Week_4/Day_4/Regularization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np \n",
    "import pandas as pd \n",
    "import random\n",
    "from matplotlib.pylab import rcParams\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Ridge\n",
    "from sklearn.linear_model import Lasso\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Penalize Magnitude of Coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa9bf22a730>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Importing libraries. The same will be used throughout the article.\n",
    "rcParams['figure.figsize'] = 12, 10\n",
    "\n",
    "#Define input array with angles from 60deg to 300deg converted to radians\n",
    "x = np.array([i*np.pi/180 for i in range(60,300,4)])\n",
    "np.random.seed(10)  #Setting seed for reproducibility\n",
    "y = np.sin(x) + np.random.normal(0,0.15,len(x))\n",
    "data = pd.DataFrame(np.column_stack([x,y]),columns=['x','y'])\n",
    "plt.plot(data['x'],data['y'],'.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          x         y       x_2       x_3       x_4       x_5       x_6  \\\n",
      "0  1.047198  1.065763  1.096623  1.148381  1.202581  1.259340  1.318778   \n",
      "1  1.117011  1.006086  1.247713  1.393709  1.556788  1.738948  1.942424   \n",
      "2  1.186824  0.695374  1.408551  1.671702  1.984016  2.354677  2.794587   \n",
      "3  1.256637  0.949799  1.579137  1.984402  2.493673  3.133642  3.937850   \n",
      "4  1.326450  1.063496  1.759470  2.333850  3.095735  4.106339  5.446854   \n",
      "\n",
      "        x_7       x_8        x_9       x_10       x_11       x_12       x_13  \\\n",
      "0  1.381021  1.446202   1.514459   1.585938   1.660790   1.739176   1.821260   \n",
      "1  2.169709  2.423588   2.707173   3.023942   3.377775   3.773011   4.214494   \n",
      "2  3.316683  3.936319   4.671717   5.544505   6.580351   7.809718   9.268760   \n",
      "3  4.948448  6.218404   7.814277   9.819710  12.339811  15.506664  19.486248   \n",
      "4  7.224981  9.583578  12.712139  16.862020  22.366630  29.668222  39.353420   \n",
      "\n",
      "        x_14       x_15  \n",
      "0   1.907219   1.997235  \n",
      "1   4.707635   5.258479  \n",
      "2  11.000386  13.055521  \n",
      "3  24.487142  30.771450  \n",
      "4  52.200353  69.241170  \n"
     ]
    }
   ],
   "source": [
    "for i in range(2,16):  #power of 1 is already there\n",
    "    colname = 'x_%d'%i      #new var will be x_power\n",
    "    data[colname] = data['x']**i\n",
    "print(data.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import Linear Regression model from scikit-learn.\n",
    "def linear_regression(data, power, models_to_plot):\n",
    "    #initialize predictors:\n",
    "    predictors=['x']\n",
    "    if power>=2:\n",
    "        predictors.extend(['x_%d'%i for i in range(2,power+1)])\n",
    "    \n",
    "    #Fit the model\n",
    "    linreg = LinearRegression(normalize=True)\n",
    "    linreg.fit(data[predictors],data['y'])\n",
    "    y_pred = linreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered power\n",
    "    if power in models_to_plot:\n",
    "        plt.subplot(models_to_plot[power])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for power: %d'%power)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([linreg.intercept_])\n",
    "    ret.extend(linreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize a dataframe to store the results:\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['model_pow_%d'%i for i in range(1,16)]\n",
    "coef_matrix_simple = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "#Define the powers for which a plot is required:\n",
    "models_to_plot = {1:231,3:232,6:233,9:234,12:235,15:236}\n",
    "\n",
    "#Iterate through all powers and assimilate results\n",
    "for i in range(1,16):\n",
    "    coef_matrix_simple.iloc[i-1,0:i+2] = linear_regression(data, power=i, models_to_plot=models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>model_pow_1</th>\n",
       "      <td>3.3</td>\n",
       "      <td>2</td>\n",
       "      <td>-0.62</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_2</th>\n",
       "      <td>3.3</td>\n",
       "      <td>1.9</td>\n",
       "      <td>-0.58</td>\n",
