Programming Exercise 5 - Regularized Linear Regression and Bias vs Variance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 5: Regularized Linear Regression and Bias vs Variance\n",
    "\n",
    "> In this exercise, you will implement regularized linear regression and use it to study models with different bias-variance properties. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Regularized Linear Regression\n",
    "\n",
    "### 1.1 Visualizing the Dataset\n",
    "\n",
    "> You will implement regularized linear regression to predict the amount of water flowing out of a dam using the change of water level in a reservoir."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['__header__', '__version__', '__globals__', 'X', 'y', 'Xtest', 'ytest', 'Xval', 'yval'])"
      ]
     },
     "execution_count": 476,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.io\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "mat = scipy.io.loadmat('data/ex5data1.mat')\n",
    "mat.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset has training, cross validation and test sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>water_level</th>\n",
       "      <td>-15.936758</td>\n",
       "      <td>-29.152979</td>\n",
       "      <td>36.189549</td>\n",
       "      <td>37.492187</td>\n",
       "      <td>-48.058829</td>\n",
       "      <td>-8.941458</td>\n",
       "      <td>15.307793</td>\n",
       "      <td>-34.706266</td>\n",
       "      <td>1.389154</td>\n",
       "      <td>-44.383760</td>\n",
       "      <td>7.013502</td>\n",
       "      <td>22.762749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>water_flowing</th>\n",
       "      <td>2.134311</td>\n",
       "      <td>1.173257</td>\n",
       "      <td>34.359109</td>\n",
       "      <td>36.837955</td>\n",
       "      <td>2.808965</td>\n",
       "      <td>2.121072</td>\n",
       "      <td>14.710268</td>\n",
       "      <td>2.614184</td>\n",
       "      <td>3.740172</td>\n",
       "      <td>3.731691</td>\n",
       "      <td>7.627659</td>\n",
       "      <td>22.752428</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      0          1          2          3          4   \\\n",
       "water_level   -15.936758 -29.152979  36.189549  37.492187 -48.058829   \n",
       "water_flowing   2.134311   1.173257  34.359109  36.837955   2.808965   \n",
       "\n",
       "                     5          6          7         8          9         10  \\\n",
       "water_level   -8.941458  15.307793 -34.706266  1.389154 -44.383760  7.013502   \n",
       "water_flowing  2.121072  14.710268   2.614184  3.740172   3.731691  7.627659   \n",
       "\n",
       "                      11  \n",
       "water_level    22.762749  \n",
       "water_flowing  22.752428  "
      ]
     },
     "execution_count": 477,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data = {'water_level': mat['X'].T[0], 'water_flowing': mat['y'].T[0]})\n",
    "df.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "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='water_level', y='water_flowing', data=df)\n",
    "ax.set(xlabel='Change in water level', ylabel='Water flowing out of the dam', title='Dataset');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Regularized Linear Regression Cost Function\n",
    "\n",
    "$$ J(\\theta) = \\frac{1}{2m} (\\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})^2) + \\frac{\\lambda}{2m}(\\sum_{j=1}^n\\theta_j^2)$$\n",
    "\n",
    "The regularization parameter $\\lambda$ puts a penalty on the overal cos $J$ and help preventing overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression_cost(X, y, theta, lambda_r):\n",
    "    m = X.shape[0]\n",
    "    h = X.dot(theta)\n",
    "    J = (1/(2*m)) * ((h-y).T.dot(h-y)) + (lambda_r/(2*m)) * np.sum(theta[1:,:]**2)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 480,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at theta = [1 ; 1]: [[ 303.99319222]] \n",
      "(this value should be about 303.993192)\n"
     ]
    }
   ],
   "source": [
    "theta = np.ones(shape=(X.shape[1],1))\n",
    "m = len(df)\n",
    "X = np.hstack((np.ones((m,1)), df.water_level.values.reshape(-1,1)))\n",
    "y = df.water_flowing.values.reshape(-1,1)\n",
    "J = linear_regression_cost(X, y, theta, 1)\n",
    "print('Cost at theta = [1 ; 1]:', J, '\\n(this value should be about 303.993192)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Regularized Linear Regression Gradient\n",
    "\n",
    "$$\\frac{\\partial J(\\theta)}{\\partial\\theta_0} = \\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)} \\text{for} \\ j=0$$\n",
    "\n",
