3.4_Logistic_Regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/rccrdmr/MAT422-Mathematics-for-DataScience/blob/main/3.4_Logistic_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# 3.4 Logistic Regression"
      ],
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        "id": "eUGYuwXQ0EkM"
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      "cell_type": "markdown",
      "source": [
        "Logistic Regression is a binary classification model that uses a logistic function to predict the probability of a binary outcome (0 or 1). This approach can be extended to multiple classes and is widely used in tasks like image classification and text categorization.\n",
        "\n",
        "### Problem Setup\n",
        "\n",
        "Given input data in the form $\\{(\\alpha_i, b_i) : i = 1, \\ldots, n\\}$:\n",
        "- **Features**: $\\alpha_i \\in \\mathbb{R}^d$\n",
        "- **Labels**: $b_i \\in \\{0,1\\}$\n",
        "\n",
        "We represent these as:\n",
        "- Matrix $A \\in \\mathbb{R}^{n \\times d}$ with rows $\\alpha_j^T$, and\n",
        "- Vector $b = (b_1, \\ldots, b_n)^T \\in \\{0,1\\}^n$\n",
        "\n",
        "The goal is to find a function that approximates the probability of $b_i = 1$ as a function of $\\alpha_i$.\n",
        "\n",
        "### Model\n",
        "\n",
        "The logistic regression model represents the **log-odds** of class 1 as a linear function of the features:\n",
        "\n",
        "$$\n",
        "\\log \\frac{p(\\alpha; x)}{1 - p(\\alpha; x)} = \\alpha^T x\n",
        "$$\n",
        "\n",
        "Rearranging, we get the **probability function**:\n",
        "\n",
        "$$\n",
        "p(\\alpha; x) = \\sigma(\\alpha^T x)\n",
        "$$\n",
        "\n",
        "where the **sigmoid function** $\\sigma(t)$ maps values to a range between 0 and 1:\n",
        "\n",
        "$$\n",
        "\\sigma(t) = \\frac{1}{1 + e^{-t}}\n",
        "$$\n",
        "\n",
        "### Loss Function: Cross-Entropy\n",
        "\n",
        "To optimize the model, we use **cross-entropy loss**. This measures how well the predicted probabilities align with the true labels:\n",
        "\n",
        "$$\n",
        "\\ell(x; A, b) = -\\frac{1}{n} \\sum_{i=1}^n \\left(b_i \\log(\\sigma(\\alpha_i^T x)) + (1 - b_i) \\log(1 - \\sigma(\\alpha_i^T x))\\right)\n",
        "$$\n",
        "\n",
        "### Gradient Calculation\n",
        "\n",
        "To minimize the loss function, we calculate its **gradient**:\n",
        "\n",
        "$$\n",
        "\\nabla_x \\ell(x; A, b) = -\\frac{1}{n} \\sum_{i=1}^n (b_i - \\sigma(\\alpha_i^T x)) \\alpha_i\n",
        "$$\n",
        "\n",
        "### Gradient Descent Update Rule\n",
        "\n",
        "Using **gradient descent**, we iteratively update $x$ in the direction of the negative gradient. Let $\\beta$ be the learning rate:\n",
        "\n",
        "$$\n",
        "x_{k+1} = x_k + \\beta \\left(b_i - \\sigma(\\alpha_i^T x)\\right) \\alpha_i\n",
        "$$\n",
        "\n",
        "In **stochastic gradient descent** (SGD), we select a random sample $I$ to update as follows:\n",
        "\n",
        "$$\n",
        "x_{k+1} = x_k + \\beta (b_I - \\sigma(\\alpha_I^T x_k)) \\alpha_I\n",
        "$$\n",
        "\n",
        "### Summary\n",
        "\n",
        "1. **Model**: Logistic regression models probabilities with a sigmoid function.\n",
        "2. **Optimization**: We minimize cross-entropy loss.\n",
        "3. **Gradient Descent**: Update parameters using the gradient to minimize the loss iteratively.\n",
        "\n",
        "This structured approach provides a clear view of logistic regression, its components, and its optimization process.\n"
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "## Logistic Regression Example: Predicting Insurance Subscription"
      ],
      "metadata": {
        "id": "8UUjP-9Qzvbb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This example demonstrates the core concepts of logistic regression:\n",
        "- Logit Function\n",
        "- Sigmoid Function\n",
        "- Cross-Entropy Loss\n",
        "- Gradient Descent\n",
        "- Scikit-Learn Logistic Regression Demo\n",
        "\n",
        "We'll use a dataset where the goal is to predict whether a customer will subscribe to an insurance service based on their age."
