1.3_Linear_Regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNmbX7IroRAxqU1MBPwvlFF",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/rccrdmr/MAT422-Mathematics-for-DataScience/blob/main/1_3_Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1.3 Linear Regression\n",
        "_______________________________\n",
        "###Topics:\n",
        "* 1.3.1. QR decomposition\n",
        "* 1.3.2. Least-squares problems\n",
        "* 1.3.3. Linear regression"
      ],
      "metadata": {
        "id": "C1apI4O2z3uo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear regression is frequently used in practical applications due to its simplicity. The model depends linearly on its unknown parameters, making it easier to fit and analyze compared to models that are non-linearly related to their parameters. This section introduces QR decomposition, the least-squares problem, and its connection to linear regression.\n"
      ],
      "metadata": {
        "id": "mEEVLbUY1X17"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.3.1. QR Decomposition"
      ],
      "metadata": {
        "id": "-0jSl2Mo0ZJx"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "QR decomposition is a useful method to solve the linear least-squares problem. It begins with the Gram-Schmidt algorithm, which generates an orthonormal basis $\\text{span}(a_1, \\ldots, a_m)$ from a linearly independent set of $\\text{span}(a_1, \\ldots, a_m)$.\n",
        "\n",
        "Let:\n",
        "$$\n",
        "A =\n",
        "\\begin{pmatrix}\n",
        "| & | & & | \\\\\n",
        "a_1 & a_2 & \\cdots & a_m \\\\\n",
        "| & | & & |\n",
        "\\end{pmatrix}\n",
        "\\quad \\text{and} \\quad\n",
        "Q =\n",
        "\\begin{pmatrix}\n",
        "| & | & & | \\\\\n",
        "q_1 & q_2 & \\cdots & q_m \\\\\n",
        "| & | & & |\n",
        "\\end{pmatrix}\n",
        "$$\n",
        "where $A$ and $Q$ are $n \\times m$ matrices. The output of Gram-Schmidt is the QR decomposition:\n",
        "$$\n",
        "A = QR\n",
        "$$\n",
        "where $R$ is an upper triangular matrix containing the coefficients of the linear combination of $q_j$'s that produces $a_i$.\n"
      ],
      "metadata": {
        "id": "9vH7_bfO18QT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.3.2 Least-squares problems"
      ],
      "metadata": {
        "id": "rLXfGYSD0iQR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The least-squares method solves inconsistent linear systems, especially when there are more equations than unknowns. It finds an approximate solution by minimizing the difference between the observed and predicted values. The normal equations, $A^T A x = A^T b$, provide a way to solve this problem."
      ],
      "metadata": {
        "id": "Gg_w5MEA4nJH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Theorem (Normal Equations):**\n",
        "\n",
        "Let $A \\in \\mathbb{R}^{n \\times m}$ be an $n \\times m$ matrix with linearly independent columns, and let $b \\in \\mathbb{R}^n$ be a vector. The solution to the least-squares problem\n",
        "$$\n",
        "\\min_{x \\in \\mathbb{R}^m} \\|Ax - b\\|\n",
        "$$\n",
        "satisfies the normal equations:\n",
        "$$\n",
        "A^T A x = A^T b\n",
        "$$\n"
      ],
      "metadata": {
        "id": "9J9wy6p05oHT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Over-determined system (3x2)\n",
        "A = np.array([[1, 2], [3, 4], [5, 6]])\n",
        "b = np.array([7, 8, 9])\n",
        "\n",
        "# Normal equations: (A^T A) x = A^T b\n",
        "AtA = A.T @ A\n",
        "Atb = A.T @ b\n",
        "\n",
        "# Solving the normal equations\n",
        "x_normal = np.linalg.solve(AtA, Atb)\n",
        "\n",
        "print(\"Solution using normal equations:\", x_normal)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oLfWLZOsCd0z",
        "outputId": "76c693de-7127-460c-d416-e09c4fc62bf0"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Solution using normal equations: [-6.   6.5]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Theorem (Least Squares via QR Decomposition):**\n",
        "\n",
        "Let $A \\in \\mathbb{R}^{n \\times m}$ be an $n \\times m$ matrix with linearly independent columns, let $b \\in \\mathbb{R}^n$ be a vector, and let $A = QR$ be a QR decomposition of $A$, where $Q$ is a $n \\times m$ matrix with $Q^T Q = I_{m \\times m}$ and $R$ is upper triangular. The solution to the least-squares problem\n",