    "$$\\frac{\\partial J(\\theta)}{\\partial\\theta_j} = (\\frac{1}{m} \\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j \\text{for} \\ j\\ge1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression_cost_function(theta, X, y, lambda_r):\n",
    "    m = X.shape[0]\n",
    "    theta = theta[:, np.newaxis] \n",
    "    \n",
    "    h = X.dot(theta)\n",
    "    J = (1/(2*m)) * ((h-y).T.dot(h-y)) + (lambda_r/(2*m)) * np.sum(theta[1:,:]**2)\n",
    "    \n",
    "    grad = (1/m) * (h-y).T.dot(X) + (lambda_r/m) * theta.T\n",
    "    grad[0, 0] = (1/m) * (h-y).T.dot(X[:,0])\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient at theta = [1 ; 1]: [[ -15.30301567  598.25074417]] \n",
      "(this value should be about [-15.303016; 598.250744]\n"
     ]
    }
   ],
   "source": [
    "theta = np.ones(shape=(X.shape[1]))\n",
    "J, grad = linear_regression_cost_function(theta, X, y, 1);\n",
    "print('Gradient at theta = [1 ; 1]:', grad, '\\n(this value should be about [-15.303016; 598.250744]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Fitting Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "def train_linear_regression(X, y, lambda_r):\n",
    "    theta = np.ones(shape=(X.shape[1]))\n",
    "    opt_results = opt.minimize(linear_regression_cost_function, theta, args=(X, y, lambda_r), \n",
    "                                method='L-BFGS-B', jac=True, options={'maxiter':200})\n",
    "    return opt_results['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_r = 0\n",
    "theta_final = train_linear_regression(X, y, lambda_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "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='water_level', y='water_flowing', data=df)\n",
    "plt.plot(X[:,1], X.dot(theta_final), color='r')\n",
    "ax.set(xlabel='Change in water level', ylabel='Water flowing out of the dam', title='Linear Fit');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Since the data is not linear, linear regression can't have a good fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Bias-variance\n",
    "\n",
    "High bias: underfitting\n",
    "<br>\n",
    "High variance: overfitting\n",
    "\n",
    "### 2.1 Learning Curves\n",
    "\n",
    "Plots training and validation error as a function of training set size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "      <th>19</th>\n",
       "      <th>20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>water_level</th>\n",
       "      <td>-16.746536</td>\n",
       "      <td>-14.577471</td>\n",
       "      <td>34.515759</td>\n",
       "      <td>-47.010076</td>\n",
       "      <td>36.975119</td>\n",
       "      <td>-40.68611</td>\n",
       "      <td>-4.472011</td>\n",
       "      <td>26.533635</td>\n",
       "      <td>-42.797683</td>\n",
       "      <td>25.374099</td>\n",
       "      <td>...</td>\n",
       "      <td>27.311769</td>\n",
       "      <td>-3.263862</td>\n",
       "      <td>-1.818276</td>\n",
       "      <td>-40.719662</td>\n",
       "      <td>-50.013244</td>\n",
       "      <td>-17.411772</td>\n",
       "      <td>3.588194</td>\n",
       "      <td>7.085480</td>\n",
       "      <td>46.282369</td>\n",
       "      <td>14.612289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>water_flowing</th>\n",
       "      <td>4.170202</td>\n",
       "      <td>4.067263</td>\n",
       "      <td>31.873068</td>\n",
       "      <td>10.623656</td>\n",
       "      <td>31.836021</td>\n",
       "      <td>4.95937</td>\n",
       "      <td>4.451599</td>\n",
       "      <td>22.276318</td>\n",
       "      <td>-0.000044</td>\n",
       "      <td>20.503802</td>\n",
       "      <td>...</td>\n",
       "      <td>19.365053</td>\n",
       "      <td>4.883763</td>\n",
       "      <td>11.097159</td>\n",
       "      <td>7.461708</td>\n",
       "      <td>1.476935</td>\n",
       "      <td>2.719164</td>\n",
       "      <td>10.926901</td>\n",
       "      <td>8.348712</td>\n",
       "      <td>52.781928</td>\n",
       "      <td>13.357340</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                      0          1          2          3          4   \\\n",
       "water_level   -16.746536 -14.577471  34.515759 -47.010076  36.975119   \n",
       "water_flowing   4.170202   4.067263  31.873068  10.623656  31.836021   \n",
       "\n",
       "                     5         6          7          8          9   ...  \\\n",
       "water_level   -40.68611 -4.472011  26.533635 -42.797683  25.374099  ...   \n",
       "water_flowing   4.95937  4.451599  22.276318  -0.000044  20.503802  ...   \n",
       "\n",
       "                      11        12         13         14         15  \\\n",
       "water_level    27.311769 -3.263862  -1.818276 -40.719662 -50.013244   \n",
