ml_assignment1_linearregression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a24de7c-aa1b-4829-8d04-34f072600edd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "53f380fb-7d55-4e72-a53f-d8b00919acfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([9.1, 8. , 9.1, 8.4, 6.9]),\n",
       " array([0.99523, 0.99007, 0.99769, 0.99386, 0.99508]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linearX_np = np.loadtxt(\"linearX.csv\")\n",
    "linearY_np = np.loadtxt(\"linearY.csv\")\n",
    "\n",
    "# Confirm successful loading by displaying the first few values\n",
    "linearX_np[:5], linearY_np[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "87b9855b-507f-4427-9722-0e4bbd33912b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 5 normalized X values: [ 0.60239429 -0.03598116  0.60239429  0.19615537 -0.67435661]\n",
      "First 5 normalized Y values: [-0.67945662 -3.20157458  0.52294845 -1.34908871 -0.752774  ]\n"
     ]
    }
   ],
   "source": [
    "# Normalize the dataset\n",
    "linearX_np = (linearX_np - np.mean(linearX_np)) / np.std(linearX_np)\n",
    "linearY_np = (linearY_np - np.mean(linearY_np)) / np.std(linearY_np)\n",
    "\n",
    "# Display normalized data to confirm\n",
    "print(\"First 5 normalized X values:\", linearX_np[:5])\n",
    "print(\"First 5 normalized Y values:\", linearY_np[:5])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ff59925a-f6e1-4222-b15a-50d646bd6d71",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize parameters\n",
    "theta_0 = 0  # Intercept\n",
    "theta_1 = 0  # Slope\n",
    "learning_rate = 0.1\n",
    "num_iterations = 100\n",
    "\n",
    "# Compute cost function\n",
    "def compute_cost(theta_0, theta_1, X, Y):\n",
    "    m = len(Y)\n",
    "    predictions = theta_0 + theta_1 * X\n",
    "    cost = (1 / (2 * m)) * np.sum((predictions - Y) ** 2)\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "20d1d3da-40e9-4a00-892a-c07886b5cec9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0: Cost = 0.4592346067458747\n",
      "Iteration 10: Cost = 0.3065740213428849\n",
      "Iteration 20: Cost = 0.28801405808175157\n",
      "Iteration 30: Cost = 0.2857575998391391\n",
      "Iteration 40: Cost = 0.285483267194779\n",
      "Iteration 50: Cost = 0.2854499147496327\n",
      "Iteration 60: Cost = 0.2854458598709294\n",
      "Iteration 70: Cost = 0.2854453668923419\n",
      "Iteration 80: Cost = 0.28544530695765447\n",
      "Iteration 90: Cost = 0.28544529967099563\n",
      "Final values: theta_0 = -5.9678685604414e-14 , theta_1 = 0.6550470269268625\n"
     ]
    }
   ],
   "source": [
    "# Perform Batch Gradient Descent\n",
    "m = len(linearX_np)\n",
    "cost_history = []\n",
    "\n",
    "for i in range(num_iterations):\n",
    "    predictions = theta_0 + theta_1 * linearX_np\n",
    "    error = predictions - linearY_np\n",
    "\n",
    "    # Compute gradients\n",
    "    gradient_theta_0 = (1 / m) * np.sum(error)\n",
    "    gradient_theta_1 = (1 / m) * np.sum(error * linearX_np)\n",
    "\n",
    "    # Update parameters\n",
    "    theta_0 -= learning_rate * gradient_theta_0\n",
    "    theta_1 -= learning_rate * gradient_theta_1\n",
    "\n",
    "    # Store cost\n",
    "    cost = compute_cost(theta_0, theta_1, linearX_np, linearY_np)\n",
    "    cost_history.append(cost)\n",
    "\n",
    "    # Print progress every 10 iterations\n",
    "    if i % 10 == 0:\n",
    "        print(f\"Iteration {i}: Cost = {cost}\")\n",
    "\n",
    "# Final parameters\n",
    "print(\"Final values: theta_0 =\", theta_0, \", theta_1 =\", theta_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e4bad2ad-7f46-4299-b232-ee071aaf3a51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Plot the cost function vs iterations\n",
    "plt.plot(range(iterations), cost_history, color=\"blue\", label=\"Cost Function\")\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.title(\"Cost Function vs Iterations\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c2372d5e-9643-40dd-8fbc-c9dd7e60eee4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the dataset and the fitted line\n",
    "plt.scatter(linearX_np, linearY_np, color=\"blue\", label=\"Data Points\")\n",
    "plt.plot(linearX_np, theta_0 + theta_1 * linearX_np, color=\"red\", label=\"Fitted Line\")\n",
