Programming Exercise 1 - Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 1: Linear Regression\n",
    "\n",
    "> In this exercise, you will implement linear regression and get to see it work on data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Linear Regression with One Variable\n",
    "\n",
    "> In this part of this exercise, you will implement linear regression with one variable to predict profits for a food truck. Suppose you are the CEO of a restaurant franchise and are considering different cities for opening a new outlet. The chain already has trucks in various cities and you have data for profits and populations from the cities. You would like to use this data to help you select which city to expand to next.\n",
    "The file ex1data1.txt contains the dataset for our linear regression prob- lem. The first column is the population of a city and the second column is the profit of a food truck in that city. A negative value for profit indicates a loss.\n",
    "\n",
    "### 1.1 Plotting the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/ex1data1.txt', sep=',', header=None)\n",
    "df.columns = ['population', 'profit']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(x='population', y='profit', data=df)\n",
    "ax.set(xlabel='Population of City in 10,000s', ylabel='Profit in $10,000s', title='Scatter plot of training data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows that they have a linear relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Gradient Descent\n",
    "\n",
    "Fit the linear regression parameters $\\theta$ to the dataset using gradient descent\n",
    "\n",
    "#### 1.2.1 Update Equations\n",
    "\n",
    "The hypothesis of linear regression is:\n",
    "\n",
    "$$ h_\\theta(x) = \\theta^Tx = \\theta_0 + \\theta_1x_1$$\n",
    "\n",
    "The objective of linear regression is to minimize the cost function (Root Mean Square Error RMSE):\n",
    "\n",
    "$$ J(\\theta) = \\frac{1}{2m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})^2 $$\n",
    "\n",
    "To minimize the cost of $J(\\theta)$ we will use the batch gradient descent algorithm. In batch gradient descent, each iteration performs the update\n",
    "\n",
    "$$ \\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)} $$ \n",
    "\n",
    "(simultaneously update $\\theta_j$ for all $j$). With each step of gradient descent, your parameters $\\theta_j$ come closer to the optimal values that will achieve the lowest cost $J(\\theta)$.\n",
    "\n",
    "#### 1.2.2 Implementation\n",
    "\n",
    "The need to add another dimension to our data to accommodate the $\\theta_0$ intercept term. This allows us to treat $\\theta_0$ as simply another feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = df.shape[0]\n",
    "X = np.hstack((np.ones((m,1)), df.population.values.reshape(-1,1)))\n",
    "y = np.array(df.profit.values).reshape(-1,1)\n",
    "theta = np.zeros(shape=(X.shape[1],1))\n",
    "\n",
    "iterations = 1500\n",
    "alpha = 0.01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.3 Computing the Cost $J(\\theta)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost_one_variable(X, y, theta):\n",
    "    m = y.shape[0]\n",
    "    h = X.dot(theta)\n",
    "    J = (1/(2*m)) * (np.sum((h - y)**2))\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With theta = [0 ; 0]\n",
      "Cost computed = 32.0727338775\n",
      "Expected cost value (approx) 32.07\n"
     ]
    }
   ],
   "source": [
    "J = compute_cost_one_variable(X, y, theta)\n",
    "print('With theta = [0 ; 0]\\nCost computed =', J)\n",
    "print('Expected cost value (approx) 32.07')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With theta = [-1 ; 2]\n",
      "Cost computed = 54.242455082\n",
      "Expected cost value (approx) 54.24\n"
     ]
    }
   ],
   "source": [
    "J = compute_cost_one_variable(X, y, [[-1],[2]])\n",
    "print('With theta = [-1 ; 2]\\nCost computed =', J)\n",
    "print('Expected cost value (approx) 54.24')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2.4 Gradient Descent\n",
    "Gradient descent is a generic optimization algorithm that measures the local gradient of the cost function with regards to the parameter $\\theta$ and goes in the direction of descending gradient.\n",
    "\n",
    "Algorithm:\n",
    "\n",
    "repeat until convergence:\n",
    "$$\\theta_j := \\theta_j - \\alpha \\frac{\\partial}{\\partial\\theta_j}J(\\theta_0, \\theta_1) = \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)} $$ \n",
    "\n",