       "water_flowing  19.365053  4.883763  11.097159   7.461708   1.476935   \n",
       "\n",
       "                      16         17        18         19         20  \n",
       "water_level   -17.411772   3.588194  7.085480  46.282369  14.612289  \n",
       "water_flowing   2.719164  10.926901  8.348712  52.781928  13.357340  \n",
       "\n",
       "[2 rows x 21 columns]"
      ]
     },
     "execution_count": 486,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_val = pd.DataFrame(data = {'water_level': mat['Xval'].T[0], 'water_flowing': mat['yval'].T[0]})\n",
    "df_val.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xval = df_val.water_level.values.reshape(-1,1)\n",
    "Xval = np.hstack((np.ones((Xval.shape[0],1)), Xval))\n",
    "yval = df_val.water_flowing.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [],
   "source": [
    "def learning_curve(X, y, Xval, yval, lambda_r):\n",
    "    m = X.shape[0]\n",
    "    error_train = np.zeros((m,1))\n",
    "    error_val = np.zeros((m,1))\n",
    "    for i in range(1,m):\n",
    "        theta = train_linear_regression(X[:i, :], y[:i], lambda_r)\n",
    "        error_train[i], _ = linear_regression_cost_function(theta, X[:i,:], y[:i], 0)\n",
    "        error_val[i], _ = linear_regression_cost_function(theta, Xval, yval, 0)\n",
    "    return error_train, error_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_r = 0\n",
    "error_train, error_val = learning_curve(X, y, Xval, yval, lambda_r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x=range(1,m), y=error_train.T[0][1:])\n",
    "ax = sns.lineplot(x=range(1,m), y=error_val.T[0][1:])\n",
    "ax.set(xlabel='Number of training examples', ylabel='Error', title='Learning curve for linear regression');\n",
    "ax.legend(['Train', 'Cross Validation']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>error_train</th>\n",
       "      <td>9.860761e-32</td>\n",
       "      <td>3.334883e-15</td>\n",
       "      <td>3.286595</td>\n",
       "      <td>2.842678</td>\n",
       "      <td>13.154049</td>\n",
       "      <td>19.443963</td>\n",
       "      <td>20.098522</td>\n",
       "      <td>18.172859</td>\n",
       "      <td>22.609405</td>\n",
       "      <td>23.261462</td>\n",
       "      <td>24.31725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>error_val</th>\n",
       "      <td>1.698707e+02</td>\n",
       "      <td>1.103004e+02</td>\n",
       "      <td>45.010231</td>\n",
       "      <td>48.368911</td>\n",
       "      <td>35.865163</td>\n",
       "      <td>33.829961</td>\n",
       "      <td>31.970985</td>\n",
       "      <td>30.862444</td>\n",
       "      <td>31.135997</td>\n",
       "      <td>28.936204</td>\n",
       "      <td>29.55143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       0             1          2          3          4   \\\n",
       "error_train  9.860761e-32  3.334883e-15   3.286595   2.842678  13.154049   \n",
       "error_val    1.698707e+02  1.103004e+02  45.010231  48.368911  35.865163   \n",
       "\n",
       "                    5          6          7          8          9         10  \n",
       "error_train  19.443963  20.098522  18.172859  22.609405  23.261462  24.31725  \n",
       "error_val    33.829961  31.970985  30.862444  31.135997  28.936204  29.55143  "
      ]
     },
     "execution_count": 491,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_error = pd.DataFrame(data={'error_train': error_train.T[0][1:], 'error_val': error_val.T[0][1:]})\n",
    "df_error.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both train error and cross validation error are high when the number of training examples is increased, that is, **high bias problem**, the model is too simple and unable to fit the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Polynomial Regression\n",
    "\n",
    "We can add more features to try to solve the underfitting problem. \n",
    "\n",
    "Polynomial regression hypothesis for the current problem:\n",
    "\n",
    "$$h_\\theta(x) = \\theta_0 + \\theta_1 * (waterLevel) + \\theta_2 * (waterLevel)^2 + ... + \\theta_p * (waterLevel)^p = \\theta_0 + \\theta_1x_1 + \\theta_2x_2 + ... + \\theta_px_p$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 492,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_features(X, p):\n",
    "    X_poly = np.zeros((X.shape[0], p))\n",
    "    for i in range(p):\n",
    "        X_poly[:,i] = X**(i+1)\n",
    "    return X_poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Learning Polynomial Regression\n",
    "\n",
    "Normalizing features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "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": 494,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = 8\n",