    "plt.xlabel(\"X (Normalized)\")\n",
    "plt.ylabel(\"Y (Normalized)\")\n",
    "plt.title(\"Dataset and Fitted Line\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "06bbe58c-e261-451c-9946-f715acb11144",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Function to perform gradient descent for a given learning rate\n",
    "def gradient_descent(X, Y, lr, iterations=50):\n",
    "    theta_0, theta_1 = 0, 0\n",
    "    m = len(X)\n",
    "    cost_history = []\n",
    "\n",
    "    for i in range(iterations):\n",
    "        predictions = theta_0 + theta_1 * X\n",
    "        error = predictions - Y\n",
    "        \n",
    "        # Compute gradients\n",
    "        gradient_theta_0 = (1 / m) * np.sum(error)\n",
    "        gradient_theta_1 = (1 / m) * np.sum(error * X)\n",
    "        \n",
    "        # Update parameters\n",
    "        theta_0 -= lr * gradient_theta_0\n",
    "        theta_1 -= lr * gradient_theta_1\n",
    "        \n",
    "        # Compute and store the cost\n",
    "        cost = compute_cost(theta_0, theta_1, X, Y)\n",
    "        cost_history.append(cost)\n",
    "\n",
    "    return cost_history\n",
    "\n",
    "# Test for different learning rates\n",
    "learning_rates = [0.005, 0.5, 5]\n",
    "iterations = 50\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "for lr in learning_rates:\n",
    "    cost_history = gradient_descent(linearX_np, linearY_np, lr, iterations)\n",
    "    plt.plot(range(iterations), cost_history, label=f\"lr = {lr}\")\n",
    "\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Cost\")\n",
    "plt.title(\"Cost Function vs Iterations for Different Learning Rates\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2c47cc9a-4a8f-4dc2-b80c-5a6358de3603",
   "metadata": {},
   "outputs": [],
   "source": [
    "def stochastic_gradient_descent(X, Y, lr, iterations=50):\n",
    "    theta_0, theta_1 = 0, 0\n",
    "    m = len(X)\n",
    "    cost_history = []\n",
    "\n",
    "    for i in range(iterations):\n",
    "        for j in range(m):  # Loop through each sample\n",
    "            x_sample = X[j]\n",
    "            y_sample = Y[j]\n",
    "\n",
    "            # Compute prediction and error for one sample\n",
    "            prediction = theta_0 + theta_1 * x_sample\n",
    "            error = prediction - y_sample\n",
    "\n",
    "            # Update parameters\n",
    "            theta_0 -= lr * error\n",
    "            theta_1 -= lr * error * x_sample\n",
    "\n",
    "        # Compute cost for the entire dataset after each iteration\n",
    "        cost = compute_cost(theta_0, theta_1, X, Y)\n",
    "        cost_history.append(cost)\n",
    "\n",
    "    return cost_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9458723-bbe7-46cb-aacc-bd0fee595b31",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mini_batch_gradient_descent(X, Y, lr, batch_size=10, iterations=50):\n",
    "    theta_0, theta_1 = 0, 0\n",
    "    m = len(X)\n",
    "    cost_history = []\n",
    "\n",
    "    for i in range(iterations):\n",
    "        # Shuffle data\n",
    "        indices = np.random.permutation(m)\n",
    "        X_shuffled = X[indices]\n",
    "        Y_shuffled = Y[indices]\n",
    "\n",
    "        # Process mini-batches\n",
    "        for start in range(0, m, batch_size):\n",
    "            end = start + batch_size\n",
    "            X_batch = X_shuffled[start:end]\n",
    "            Y_batch = Y_shuffled[start:end]\n",
    "\n",
    "            # Compute predictions and error for the batch\n",
    "            predictions = theta_0 + theta_1 * X_batch\n",
    "            error = predictions - Y_batch\n",
    "\n",
    "            # Update parameters using batch\n",
    "            gradient_theta_0 = (1 / len(X_batch)) * np.sum(error)\n",
    "            gradient_theta_1 = (1 / len(X_batch)) * np.sum(error * X_batch)\n",
    "            theta_0 -= lr * gradient_theta_0\n",
    "            theta_1 -= lr * gradient_theta_1\n",
    "\n",
    "        # Compute cost for the entire dataset after each iteration\n",
    "        cost = compute_cost(theta_0, theta_1, X, Y)\n",
    "        cost_history.append(cost)\n",
    "\n",
    "    return cost_history\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}