    "where $j=0,1$; $\\alpha$ is the learning rate (the steps to update J); $\\frac{\\partial}{\\partial\\theta_j}J(\\theta_0, \\theta_1)$ is a derivative.\n",
    "\n",
    "* Learning rate to small: slow gradient descent\n",
    "* Learning rate to large: gradient descent can overshoot the minimum, may fail to converge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta, alpha, num_iters):\n",
    "    m = y.shape[0]\n",
    "    J_history = np.zeros(shape=(num_iters, 1))\n",
    "\n",
    "    for i in range(0, num_iters):\n",
    "        h = X.dot(theta)\n",
    "        diff_hy = h - y\n",
    "\n",
    "        delta = (1/m) * (diff_hy.T.dot(X))\n",
    "        theta = theta - (alpha * delta.T)\n",
    "        J_history[i] = compute_cost_one_variable(X, y, theta)\n",
    "\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta found by gradient descent:\n",
      " [[-3.89459687]\n",
      " [ 1.1929147 ]]\n",
      "Expected theta values (approx)\n",
      " -3.6303\n",
      "  1.1664\n"
     ]
    }
   ],
   "source": [
    "theta, _ = gradient_descent(X, y, theta, alpha, iterations)\n",
    "print('Theta found by gradient descent:\\n', theta)\n",
    "print('Expected theta values (approx)\\n -3.6303\\n  1.1664')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot the linear fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(x='population', y='profit', data=df)\n",
    "plt.plot(X[:,1], X.dot(theta), color='r')\n",
    "ax.set(xlabel='Population of City in 10,000s', ylabel='Profit in $10,000s', title='Training data with linear regression fit');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'For population = 35,000, we predict a profit of 2806.045736412206'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = np.array([1, 3.5]).dot(theta)\n",
    "f'For population = 35,000, we predict a profit of {y_pred[0]*10000}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'For population = 70,000, we predict a profit of 44558.06014738569'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = np.array([1, 7]).dot(theta)\n",
    "f'For population = 70,000, we predict a profit of {y_pred[0]*10000}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Visualizing $J(\\theta)$\n",
    "\n",
    "The cost function $J(\\theta)$ is bowl-shaped and has a global mininum. This minimum is the optimal point for $\\theta_0$ and $\\theta_1$, and each step of gradient descent moves closer to this point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta0_vals = np.linspace(-10, 10, 100)\n",
    "theta1_vals = np.linspace(-1, 4, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "J_vals = np.zeros(shape=(len(theta0_vals), len(theta1_vals)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0, len(theta0_vals)):\n",
    "    for j in range(0, len(theta1_vals)):\n",
    "        J_vals[i,j] = compute_cost_one_variable(X, y, [[theta0_vals[i]], [theta1_vals[j]]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.contour(theta0_vals, theta1_vals, np.transpose(J_vals), levels=np.logspace(-2,3,20))\n",
    "plt.plot(theta[0,0], theta[1,0], marker='x', color='r');\n",
    "plt.xlabel(r'$\\theta_0$');\n",
    "plt.ylabel(r'$\\theta_1$');\n",
    "plt.title('Contour, showing minimum');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Equivalent Code using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/site-packages/sklearn/linear_model/base.py:485: RuntimeWarning: internal gelsd driver lwork query error, required iwork dimension not returned. This is likely the result of LAPACK bug 0038, fixed in LAPACK 3.2.2 (released July 21, 2010). Falling back to 'gelss' driver.\n",
      "  linalg.lstsq(X, y)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(df.population.values.reshape(-1,1), \n",
    "            df.profit.values.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-3.89578088]), array([[ 1.19303364]]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Linear Regression with Multiple Variables\n",
    "\n",
    "> In this part, you will implement linear regression with multiple variables to predict the prices of houses. Suppose you are selling your house and you want to know what a good market price would be. One way to do this is to first collect information on recent houses sold and make a model of housing prices.\n",
    "The file ex1data2.txt contains a training set of housing prices in Portland, Oregon. The first column is the size of the house (in square feet), the second column is the number of bedrooms, and the third column is the price of the house.\n",
    "\n",