       "      <td>-0.006</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_3</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>3</td>\n",
       "      <td>-1.3</td>\n",
       "      <td>0.14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_4</th>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.53</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_5</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>-5.1</td>\n",
       "      <td>4.7</td>\n",
       "      <td>-1.9</td>\n",
       "      <td>0.33</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_6</th>\n",
       "      <td>0.99</td>\n",
       "      <td>-2.8</td>\n",
       "      <td>9.5</td>\n",
       "      <td>-9.7</td>\n",
       "      <td>5.2</td>\n",
       "      <td>-1.6</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-0.014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_7</th>\n",
       "      <td>0.93</td>\n",
       "      <td>19</td>\n",
       "      <td>-56</td>\n",
       "      <td>69</td>\n",
       "      <td>-45</td>\n",
       "      <td>17</td>\n",
       "      <td>-3.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_8</th>\n",
       "      <td>0.92</td>\n",
       "      <td>43</td>\n",
       "      <td>-1.4e+02</td>\n",
       "      <td>1.8e+02</td>\n",
       "      <td>-1.3e+02</td>\n",
       "      <td>58</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.4</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.0077</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_9</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.7e+02</td>\n",
       "      <td>-6.1e+02</td>\n",
       "      <td>9.6e+02</td>\n",
       "      <td>-8.5e+02</td>\n",
       "      <td>4.6e+02</td>\n",
       "      <td>-1.6e+02</td>\n",
       "      <td>37</td>\n",
       "      <td>-5.2</td>\n",
       "      <td>0.42</td>\n",
       "      <td>-0.015</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_10</th>\n",
       "      <td>0.87</td>\n",
       "      <td>1.4e+02</td>\n",
       "      <td>-4.9e+02</td>\n",
       "      <td>7.3e+02</td>\n",
       "      <td>-6e+02</td>\n",
       "      <td>2.9e+02</td>\n",
       "      <td>-87</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.026</td>\n",
       "      <td>-0.0013</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_11</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-75</td>\n",
       "      <td>5.1e+02</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-1.6e+03</td>\n",
       "      <td>9.1e+02</td>\n",
       "      <td>-3.5e+02</td>\n",
       "      <td>91</td>\n",
       "      <td>-16</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>0.0034</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_12</th>\n",
       "      <td>0.87</td>\n",
       "      <td>-3.4e+02</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-4.4e+03</td>\n",
       "      <td>6e+03</td>\n",
       "      <td>-5.2e+03</td>\n",
       "      <td>3.1e+03</td>\n",
       "      <td>-1.3e+03</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-80</td>\n",
       "      <td>12</td>\n",
       "      <td>-1.1</td>\n",
       "      <td>0.062</td>\n",
       "      <td>-0.0016</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_13</th>\n",
       "      <td>0.86</td>\n",
       "      <td>3.2e+03</td>\n",
       "      <td>-1.8e+04</td>\n",
       "      <td>4.5e+04</td>\n",
       "      <td>-6.7e+04</td>\n",
       "      <td>6.6e+04</td>\n",
       "      <td>-4.6e+04</td>\n",
       "      <td>2.3e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>2.3e+03</td>\n",
       "      <td>-4.5e+02</td>\n",
       "      <td>62</td>\n",
       "      <td>-5.7</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.0078</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_14</th>\n",
       "      <td>0.79</td>\n",
       "      <td>2.4e+04</td>\n",
       "      <td>-1.4e+05</td>\n",
       "      <td>3.8e+05</td>\n",
       "      <td>-6.1e+05</td>\n",
       "      <td>6.6e+05</td>\n",
       "      <td>-5e+05</td>\n",
       "      <td>2.8e+05</td>\n",
       "      <td>-1.2e+05</td>\n",
       "      <td>3.7e+04</td>\n",
       "      <td>-8.5e+03</td>\n",
       "      <td>1.5e+03</td>\n",
       "      <td>-1.8e+02</td>\n",
