SECOND_ORDER_ALGORTHMS.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e1289435",
   "metadata": {},
   "source": [
    "# Importing Liabraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b78a412d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import preprocessing\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54e4056d",
   "metadata": {},
   "source": [
    "# Loading Dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "28b765e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       area  bedrooms   price\n",
      "0    1056.0         2   39.07\n",
      "1    2600.0         5  120.00\n",
      "2    1440.0         2   62.00\n",
      "3    1521.0         3   95.00\n",
      "4    1200.0         2   51.00\n",
      "..      ...       ...     ...\n",
      "294  1425.0         2   70.00\n",
      "295  1450.0         3  100.00\n",
      "296  1847.0         3  105.00\n",
      "297  1100.0         2   45.00\n",
      "298   525.0         1   26.00\n",
      "\n",
      "[299 rows x 3 columns]\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"Bengaluru_House_Data.csv\")\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad21e0c3",
   "metadata": {},
   "source": [
    "# Scaling Factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "88854bf6",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The dataset should be Scaled before Training and dropping the target variable as Price\n",
    "\n",
    "\n",
    "sx=preprocessing.MinMaxScaler()\n",
    "sy=preprocessing.MinMaxScaler()\n",
    "\n",
    "scaled_X= sx.fit_transform(df.drop('price' , axis='columns'))\n",
    "scaled_X\n",
    "\n",
    "scaled_Y= sy.fit_transform(df['price'].values.reshape(df.shape[0],1))\n",
    "scaled_Y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d563c9f9",
   "metadata": {},
   "source": [
    "# Newton Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e6fa3ef2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Newton Method Weights: [0.87524708 0.54626896]\n",
      "Newton Method Bias: -0.1938958723551476\n",
      "Newton Method Final Cost: 0.016199148045335926\n"
     ]
    }
   ],
   "source": [
    "def newton_method(X, y_true, epochs, learning_rate=0.01):\n",
    "    number = X.shape[1]\n",
    "    w = np.ones(shape=(number,))\n",
    "    b = 0\n",
    "    \n",
    "    def objective_function(w, b, X, y_true):\n",
    "        y_pred = np.dot(X, w) + b\n",
    "        return np.mean((y_true - y_pred) ** 2)\n",
    "    \n",
    "    def gradient(w, b, X, y_true):\n",
    "        y_pred = np.dot(X, w) + b\n",
    "        w_grad = -(2 / X.shape[0]) * np.dot(X.T, (y_true - y_pred))\n",
    "        b_grad = -(2 / X.shape[0]) * np.sum(y_true - y_pred)\n",
    "        return w_grad, b_grad\n",
    "    \n",
    "    def hessian(X):\n",
    "        return (2 / X.shape[0]) * np.dot(X.T, X)\n",
    "    \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    for epoch in range(epochs):\n",
    "        w_grad, b_grad = gradient(w, b, X, y_true)\n",
    "        H = hessian(X)\n",
    "        w_hessian_inv = np.linalg.inv(H)\n",
    "        \n",
    "        # Update weights and bias using Newton's method\n",
    "        w -= learning_rate * np.dot(w_hessian_inv, w_grad)\n",
    "        b -= learning_rate * b_grad\n",
    "        \n",
    "        # Calculate cost\n",
    "        cost = objective_function(w, b, X, y_true)\n",
    "        if epoch % 10 == 0:\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(epoch)\n",
    "    \n",
    "    return w, b, cost, cost_list, epoch_list\n",
    "\n",
    "# Example usage\n",
    "w_newton, b_newton, cost_newton, cost_list_newton, epoch_list_newton = newton_method(scaled_X, scaled_Y.reshape(-1,), epochs=100)\n",
    "print(\"Newton Method Weights:\", w_newton)\n",
    "print(\"Newton Method Bias:\", b_newton)\n",
    "print(\"Newton Method Final Cost:\", cost_newton)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9644307f",
