training loop\n",
        "for i in range(num_iterations):\n",
        "    # Forward pass\n",
        "    y_pred = a * x + b  # shape (40,)\n",
        "    h_pred = sigmoid(y_pred)  # shape (40,)\n",
        "\n",
        "    # Compute loss (cross entropy)\n",
        "    loss = np.mean(-y*np.log(h_pred) - (1 - y)*np.log(1 - h_pred))\n",
        "\n",
        "    loss_values.append(loss)\n",
        "\n",
        "    # Backward pass (compute gradients)\n",
        "    da = np.mean((h_pred - y) * x)  # scalar\n",
        "    db = np.mean((h_pred - y) * 1)\n",
        "\n",
        "    # Update parameters\n",
        "    a -= learning_rate * da\n",
        "    b -= learning_rate * db\n",
        "\n",
        "    # Print loss every several iterations\n",
        "    if i % 1000 == 0:\n",
        "        print(f'Iteration {i}: Loss = {loss}')\n",
        "\n",
        "decision_boundary_x = np.linspace(1, 6, 400)\n",
        "decision_boundary_y = sigmoid((a * decision_boundary_x + b))\n",
        "\n",
        "plt.figure(figsize=(6, 4))\n",
        "plt.scatter(class0_data, np.zeros(num_points), color='red', label='Class 0', alpha=0.6, edgecolors='w')\n",
        "plt.scatter(class1_data, np.zeros(num_points), color='blue', label='Class 1', alpha=0.6, edgecolors='w')\n",
        "\n",
        "plt.plot(decision_boundary_x, decision_boundary_y, color='c')\n",
        "\n",
        "plt.xlabel('x')\n",
        "plt.title('Optimized function for 1D classification')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 584
        },
        "id": "k-B4NsOdzO59",
        "outputId": "2e139f05-bb31-4a3b-9bde-a56916e8e1d0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0: Loss = 0.6931471805599453\n",
            "Iteration 1000: Loss = 0.15238702261169718\n",
            "Iteration 2000: Loss = 0.08887242077824188\n",
            "Iteration 3000: Loss = 0.06423030272704132\n",
            "Iteration 4000: Loss = 0.05095931876396744\n",
            "Iteration 5000: Loss = 0.04258300998864643\n",
            "Iteration 6000: Loss = 0.036775427198827364\n",
            "Iteration 7000: Loss = 0.03249067056159806\n",
            "Iteration 8000: Loss = 0.029186708477152323\n",
            "Iteration 9000: Loss = 0.026553580603758814\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "5CeFsIwvzUuH"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}