       "      <td>15</td>\n",
       "      <td>-0.73</td>\n",
       "      <td>0.017</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_15</th>\n",
       "      <td>0.7</td>\n",
       "      <td>-3.6e+04</td>\n",
       "      <td>2.4e+05</td>\n",
       "      <td>-7.5e+05</td>\n",
       "      <td>1.4e+06</td>\n",
       "      <td>-1.7e+06</td>\n",
       "      <td>1.5e+06</td>\n",
       "      <td>-1e+06</td>\n",
       "      <td>5e+05</td>\n",
       "      <td>-1.9e+05</td>\n",
       "      <td>5.4e+04</td>\n",
       "      <td>-1.2e+04</td>\n",
       "      <td>1.9e+03</td>\n",
       "      <td>-2.2e+02</td>\n",
       "      <td>17</td>\n",
       "      <td>-0.81</td>\n",
       "      <td>0.018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "model_pow_1   3.3         2    -0.62      NaN      NaN      NaN      NaN   \n",
       "model_pow_2   3.3       1.9    -0.58   -0.006      NaN      NaN      NaN   \n",
       "model_pow_3   1.1      -1.1        3     -1.3     0.14      NaN      NaN   \n",
       "model_pow_4   1.1     -0.27      1.7    -0.53   -0.036    0.014      NaN   \n",
       "model_pow_5     1         3     -5.1      4.7     -1.9     0.33   -0.021   \n",
       "model_pow_6  0.99      -2.8      9.5     -9.7      5.2     -1.6     0.23   \n",
       "model_pow_7  0.93        19      -56       69      -45       17     -3.5   \n",
       "model_pow_8  0.92        43 -1.4e+02  1.8e+02 -1.3e+02       58      -15   \n",
       "model_pow_9  0.87   1.7e+02 -6.1e+02  9.6e+02 -8.5e+02  4.6e+02 -1.6e+02   \n",
       "model_pow_10 0.87   1.4e+02 -4.9e+02  7.3e+02   -6e+02  2.9e+02      -87   \n",
       "model_pow_11 0.87       -75  5.1e+02 -1.3e+03  1.9e+03 -1.6e+03  9.1e+02   \n",
       "model_pow_12 0.87  -3.4e+02  1.9e+03 -4.4e+03    6e+03 -5.2e+03  3.1e+03   \n",
       "model_pow_13 0.86   3.2e+03 -1.8e+04  4.5e+04 -6.7e+04  6.6e+04 -4.6e+04   \n",
       "model_pow_14 0.79   2.4e+04 -1.4e+05  3.8e+05 -6.1e+05  6.6e+05   -5e+05   \n",
       "model_pow_15  0.7  -3.6e+04  2.4e+05 -7.5e+05  1.4e+06 -1.7e+06  1.5e+06   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "model_pow_1       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_2       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_3       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_4       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_5       NaN      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_6    -0.014      NaN      NaN      NaN       NaN       NaN   \n",
       "model_pow_7       0.4   -0.019      NaN      NaN       NaN       NaN   \n",
       "model_pow_8       2.4    -0.21   0.0077      NaN       NaN       NaN   \n",
       "model_pow_9        37     -5.2     0.42   -0.015       NaN       NaN   \n",
       "model_pow_10       15    -0.81    -0.14    0.026   -0.0013       NaN   \n",
       "model_pow_11 -3.5e+02       91      -16      1.8     -0.12    0.0034   \n",
       "model_pow_12 -1.3e+03  3.8e+02      -80       12      -1.1     0.062   \n",
       "model_pow_13  2.3e+04 -8.5e+03  2.3e+03 -4.5e+02        62      -5.7   \n",
       "model_pow_14  2.8e+05 -1.2e+05  3.7e+04 -8.5e+03   1.5e+03  -1.8e+02   \n",
       "model_pow_15   -1e+06    5e+05 -1.9e+05  5.4e+04  -1.2e+04   1.9e+03   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "model_pow_1        NaN       NaN       NaN       NaN  \n",
       "model_pow_2        NaN       NaN       NaN       NaN  \n",
       "model_pow_3        NaN       NaN       NaN       NaN  \n",
       "model_pow_4        NaN       NaN       NaN       NaN  \n",
       "model_pow_5        NaN       NaN       NaN       NaN  \n",
       "model_pow_6        NaN       NaN       NaN       NaN  \n",
       "model_pow_7        NaN       NaN       NaN       NaN  \n",
       "model_pow_8        NaN       NaN       NaN       NaN  \n",
       "model_pow_9        NaN       NaN       NaN       NaN  \n",
       "model_pow_10       NaN       NaN       NaN       NaN  \n",
       "model_pow_11       NaN       NaN       NaN       NaN  \n",
       "model_pow_12   -0.0016       NaN       NaN       NaN  \n",
       "model_pow_13      0.31   -0.0078       NaN       NaN  \n",
       "model_pow_14        15     -0.73     0.017       NaN  \n",
