linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"darkgrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data\n",
    "In this example, we are going to use a dataset with one feature *x* and target *y* that we need to predict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1</td>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-4</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x  y\n",
       "0  6  6\n",
       "1  0  3\n",
       "2  4  5\n",
       "3 -1 -3\n",
       "4  2  0\n",
       "5  6  7\n",
       "6  4  4\n",
       "7 -4 -1\n",
       "8 -3  5\n",
       "9  2  0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [\n",
    "    (6, 6),\n",
    "    (0, 3),\n",
    "    (4, 5),\n",
    "    (-1, -3),\n",
    "    (2, 0),\n",
    "    (6, 7),\n",
    "    (4, 4),\n",
    "    (-4, -1),\n",
    "    (-3, 5),\n",
    "    (2, 0)\n",
    "]\n",
    "data = pd.DataFrame(data, columns=['x', 'y'])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us visualise the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='x', ylabel='y'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "sns.scatterplot(data=data, x='x', y='y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "We will implement the batch gradient descent. For the loss function we are going to use MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse(y_true: pd.Series, y_pred: pd.Series) -> float:\n",
    "    return ((y_true - y_pred) ** 2).sum() / len(y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the cell below we declare parameters of the algorithm.\n",
    "* *Iterations* specify how many times we are going to update weights. In most cases, the higher the number of iterations is, the more precisely the algorithm converges.\n",
    "* *Learning rate* (usually denoted as *alpha*) influences the scale of each update. Usually, with lower values of alpha, the algorithm converges more precisely but it takes more time for training. However, by choosing a very large value for the rate, the algorithm can highly jump over the local minima. As a result, the algorithm will not converge correctly.\n",
    "* *Batch size* allows to use several objects on each iteration for weights update. If we choose batch size to be equal to 1, then gradient descent is called stochastic.\n",
    "* *w* and *b* are initial values of weights. There exist several strategies for their initialization. In the example, we are going to assign small random values to them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 1000\n",
    "batch_size = 5\n",
    "alpha = 0.001\n",
    "w, b = np.random.rand(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this dictionary will be used for tracking parameters of each iteration\n",
    "history = {\n",
    "    'iteration': [],\n",
    "    'w': [],\n",
    "    'b': [],\n",
    "    'loss': []\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "for iteration in range(iterations):\n",
    "\n",
    "    # choosing object in batch\n",
    "    batch_indices = np.random.randint(0, len(data), batch_size)\n",
    "    batch_data = data.loc[batch_indices]\n",
    "\n",
    "    x, y, n = batch_data['x'], batch_data['y'], len(batch_data)\n",
    "    y_hat = w * batch_data['x'] + b # prediction\n",
    "\n",
    "    # weights update\n",
    "    w -= alpha * 2 / n * (x * (y_hat - y)).sum()\n",
    "    b -= alpha * 2 / n * (y_hat - y).sum()\n",
    "\n",
    "    loss = mse(data['y'], w * data['x'] + b) # total loss\n",
    "\n",
    "    # saving parameters on current iteration\n",
    "    history['iteration'].append(iteration)\n",
    "    history['w'].append(w)\n",
    "    history['b'].append(b)\n",
    "    history['loss'].append(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis of parameters\n",
    "Let us draw several plots of parameters that we tracked throughout the training process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Weights on each iteration')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 9))\n",
    "sns.lineplot(x=history['iteration'], y=history['b'], color='red', label='b')\n",
    "sns.lineplot(x=history['iteration'], y=history['w'], color='orange', label='w')\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Value')\n",
    "plt.title('Weights on each iteration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss value on each iteration')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 9))\n",
    "sns.lineplot(x=history['iteration'], y=history['loss'], color='red')\n",
    "plt.xlabel('Iteration')\n",
    "plt.ylabel('Loss')\n",
    "plt.title('Loss value on each iteration')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During the training process, the loss value should normally decrease with each iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression equation: y = 0.647 * x + 1.293\n",
      "Total loss: 6.685\n"
     ]
    }
   ],
   "source": [
    "print(f'Linear regression equation: y = {w:.3f} * x + {b:.3f}')\n",
    "print(f'Total loss: {loss:.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression line\n",
    "Since we have trained a model on a dataset with only one feature, it is easy to visualise the results in the form of a regression line on 2D-plane. If we had more than 2 features, then it would have been problematic.\n",
    "\n",
    "The closer the line fits to all of the points, the better our model is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "regression_line = pd.DataFrame(\n",
    "    data=[(x, w * x + b) for x in np.linspace(data.min().min(), data.max().max(), 500)],\n",
    "    columns=['x', 'y']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Fitting line of linear regression')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "sns.scatterplot(data=data, x='x', y='y')\n",
    "sns.scatterplot(data=regression_line, x='x', y='y', marker='x', color='orange')\n",
    "plt.title('Fitting line of linear regression')"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}