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "### Step 1: Logit Function"
      ],
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    },
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      "cell_type": "markdown",
      "source": [
        "The logit function transforms probabilities into a linear combination of features. This is useful for logistic regression, as it allows us to model the relationship between features and the probability of an event.\n",
        "\n",
        "The logit function is defined as:\n",
        "\n",
        "$$\\text{logit}(p) = \\log \\left( \\frac{p}{1-p} \\right) = \\alpha^T x$$\n",
        "\n",
        "where:\n",
        "- $p$ is the probability\n",
        "- $\\alpha$ is the vector of parameters\n",
        "- $x$ is the vector of features\n",
        "\n",
        "The regression model is defined as:\n",
        "\n",
        "$$\\hat{p} = \\sigma(\\alpha^T x)$$\n",
        "\n",
        "where:\n",
        "- $\\hat{p}$ is the predicted probability\n",
        "- $\\sigma$ is the sigmoid function"
      ],
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    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def logit(p):\n",
        "    \"\"\"Logit Function\"\"\"\n",
        "    return np.log(p / (1 - p))\n",
        "\n",
        "# Initial probabilities\n",
        "probabilities = np.array([0.2, 0.5, 0.7, 0.9])\n",
        "logit_values = logit(probabilities)\n",
        "print(\"Logit values:\", logit_values)\n"
      ],
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      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Logit values: [-1.38629436  0.          0.84729786  2.19722458]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 2: Sigmoid Function\n"
      ],
      "metadata": {
        "id": "77nMwuyLyVot"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The sigmoid function maps values from the real line to a range between 0 and 1, transforming linear combinations into probabilities."
      ],
      "metadata": {
        "id": "S8NX8NBl0Blq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def sigmoid(x):\n",
        "    \"\"\"Sigmoid Function\"\"\"\n",
        "    return 1 / (1 + np.exp(-x))\n",
        "\n",
        "X = np.arange(-10, 10, 0.1)\n",
        "Y = sigmoid(X)\n",
        "plt.figure()\n",
        "plt.plot(X, Y)\n",
        "plt.title('Sigmoid Function')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('sigmoid(x)')\n",
        "plt.grid()\n",
        "plt.show()\n"
      ],
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      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 3: Cross-Entropy Loss\n"
      ],
      "metadata": {
        "id": "fa8zrsj5yb41"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cross-entropy loss measures the difference between predicted probabilities and true labels. Let's define the cross-entropy loss function and compute it for example predictions and true labels."
      ],
      "metadata": {
        "id": "piaiX7ly0E8K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def cross_entropy_loss(y, p):\n",
        "    \"\"\"Cross-Entropy Loss\"\"\"\n",
        "    return -np.mean(y * np.log(p) + (1 - y) * np.log(1 - p))\n",
        "\n",
        "# Example true labels and predictions\n",
        "y = np.array([0, 1, 1, 0])\n",
        "p = np.array([0.1, 0.9, 0.8, 0.4])\n",
        "cel_y_p = cross_entropy_loss(y, p)\n",
        "print(\"Cross-Entropy Loss:\", cel_y_p)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RxVoeuzKybCN",
        "outputId": "21807e50-f215-4a05-fc97-d9f801146992"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Cross-Entropy Loss: 0.23617255159896325\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 4: Gradient Descent"
      ],
      "metadata": {
        "id": "mNBaeDrF0LzO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Gradient descent minimizes the loss function by iteratively updating model parameters (weights and bias). Here’s a simple implementation for logistic regression.\n"
      ],
      "metadata": {
        "id": "sfVKOLvqyf7-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Initialize weights and bias\n",
        "w = 0.1\n",
        "b = 0\n",