       "model_pow_15  -2.2e+02        17     -0.81     0.018  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_simple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ridge_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    ridgereg = Ridge(alpha=alpha,normalize=True)\n",
    "    ridgereg.fit(data[predictors],data['y'])\n",
    "    y_pred = ridgereg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([ridgereg.intercept_])\n",
    "    ret.extend(ridgereg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.8/dist-packages/sklearn/linear_model/_ridge.py:147: LinAlgWarning: Ill-conditioned matrix (rcond=3.81609e-17): result may not be accurate.\n",
      "  return linalg.solve(A, Xy, sym_pos=True,\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize predictors to be set of 15 powers of x\n",
    "predictors=['x']\n",
    "predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "#Set the different values of alpha to be tested\n",
    "alpha_ridge = [1e-15, 1e-10, 1e-8, 1e-4, 1e-3,1e-2, 1, 5, 10, 20]\n",
    "\n",
    "#Initialize the dataframe for storing coefficients.\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['alpha_%.2g'%alpha_ridge[i] for i in range(0,10)]\n",
    "coef_matrix_ridge = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "models_to_plot = {1e-15:231, 1e-10:232, 1e-4:233, 1e-3:234, 1e-2:235, 5:236}\n",
    "for i in range(10):\n",
    "    coef_matrix_ridge.iloc[i,] = ridge_regression(data, predictors, alpha_ridge[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.87</td>\n",
       "      <td>94</td>\n",
       "      <td>-3e+02</td>\n",
       "      <td>3.8e+02</td>\n",
       "      <td>-2.4e+02</td>\n",
       "      <td>68</td>\n",
       "      <td>-1.2</td>\n",
       "      <td>-3.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.19</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>-0.0077</td>\n",
       "      <td>0.0011</td>\n",
       "      <td>0.00025</td>\n",
       "      <td>-6.3e-05</td>\n",
       "      <td>4.6e-06</td>\n",
       "      <td>-9e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.92</td>\n",
       "      <td>11</td>\n",
       "      <td>-29</td>\n",
       "      <td>31</td>\n",
       "      <td>-15</td>\n",
       "      <td>2.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0.091</td>\n",
       "      <td>-0.011</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.00064</td>\n",
       "      <td>2.4e-05</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-4.2e-06</td>\n",
       "      <td>2.2e-07</td>\n",
       "      <td>2.3e-07</td>\n",
       "      <td>-2.3e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-1.5</td>\n",
       "      <td>1.7</td>\n",
       "      <td>-0.68</td>\n",
       "      <td>0.039</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.00016</td>\n",
       "      <td>-0.00036</td>\n",
       "      <td>-5.4e-05</td>\n",
       "      <td>-2.9e-07</td>\n",
       "      <td>1.1e-06</td>\n",
       "      <td>1.9e-07</td>\n",
       "      <td>2e-08</td>\n",
       "      <td>3.9e-09</td>\n",
       "      <td>8.2e-10</td>\n",
       "      <td>-4.6e-10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.026</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>4.1e-05</td>\n",
       "      <td>1.5e-05</td>\n",
       "      <td>3.7e-06</td>\n",
       "      <td>7.4e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.9e-09</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-6.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.31</td>\n",
       "      <td>-0.087</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.0028</td>\n",
       "      <td>-0.00022</td>\n",
       "      <td>1.8e-05</td>\n",
       "      <td>1.2e-05</td>\n",
       "      <td>3.4e-06</td>\n",
       "      <td>7.3e-07</td>\n",
       "      <td>1.3e-07</td>\n",
       "      <td>1.9e-08</td>\n",
       "      <td>1.7e-09</td>\n",
       "      <td>-1.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-5.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>1.4</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0.088</td>\n",
       "      <td>-0.052</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00013</td>\n",
       "      <td>7.2e-07</td>\n",
       "      <td>4.1e-06</td>\n",
