lab4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d79a5130-01f0-4e51-bd71-3aacf69d00fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Generate synthetic data\n",
    "np.random.seed(42)\n",
    "X = np.random.rand(100, 1) * 10  # 100 data points\n",
    "y = 2.5 * X + np.random.randn(100, 1)  # Linear relation with noise\n",
    "\n",
    "# Delta Learning Rule implementation for Batch Gradient Descent\n",
    "class BatchGradientDescent:\n",
    "    def __init__(self, learning_rate=0.01, n_iterations=1000):\n",
    "        self.learning_rate = learning_rate\n",
    "        self.n_iterations = n_iterations\n",
    "        self.weights = None\n",
    "        self.bias = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        m, n = X.shape\n",
    "        self.weights = np.zeros((n, 1))\n",
    "        self.bias = 0\n",
    "        self.loss_history = []\n",
    "\n",
    "        for _ in range(self.n_iterations):\n",
    "            y_pred = X.dot(self.weights) + self.bias\n",
    "            error = y_pred - y\n",
    "            loss = np.mean(error ** 2)\n",
    "            self.loss_history.append(loss)\n",
    "\n",
    "            # Gradient calculation\n",
    "            dw = (1/m) * X.T.dot(error)\n",
    "            db = (1/m) * np.sum(error)\n",
    "\n",
    "            # Update weights and bias\n",
    "            self.weights -= self.learning_rate * dw\n",
    "            self.bias -= self.learning_rate * db\n",
    "\n",
    "        return self.weights, self.bias\n",
    "\n",
    "# Delta Learning Rule implementation for Stochastic Gradient Descent\n",
    "class StochasticGradientDescent:\n",
    "    def __init__(self, learning_rate=0.01, n_iterations=1000):\n",
    "        self.learning_rate = learning_rate\n",
    "        self.n_iterations = n_iterations\n",
    "        self.weights = None\n",
    "        self.bias = None\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        m, n = X.shape\n",
    "        self.weights = np.zeros((n, 1))\n",
    "        self.bias = 0\n",
    "        self.loss_history = []\n",
    "\n",
    "        for _ in range(self.n_iterations):\n",
    "            for i in range(m):\n",
    "                xi = X[i]\n",
    "                yi = y[i]\n",
    "                \n",
    "                # Prediction\n",
    "                y_pred = xi.dot(self.weights) + self.bias\n",
    "                error = y_pred - yi\n",
    "                loss = np.mean(error ** 2)\n",
    "                self.loss_history.append(loss)\n",
    "\n",
    "                # Gradient calculation\n",
    "                dw = xi.T.dot(error)\n",
    "                db = np.sum(error)\n",
    "\n",
    "                # Update weights and bias\n",
    "                self.weights -= self.learning_rate * dw\n",
    "                self.bias -= self.learning_rate * db\n",
    "\n",
    "        return self.weights, self.bias\n",
    "\n",
    "# Instantiate and train both models\n",
    "batch_model = BatchGradientDescent(learning_rate=0.01, n_iterations=1000)\n",
    "batch_weights, batch_bias = batch_model.fit(X, y)\n",
    "\n",
    "sgd_model = StochasticGradientDescent(learning_rate=0.01, n_iterations=1000)\n",
    "sgd_weights, sgd_bias = sgd_model.fit(X, y)\n",
    "\n",
    "# Plotting the loss history\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(batch_model.loss_history, label='Batch Gradient Descent Loss', color='blue')\n",
    "plt.plot(sgd_model.loss_history, label='Stochastic Gradient Descent Loss', color='orange', alpha=0.6)\n",
    "plt.title('Loss History: Batch vs Stochastic Gradient Descent')\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Loss')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "54790e93-eae8-4098-9372-a3d9eb1e3b2d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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