        "learning_rate = 0.01\n",
        "iterations = 100\n",
        "\n",
        "# Load data from CSV\n",
        "import pandas as pd\n",
        "data = pd.read_csv(\"insurance_data.csv\")\n",
        "X_train = data.age.to_numpy()\n",
        "y_train = data.bought_insurance.to_numpy()\n",
        "\n",
        "# Gradient Descent Loop\n",
        "for i in range(iterations):\n",
        "    linear_model = w * X_train + b\n",
        "    predictions = sigmoid(linear_model)\n",
        "\n",
        "    # Calculate gradients\n",
        "    dw = np.dot(X_train, (predictions - y_train)) / len(X_train)\n",
        "    db = np.sum(predictions - y_train) / len(X_train)\n",
        "\n",
        "    # Update weights and bias\n",
        "    w -= learning_rate * dw\n",
        "    b -= learning_rate * db\n",
        "\n",
        "    if i % 10 == 0:\n",
        "        loss = cross_entropy_loss(y_train, predictions)\n",
        "        print(f\"Iteration {i}: w = {w:.4f}, b = {b:.4f}, loss = {loss:.4f}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "npedZatYygju",
        "outputId": "7c98e0f2-e96b-44e5-d6a3-210a879a62e9"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration 0: w = -0.0237, b = -0.0044, loss = 1.3912\n",
            "Iteration 10: w = 0.1311, b = -0.0147, loss = 0.9256\n",
            "Iteration 20: w = -0.0351, b = -0.0324, loss = 0.7643\n",
            "Iteration 30: w = 0.1588, b = -0.0420, loss = 1.1810\n",
            "Iteration 40: w = 0.0122, b = -0.0598, loss = 1.9083\n",
            "Iteration 50: w = -0.0194, b = -0.0745, loss = 1.4213\n",
            "Iteration 60: w = 0.0444, b = -0.0869, loss = 0.6520\n",
            "Iteration 70: w = -0.0323, b = -0.1025, loss = 1.1641\n",
            "Iteration 80: w = 0.1455, b = -0.1121, loss = 1.0014\n",
            "Iteration 90: w = -0.0001, b = -0.1291, loss = 1.6912\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "jCyxjE9N0IcV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Step 5: Logistic Regression with Scikit-Learn\n"
      ],
      "metadata": {
        "id": "RWMxEhYdyjzW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Now, let's load the dataset and use Scikit-Learn's `LogisticRegression` to fit a logistic model for the insurance subscription prediction. Then, we'll visualize the model's predictions."
      ],
      "metadata": {
        "id": "Kn9HkE4D0Q7x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "# Load data\n",
        "data = pd.read_csv(\"insurance_data.csv\")\n",
        "X_train = data[['age']]\n",
        "y_train = data['bought_insurance']\n",
        "\n",
        "# Raw data\n",
        "plt.figure()\n",
        "plt.scatter(X_train, y_train)\n",
        "plt.title(\"Insurance Raw Data\")\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Insurance Subscription (0/1)\")\n",
        "plt.show()\n",
        "\n",
        "# Train Logistic Regression Model\n",
        "model = LogisticRegression()\n",
        "model.fit(X_train, y_train)\n",
        "print(\"Model Coefficients:\", model.coef_)\n",
        "print(\"Model Intercept:\", model.intercept_)\n",
        "\n",
        "X_test = pd.DataFrame(np.arange(15, 70), columns=['age'])\n",
        "\n",
        "# Calculate probabilities and predictions\n",
        "model_probs = model.predict_proba(X_test)[:, 1]\n",
        "model_preds = model.predict(X_test)\n",
        "\n",
        "# Model Predictions\n",
        "plt.figure()\n",
        "plt.scatter(X_train, y_train, label=\"Raw Data\")\n",
        "plt.plot(X_test['age'], model_probs, color=\"r\", label=\"Sigmoid Function\")\n",
        "plt.plot(X_test['age'], model_preds, color=\"g\", label=\"Model Predictions\")\n",
        "plt.title(\"Insurance Logistic Regression Model\")\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Probability of Subscription\")\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 962
        },
        "id": "8oiYYR2hynBs",
        "outputId": "0c9b7b70-ad73-4e0b-f6d5-a17225f1aa75"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model Coefficients: [[0.13546543]]\n",
            "Model Intercept: [-5.26279121]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "8nQSMsJfyooa"
      }
    }
  ]
}