       "      <td>1.3e-06</td>\n",
       "      <td>3e-07</td>\n",
       "      <td>5.6e-08</td>\n",
       "      <td>9e-09</td>\n",
       "      <td>1.1e-09</td>\n",
       "      <td>4.3e-11</td>\n",
       "      <td>-3.1e-11</td>\n",
       "      <td>-1.5e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>5.6</td>\n",
       "      <td>0.97</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>-0.019</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>-0.00047</td>\n",
       "      <td>-7e-05</td>\n",
       "      <td>-9.9e-06</td>\n",
       "      <td>-1.3e-06</td>\n",
       "      <td>-1.4e-07</td>\n",
       "      <td>-9.3e-09</td>\n",
       "      <td>1.3e-09</td>\n",
       "      <td>7.8e-10</td>\n",
       "      <td>2.4e-10</td>\n",
       "      <td>6.2e-11</td>\n",
       "      <td>1.4e-11</td>\n",
       "      <td>3.2e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>14</td>\n",
       "      <td>0.55</td>\n",
       "      <td>-0.059</td>\n",
       "      <td>-0.0085</td>\n",
       "      <td>-0.0014</td>\n",
       "      <td>-0.00024</td>\n",
       "      <td>-4.1e-05</td>\n",
       "      <td>-6.9e-06</td>\n",
       "      <td>-1.1e-06</td>\n",
       "      <td>-1.9e-07</td>\n",
       "      <td>-3.1e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-8.2e-10</td>\n",
       "      <td>-1.3e-10</td>\n",
       "      <td>-2e-11</td>\n",
       "      <td>-3e-12</td>\n",
       "      <td>-4.2e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>18</td>\n",
       "      <td>0.4</td>\n",
       "      <td>-0.037</td>\n",
       "      <td>-0.0055</td>\n",
       "      <td>-0.00095</td>\n",
       "      <td>-0.00017</td>\n",
       "      <td>-3e-05</td>\n",
       "      <td>-5.2e-06</td>\n",
       "      <td>-9.2e-07</td>\n",
       "      <td>-1.6e-07</td>\n",
       "      <td>-2.9e-08</td>\n",
       "      <td>-5.1e-09</td>\n",
       "      <td>-9.1e-10</td>\n",
       "      <td>-1.6e-10</td>\n",
       "      <td>-2.9e-11</td>\n",
       "      <td>-5.1e-12</td>\n",
       "      <td>-9.1e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_20</th>\n",
       "      <td>23</td>\n",
       "      <td>0.28</td>\n",
       "      <td>-0.022</td>\n",
       "      <td>-0.0034</td>\n",
       "      <td>-0.0006</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-2e-05</td>\n",
       "      <td>-3.6e-06</td>\n",
       "      <td>-6.6e-07</td>\n",
       "      <td>-1.2e-07</td>\n",
       "      <td>-2.2e-08</td>\n",
       "      <td>-4e-09</td>\n",
       "      <td>-7.5e-10</td>\n",
       "      <td>-1.4e-10</td>\n",
       "      <td>-2.5e-11</td>\n",
       "      <td>-4.7e-12</td>\n",
       "      <td>-8.7e-13</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.87        94   -3e+02  3.8e+02 -2.4e+02       68     -1.2   \n",
       "alpha_1e-10  0.92        11      -29       31      -15      2.9     0.17   \n",
       "alpha_1e-08  0.95       1.3     -1.5      1.7    -0.68    0.039    0.016   \n",
       "alpha_0.0001 0.96      0.56     0.55    -0.13   -0.026  -0.0028 -0.00011   \n",
       "alpha_0.001     1      0.82     0.31   -0.087    -0.02  -0.0028 -0.00022   \n",
       "alpha_0.01    1.4       1.3   -0.088   -0.052    -0.01  -0.0014 -0.00013   \n",
       "alpha_1       5.6      0.97    -0.14   -0.019   -0.003 -0.00047   -7e-05   \n",
       "alpha_5        14      0.55   -0.059  -0.0085  -0.0014 -0.00024 -4.1e-05   \n",
       "alpha_10       18       0.4   -0.037  -0.0055 -0.00095 -0.00017   -3e-05   \n",
       "alpha_20       23      0.28   -0.022  -0.0034  -0.0006 -0.00011   -2e-05   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15      -3.7      0.3     0.19   -0.021   -0.0077    0.0011   \n",
       "alpha_1e-10    -0.091   -0.011    0.002  0.00064   2.4e-05    -2e-05   \n",
       "alpha_1e-08   0.00016 -0.00036 -5.4e-05 -2.9e-07   1.1e-06   1.9e-07   \n",
       "alpha_0.0001  4.1e-05  1.5e-05  3.7e-06  7.4e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.001   1.8e-05  1.2e-05  3.4e-06  7.3e-07   1.3e-07   1.9e-08   \n",
       "alpha_0.01    7.2e-07  4.1e-06  1.3e-06    3e-07   5.6e-08     9e-09   \n",
       "alpha_1      -9.9e-06 -1.3e-06 -1.4e-07 -9.3e-09   1.3e-09   7.8e-10   \n",
