LinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y = mx + c$$\n",
    "Mean squre error: $$\\frac{1}{N} \\sum_{i=1} ^ {n} (y_{i} - (mx_{i} + c))^{2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training:\n",
    "* Initialize slope as zero\n",
    "* Initialize intercept as zero\n",
    "\n",
    "Given a data point:\n",
    "* Predict result by using y = mx + c\n",
    "* Calculate error\n",
    "* Use gradient descent to figure out new weights and bias values\n",
    "* Repeat n times\n",
    "\n",
    "Testing: <br>\n",
    "* Given a data point: Put in the values from the data point into the equation y = mx + c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{dJ}{dm} = \\frac{1}{N}\\sum _{i=1} ^{n} 2x_{i}(\\hat{y} - y_{i})$$\n",
    "\n",
    "$$\\frac{dJ}{dc} = \\frac{1}{N}\\sum _{i=1} ^{n}(\\hat{y} - y_{i})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LinearRegression:\n",
    "    def __init__(self, learning_rate, number_of_iterations):\n",
    "        \"\"\"\n",
    "        Initialize the linear regression model with a learning rate and number of iterations.\n",
    "\n",
    "        Parameters:\n",
    "        - learning_rate: The learning rate for gradient descent.\n",
    "        - number_of_iterations: The number of iterations for gradient descent.\n",
    "        \"\"\"\n",
    "        self.learning_rate = learning_rate \n",
    "        self.number_of_iterations = number_of_iterations\n",
    "        self.slope = None\n",
    "        self.intercept = None\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        \"\"\"\n",
    "        Fit the linear regression model to the training data.\n",
    "\n",
    "        Parameters:\n",
    "        - X: The input features of the training data.\n",
    "        - y: The target values of the training data.\n",
    "        \"\"\"\n",
    "        n_samples, n_features = X.shape\n",
    "        self.slope = np.zeros(n_features)\n",
    "        self.intercept = 0\n",
    "        for _ in range(self.number_of_iterations):\n",
    "            # Perform gradient descent for the specified number of iterations\n",
    "            y_predict = np.dot(X, self.slope) + self.intercept\n",
    "            # Calculate the predicted values based on the current model parameters\n",
    "            dm = (1/n_samples) * np.dot(X.T, (y_predict - y))\n",
    "            # Calculate the derivative of the cost function with respect to the slope\n",
    "            dc = (1/n_samples) * np.sum(y_predict - y)\n",
    "            # Calculate the derivative of the cost function with respect to the intercept\n",
    "            self.slope = self.slope - self.learning_rate * dm\n",
    "            # Update the slope using the gradient descent update rule\n",
    "            self.intercept = self.intercept - self.learning_rate * dc\n",
    "            # Update the intercept using the gradient descent update rule\n",
    "\n",
    "    def predict(self, X):\n",
    "        \"\"\"\n",
    "        Make predictions for the given input data.\n",
    "\n",
    "        Parameters:\n",
    "        - X: The input features of the data points to predict.\n",
    "\n",
    "        Returns:\n",
    "        - y_predict: The predicted target values.\n",
    "        \"\"\"\n",
    "        y_predict = np.dot(X, self.slope) + self.intercept\n",
    "        # Calculate the predicted values based on the learned model parameters\n",
    "        return y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = datasets.make_regression(n_samples=100, n_features=1, noise=20, random_state=4)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure = plt.figure(figsize=(10, 8))\n",
    "plt.scatter(X[:, 0], y, color='b', marker='o', s=30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "regression = LinearRegression(0.1, 1000)\n",
    "regression.fit(X_train, y_train)\n",
    "predictions = regression.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_square_error(y_test, predictions):\n",
    "    return np.mean((y_test - predictions) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "305.77413162286416\n"
     ]
    }
   ],
   "source": [
    "mse = mean_square_error(y_test, predictions)\n",
    "print(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_predicted_line = regression.predict(X)\n",
    "cmap = plt.get_cmap('viridis')\n",
    "fig = plt.figure(figsize=(10, 8))\n",
    "m_1 = plt.scatter(X_train, y_train, color=cmap(0.9), s=10)\n",
    "m_2 = plt.scatter(X_test, y_test, color=cmap(0.5), s=10)\n",
    "plt.plot(X, y_predicted_line, color='black', linewidth=2, label=\"Prediction\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}