   "metadata": {},
   "source": [
    "# Broyden-Fletcher-Goldfarb-Shanno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cef49398",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BFGS Weights: [0.51664705 0.17197836]\n",
      "BFGS Bias: -0.03585552849775953\n",
      "BFGS Final Cost: 0.006220640675080779\n"
     ]
    }
   ],
   "source": [
    "def objective_function(w_b, X, y_true):\n",
    "    w = w_b[:-1]\n",
    "    b = w_b[-1]\n",
    "    y_pred = np.dot(X, w) + b\n",
    "    return np.mean((y_true - y_pred) ** 2)\n",
    "\n",
    "def gradient(w_b, X, y_true):\n",
    "    w = w_b[:-1]\n",
    "    b = w_b[-1]\n",
    "    y_pred = np.dot(X, w) + b\n",
    "    w_grad = -(2 / X.shape[0]) * np.dot(X.T, (y_true - y_pred))\n",
    "    b_grad = -(2 / X.shape[0]) * np.sum(y_true - y_pred)\n",
    "    return np.concatenate([w_grad, [b_grad]])\n",
    "\n",
    "def bfgs_optimization(X, y_true):\n",
    "    number = X.shape[1]\n",
    "    w_b_initial = np.ones(number + 1)\n",
    "    result = minimize(\n",
    "        fun=objective_function,\n",
    "        x0=w_b_initial,\n",
    "        args=(X, y_true),\n",
    "        jac=gradient,\n",
    "        method='BFGS'\n",
    "    )\n",
    "    w_b_opt = result.x\n",
    "    w = w_b_opt[:-1]\n",
    "    b = w_b_opt[-1]\n",
    "    cost = result.fun\n",
    "    return w, b, cost\n",
    "\n",
    "# Example usage\n",
    "w_bfgs, b_bfgs, cost_bfgs = bfgs_optimization(scaled_X, scaled_Y.reshape(-1,))\n",
    "print(\"BFGS Weights:\", w_bfgs)\n",
    "print(\"BFGS Bias:\", b_bfgs)\n",
    "print(\"BFGS Final Cost:\", cost_bfgs)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b59a5513",
   "metadata": {},
   "source": [
    "# Limited-memory Broyden-Fletcher-Goldfarb-Shanno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ec840154",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L-BFGS Weights: [0.51663725 0.1719845 ]\n",
      "L-BFGS Bias: -0.03585320005765706\n",
      "L-BFGS Final Cost: 0.0062206406700436295\n"
     ]
    }
   ],
   "source": [
    "def lbfgs_optimization(X, y_true):\n",
    "    number = X.shape[1]\n",
    "    w_b_initial = np.ones(number + 1)\n",
    "    result = minimize(\n",
    "        fun=objective_function,\n",
    "        x0=w_b_initial,\n",
    "        args=(X, y_true),\n",
    "        jac=gradient,\n",
    "        method='L-BFGS-B'\n",
    "    )\n",
    "    w_b_opt = result.x\n",
    "    w = w_b_opt[:-1]\n",
    "    b = w_b_opt[-1]\n",
    "    cost = result.fun\n",
    "    return w, b, cost\n",
    "\n",
    "# Example usage\n",
    "w_lbfgs, b_lbfgs, cost_lbfgs = lbfgs_optimization(scaled_X, scaled_Y.reshape(-1,))\n",
    "print(\"L-BFGS Weights:\", w_lbfgs)\n",
    "print(\"L-BFGS Bias:\", b_lbfgs)\n",
    "print(\"L-BFGS Final Cost:\", cost_lbfgs)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a84631",
   "metadata": {},
   "source": [
    "# Comparing 3 Algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c4ae6aa3",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Newton Method Final Cost: 0.0162\n",
      "BFGS Final Cost: 0.0062\n",
      "L-BFGS Final Cost: 0.0062\n"
     ]
    }
   ],
   "source": [
    "plt.figure(figsize=(4,4))\n",
    "plt.plot(epoch_list_newton, cost_list_newton, label='Newton Method', color='blue')\n",
    "plt.axhline(y=cost_bfgs, color='green', linestyle='--', label='BFGS')\n",
    "plt.axhline(y=cost_lbfgs, color='red', linestyle='--', label='L-BFGS')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost over Epochs for Different Optimization Algorithms')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "\n",
    "# Display final costs for comparison\n",
    "print(f\"Newton Method Final Cost: {cost_newton:.4f}\")\n",
    "print(f\"BFGS Final Cost: {cost_bfgs:.4f}\")\n",
    "print(f\"L-BFGS Final Cost: {cost_lbfgs:.4f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a9d35bee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}