    "### 2.1 Feature Normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>house_size</th>\n",
       "      <td>47.0</td>\n",
       "      <td>2000.680851</td>\n",
       "      <td>794.702354</td>\n",
       "      <td>852.0</td>\n",
       "      <td>1432.0</td>\n",
       "      <td>1888.0</td>\n",
       "      <td>2269.0</td>\n",
       "      <td>4478.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bedrooms</th>\n",
       "      <td>47.0</td>\n",
       "      <td>3.170213</td>\n",
       "      <td>0.760982</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>house_price</th>\n",
       "      <td>47.0</td>\n",
       "      <td>340412.659574</td>\n",
       "      <td>125039.899586</td>\n",
       "      <td>169900.0</td>\n",
       "      <td>249900.0</td>\n",
       "      <td>299900.0</td>\n",
       "      <td>384450.0</td>\n",
       "      <td>699900.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             count           mean            std       min       25%  \\\n",
       "house_size    47.0    2000.680851     794.702354     852.0    1432.0   \n",
       "bedrooms      47.0       3.170213       0.760982       1.0       3.0   \n",
       "house_price   47.0  340412.659574  125039.899586  169900.0  249900.0   \n",
       "\n",
       "                  50%       75%       max  \n",
       "house_size     1888.0    2269.0    4478.0  \n",
       "bedrooms          3.0       4.0       5.0  \n",
       "house_price  299900.0  384450.0  699900.0  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.read_csv('data/ex1data2.txt', sep=',', header=None)\n",
    "df2.columns = ['house_size', 'bedrooms', 'house_price']\n",
    "df2.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> By looking at the values, note that house sizes are about 1000 times the number of bedrooms. When features differ by orders of magnitude, first performing feature scaling can make gradient descent converge much more quickly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can speed up gradient descent by having each of our input values in roughly the same range, ideally $-1 \\leq x_i \\leq1$ or $-0.5 \\leq x_i \\leq0.5$.\n",
    "\n",
    "* Feature scaling: involves dividing the input values by the range (i.e. the maximum value minus the minimum value) of the input variable\n",
    "* Mean normalization: involves subtracting the average value for an input variable from the values for that input variable\n",
    "\n",
    "$x_i := \\frac{x_i - \\mu_i}{s_i}$, wher $\\mu_i$ is the average of all the values for features (i) and $s_i$ is the range of values (max-min), the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def feature_normalize(X, mean=np.zeros(1), std=np.zeros(1)):\n",
    "    X = np.array(X)\n",
    "    if len(mean.shape) == 1 or len(std.shape) == 1:\n",
    "        mean = np.mean(X, axis=0)\n",
    "        std = np.std(X, axis=0, ddof=1)\n",
    "\n",
    "    X = (X - mean)/std\n",
    "    return X, mean, std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_norm, mu, sigma = feature_normalize(df2[['house_size', 'bedrooms']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>house_size_normalized</th>\n",
       "      <td>47.0</td>\n",
       "      <td>3.779483e-17</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-1.445423</td>\n",
       "      <td>-0.715590</td>\n",
       "      <td>-0.141790</td>\n",
       "      <td>0.337635</td>\n",
       "      <td>3.117292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bedrooms_normalized</th>\n",
       "      <td>47.0</td>\n",
       "      <td>2.746030e-16</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-2.851859</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>-0.223675</td>\n",
       "      <td>1.090417</td>\n",
       "      <td>2.404508</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       count          mean  std       min       25%       50%  \\\n",
       "house_size_normalized   47.0  3.779483e-17  1.0 -1.445423 -0.715590 -0.141790   \n",
       "bedrooms_normalized     47.0  2.746030e-16  1.0 -2.851859 -0.223675 -0.223675   \n",
       "\n",
       "                            75%       max  \n",
       "house_size_normalized  0.337635  3.117292  \n",
       "bedrooms_normalized    1.090417  2.404508  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2['house_size_normalized'] = X_norm[:,0]\n",
    "df2['bedrooms_normalized'] = X_norm[:,1]\n",
    "df2[['house_size_normalized', 'bedrooms_normalized']].describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Gradient Descent\n",
    "\n",