    "X_poly = poly_features(mat['X'].T[0], p)\n",
    "X_poly, mu, sigma = feature_normalize(X_poly)\n",
    "X_poly = np.hstack((np.ones((X_poly.shape[0],1)), X_poly))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 495,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_poly_test = poly_features(mat['Xtest'].T[0], p)\n",
    "X_poly_test, _, _ = feature_normalize(X_poly_test, mu, sigma)\n",
    "X_poly_test = np.hstack((np.ones((X_poly_test.shape[0],1)), X_poly_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 496,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_poly_val = poly_features(mat['Xval'].T[0], p)\n",
    "X_poly_val, _, _ = feature_normalize(X_poly_val, mu, sigma)\n",
    "X_poly_val = np.hstack((np.ones((X_poly_val.shape[0],1)), X_poly_val))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training model and plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 497,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_and_plot_fit_learning_curve(X, X_poly, y, X_poly_val, yval, lambda_r):\n",
    "    theta = train_linear_regression(X_poly, y, lambda_r)\n",
    "\n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.subplot(121)\n",
    "    ax = sns.scatterplot(x=X[:,1], y=y.T[0])\n",
    "    x = np.arange(np.min(X)-15.0, np.max(X)+25.0, 0.05)\n",
    "    plot_X_poly = poly_features(x, p)\n",
    "    plot_X_poly, _, _ = feature_normalize(plot_X_poly, mu, sigma)\n",
    "    plot_X_poly = np.hstack((np.ones((plot_X_poly.shape[0],1)), plot_X_poly))\n",
    "    plt.plot(x, plot_X_poly.dot(theta), 'k--', color='r')\n",
    "    ax.set(xlabel='Change in water level', ylabel='Water flowing out of the dam', \n",
    "           title='Polynomial Regression Fit ($\\lambda$ = {})'.format(lambda_r));\n",
    "    \n",
    "    error_train, error_val = learning_curve(X_poly, y, X_poly_val, yval, lambda_r)\n",
    "    plt.subplot(122)\n",
    "    sns.lineplot(x=range(1,m), y=error_train.T[0][1:])\n",
    "    ax = sns.lineplot(x=range(1,m), y=error_val.T[0][1:])\n",
    "    ax.set(xlabel='Number of training examples', ylabel='Error', \n",
    "           title='Polynomial Regression Learning Curve ($\\lambda$ = {})'.format(lambda_r));\n",
    "    ax.legend(['Train', 'Cross Validation']);\n",
    "    \n",
    "    plt.subplots_adjust(wspace=0.2)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 498,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_r = 0.0\n",
    "train_and_plot_fit_learning_curve(X, X_poly, y, X_poly_val, yval, lambda_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots shows the overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Adjusting the regularization parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_r = 1.0\n",
    "train_and_plot_fit_learning_curve(X, X_poly, y, X_poly_val, yval, lambda_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $\\lambda=1$, the model does not have the high-bias or high-variance problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambda_r = 100.0\n",
    "train_and_plot_fit_learning_curve(X, X_poly, y, X_poly_val, yval, lambda_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $\\lambda=100$, the model is underfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Selecting $\\lambda$ using a cross validation set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [],
   "source": [
    "def validation_curve(X, y, Xval, yval):\n",
    "    lambda_values = np.array([0, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10])\n",
    "    error_train = np.zeros((len(lambda_values),1))\n",
    "    error_val = np.zeros((len(lambda_values),1))\n",
    "    for i,l in enumerate(lambda_values):\n",
    "        theta = train_linear_regression(X, y, l)\n",
    "        error_train[i], _ = linear_regression_cost_function(theta, X, y, 0)\n",
    "        error_val[i], _ = linear_regression_cost_function(theta, Xval, yval, 0)\n",
    "    return lambda_values, error_train, error_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda_values, error_train, error_val = validation_curve(X_poly, y, X_poly_val, yval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 503,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(x=np.array(lambda_values), y=error_train.T[0])\n",
    "ax = sns.lineplot(x=lambda_values, y=error_val.T[0])\n",
    "ax.set(xlabel='$\\lambda$', ylabel='Error', title='Validation curve');\n",
    "ax.legend(['Train', 'Cross Validation']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 11.64373681]])"
      ]
     },
     "execution_count": 504,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = train_linear_regression(X_poly, y, 3.0)\n",
    "J, grad = linear_regression_cost_function(theta, X_poly_test, mat['ytest'], 0)\n",
    "J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}