        "$$\n",
        "\\min_{x \\in \\mathbb{R}^m} \\|Ax - b\\|\n",
        "$$\n",
        "satisfies\n",
        "$$\n",
        "R x^* = Q^T b\n",
        "$$\n"
      ],
      "metadata": {
        "id": "F8A-BawF5pZ-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.linalg import qr\n",
        "\n",
        "A = np.array([[1, 2], [3, 4], [5, 6]])\n",
        "b = np.array([7, 8, 9])\n",
        "\n",
        "# QR decomposition\n",
        "Q, R = qr(A)\n",
        "\n",
        "# Solve Rx = Q^T * b using least-squares solution\n",
        "x_qr, residuals, rank, s = np.linalg.lstsq(R, Q.T @ b, rcond=None)\n",
        "\n",
        "print(\"Solution using QR decomposition (least squares):\", x_qr)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NkkmvHdcBrOg",
        "outputId": "71ddcf64-7475-4f80-e67d-dee5227c9eb0"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Solution using QR decomposition (least squares): [-6.   6.5]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1.3.3 Linear Regression"
      ],
      "metadata": {
        "id": "P7OAFky40oPd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Given input data points $\\{(x_i, y_i)\\}_{i=1}^{n}$, where each $x_i = (x_{i1}, \\dots, x_{id})^T$, we aim to fit an affine function to the data. The objective is to find coefficients $\\beta_j$ that minimize the sum of squared residuals:\n",
        "$$\n",
        "\\sum_{i=1}^{n} (y_i - \\hat{y}_i)^2,\n",
        "$$\n",
        "where the predicted values are given by:\n",
        "$$\n",
        "\\hat{y}_i = \\beta_0 + \\sum_{j=1}^{d} \\beta_j x_{ij}.\n",
        "$$\n",
        "\n",
        "This is a least-squares problem, and in matrix form, it can be expressed as:\n",
        "\n",
        "$$\n",
        "y =\n",
        "\\begin{pmatrix}\n",
        "y_1 \\\\\n",
        "y_2 \\\\\n",
        "\\vdots \\\\\n",
        "y_n\n",
        "\\end{pmatrix}, \\quad\n",
        "A =\n",
        "\\begin{pmatrix}\n",
        "1 & x_{11} & \\dots & x_{1d} \\\\\n",
        "1 & x_{21} & \\dots & x_{2d} \\\\\n",
        "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
        "1 & x_{n1} & \\dots & x_{nd}\n",
        "\\end{pmatrix}, \\quad\n",
        "\\beta =\n",
        "\\begin{pmatrix}\n",
        "\\beta_0 \\\\\n",
        "\\beta_1 \\\\\n",
        "\\vdots \\\\\n",
        "\\beta_d\n",
        "\\end{pmatrix}.\n",
        "$$\n",
        "\n",
        "The least-squares problem then becomes:\n",
        "$$\n",
        "\\min_{\\beta} \\| y - A \\beta \\|^2.\n",
        "$$\n",
        "\n",
        "This is exactly the least-squares problem discussed in the previous section and can be solved using the normal equations or QR decomposition."
      ],
      "metadata": {
        "id": "COr-pBJl9QO1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "# Dataset with noise\n",
        "np.random.seed(42)\n",
        "X = np.random.rand(100, 1) * 10\n",
        "y = 4 * X[:, 0] + 7 + np.random.randn(100) * 2\n",
        "\n",
        "# Linear Regression\n",
        "model = LinearRegression()\n",
        "model.fit(X, y)\n",
        "\n",
        "# Coefficients and intercept\n",
        "beta = model.coef_\n",
        "beta_0 = model.intercept_\n",
        "\n",
        "# Predictions\n",
        "y_pred = model.predict(X)\n",
        "\n",
        "# Plot\n",
        "plt.scatter(X, y, color='blue', label='Actual values', alpha=0.6)\n",
        "plt.plot(X, y_pred, color='red', linestyle='-', label='Predicted line')\n",
        "plt.text(1, 35, f\"Coefficients: {np.round(beta, 2)}\", fontsize=10)\n",
        "plt.text(1, 32, f\"Intercept: {round(beta_0, 2)}\", fontsize=10)\n",
        "plt.xlabel('Feature')\n",
        "plt.ylabel('Target')\n",
        "plt.title('Linear Regression: Actual vs Predicted with Residuals')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print(\"Coefficients (β):\", beta)\n",
        "print(\"Intercept (β0):\", beta_0)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 508
        },
        "id": "TRpf9O6KHtL0",
        "outputId": "696b72c8-a1db-4751-d6f5-d5e3e2efd97a"
      },
      "execution_count": 33,
      "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": [
            "Coefficients (β): [3.90804535]\n",
            "Intercept (β0): 7.4301923150935\n"
          ]
        }
      ]
    }
  ]
}