    "The only difference from univariate regression problem is that now there is one more feature in the matrix X. The hypothesis function and the batch gradient descent update rule remain unchanged.\n",
    "\n",
    "Note: In the multivariate case, the cost function can also be written in the following vectorized form:\n",
    "\n",
    "$$J(\\theta) = \\frac{1}{2m}(X\\theta-y)^T(X\\theta-y)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(X, y, theta):\n",
    "    m = y.shape[0]\n",
    "    h = X.dot(theta)\n",
    "    J = (1/(2*m)) * ((h-y).T.dot(h-y))\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, theta, alpha, num_iters):\n",
    "    m = y.shape[0]\n",
    "    J_history = np.zeros(shape=(num_iters, 1))\n",
    "\n",
    "    for i in range(0, num_iters):\n",
    "        h = X.dot(theta)\n",
    "        diff_hy = h - y\n",
    "\n",
    "        delta = (1/m) * (diff_hy.T.dot(X))\n",
    "        theta = theta - (alpha * delta.T)\n",
    "        J_history[i] = compute_cost(X, y, theta)\n",
    "\n",
    "    return theta, J_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.1 Selecting Learning Rates\n",
    "\n",
    "Tips:\n",
    "* Make a plot with number of iterations on the x-axis. Now plot the cost function, $J(\\theta)$ over the number of iterations of gradient descent. If $J(\\theta)$  ever increases, then you probably need to decrease $\\alpha$.\n",
    "* Declare convergence if $J(\\theta)$ decreases by less than E in one iteration, where E is some small value such as $10^{−3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = df2.shape[0]\n",
    "X = np.hstack((np.ones((m,1)),X_norm))\n",
    "y = np.array(df2.house_price.values).reshape(-1,1)\n",
    "theta = np.zeros(shape=(X.shape[1],1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = [0.3, 0.1, 0.03, 0.01]\n",
    "colors = ['b','r','g','c']\n",
    "num_iters = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(0, len(alpha)):\n",
    "    theta = np.zeros(shape=(X.shape[1],1))\n",
    "    theta, J_history = gradient_descent(X, y, theta, alpha[i], num_iters)\n",
    "    plt.plot(range(len(J_history)), J_history, colors[i], label='Alpha {}'.format(alpha[i]))\n",
    "plt.xlabel('Number of iterations');\n",
    "plt.ylabel('Cost J');\n",
    "plt.title('Selecting learning rates');\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta found by gradient descent:\n",
      "[[ 340412.65957372]\n",
      " [ 110630.26530813]\n",
      " [  -6648.6893001 ]]\n"
     ]
    }
   ],
   "source": [
    "iterations = 250\n",
    "alpha = 0.1\n",
    "theta, _ = gradient_descent(X, y, theta, alpha, iterations)\n",
    "\n",
    "print('Theta found by gradient descent:')\n",
    "print(theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Estimate the price of a 1650 sq-ft, 3 bedrooms house"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Price of a house with 1650 square feet and 3 bedrooms: 293081.6351422163$'"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqft = (1650 - mu[0])/sigma[0]\n",
    "bedrooms = (3 - mu[1])/sigma[1]\n",
    "y_pred = theta[0] + theta[1]*sqft + theta[2]*bedrooms\n",
    "f'Price of a house with 1650 square feet and 3 bedrooms: {y_pred[0]}$'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Normal Equations\n",
    "\n",
    "A closed-form solution to find $\\theta$ without iteration.\n",
    "\n",
    "$$\\theta = (X^TX)^{-1}X^Ty$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normal_eqn(X, y):\n",
    "    inv = np.linalg.pinv(X.T.dot(X))\n",
    "    theta = inv.dot(X.T).dot(y)\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 89597.90954333],\n",
       "       [   139.21067402],\n",
       "       [ -8738.01911248]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xe = np.hstack((np.ones((m,1)),df2[['house_size', 'bedrooms']].values))\n",
    "theta_e = normal_eqn(Xe, y)\n",
    "theta_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Price of a house with 1650 square feet and 3 bedrooms: 293081.46433495067$'"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = theta_e[0] + theta_e[1]*1650 + theta_e[2]*3\n",
    "f'Price of a house with 1650 square feet and 3 bedrooms: {y_pred[0]}$'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Equivalent Code using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None,\n",
       "         normalize=False)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_norm, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 340412.65957447]), array([[ 110631.05027885,   -6649.47427082]]))"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}