       "alpha_5      -6.9e-06 -1.1e-06 -1.9e-07 -3.1e-08  -5.1e-09  -8.2e-10   \n",
       "alpha_10     -5.2e-06 -9.2e-07 -1.6e-07 -2.9e-08  -5.1e-09  -9.1e-10   \n",
       "alpha_20     -3.6e-06 -6.6e-07 -1.2e-07 -2.2e-08    -4e-09  -7.5e-10   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    0.00025  -6.3e-05   4.6e-06    -9e-08  \n",
       "alpha_1e-10   -4.2e-06   2.2e-07   2.3e-07  -2.3e-08  \n",
       "alpha_1e-08      2e-08   3.9e-09   8.2e-10  -4.6e-10  \n",
       "alpha_0.0001   1.9e-09  -1.3e-10  -1.5e-10  -6.2e-11  \n",
       "alpha_0.001    1.7e-09  -1.5e-10  -1.4e-10  -5.2e-11  \n",
       "alpha_0.01     1.1e-09   4.3e-11  -3.1e-11  -1.5e-11  \n",
       "alpha_1        2.4e-10   6.2e-11   1.4e-11   3.2e-12  \n",
       "alpha_5       -1.3e-10    -2e-11    -3e-12  -4.2e-13  \n",
       "alpha_10      -1.6e-10  -2.9e-11  -5.1e-12  -9.1e-13  \n",
       "alpha_20      -1.4e-10  -2.5e-11  -4.7e-12  -8.7e-13  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Set the display format to be scientific for ease of analysis\n",
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alpha_1e-15     0\n",
       "alpha_1e-10     0\n",
       "alpha_1e-08     0\n",
       "alpha_0.0001    0\n",
       "alpha_0.001     0\n",
       "alpha_0.01      0\n",
       "alpha_1         0\n",
       "alpha_5         0\n",
       "alpha_10        0\n",
       "alpha_20        0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_matrix_ridge.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lasso regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lasso_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    lassoreg = Lasso(alpha=alpha,normalize=True, max_iter=1e5)\n",
    "    lassoreg.fit(data[predictors],data['y'])\n",
    "    y_pred = lassoreg.predict(data[predictors])\n",
    "    \n",
    "    #Check if a plot is to be made for the entered alpha\n",
    "    if alpha in models_to_plot:\n",
    "        plt.subplot(models_to_plot[alpha])\n",
    "        plt.tight_layout()\n",
    "        plt.plot(data['x'],y_pred)\n",
    "        plt.plot(data['x'],data['y'],'.')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((y_pred-data['y'])**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([lassoreg.intercept_])\n",
    "    ret.extend(lassoreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.8/dist-packages/sklearn/linear_model/_coordinate_descent.py:529: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.47835738259036853, tolerance: 0.00369480384218441\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "/usr/local/lib/python3.8/dist-packages/sklearn/linear_model/_coordinate_descent.py:529: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.4782818399057239, tolerance: 0.00369480384218441\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "/usr/local/lib/python3.8/dist-packages/sklearn/linear_model/_coordinate_descent.py:529: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.47079330190410706, tolerance: 0.00369480384218441\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictors=['x']\n",
    "predictors.extend(['x_%d'%i for i in range(2,16)])\n",
    "\n",
    "#Define the alpha values to test\n",
    "alpha_lasso = [1e-15, 1e-10, 1e-8, 1e-5,1e-4, 1e-3,1e-2, 1, 5, 10]\n",
    "\n",
    "#Initialize the dataframe to store coefficients\n",
    "col = ['rss','intercept'] + ['coef_x_%d'%i for i in range(1,16)]\n",
    "ind = ['alpha_%.2g'%alpha_lasso[i] for i in range(0,10)]\n",
    "coef_matrix_lasso = pd.DataFrame(index=ind, columns=col)\n",
    "\n",
    "#Define the models to plot\n",
    "models_to_plot = {1e-10:231, 1e-5:232,1e-4:233, 1e-3:234, 1e-2:235, 1:236}\n",
    "\n",
    "#Iterate over the 10 alpha values:\n",
    "for i in range(10):\n",
    "    coef_matrix_lasso.iloc[i,] = lasso_regression(data, predictors, alpha_lasso[i], models_to_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>rss</th>\n",
       "      <th>intercept</th>\n",
       "      <th>coef_x_1</th>\n",
       "      <th>coef_x_2</th>\n",
       "      <th>coef_x_3</th>\n",
       "      <th>coef_x_4</th>\n",
       "      <th>coef_x_5</th>\n",
       "      <th>coef_x_6</th>\n",
       "      <th>coef_x_7</th>\n",
       "      <th>coef_x_8</th>\n",
       "      <th>coef_x_9</th>\n",
       "      <th>coef_x_10</th>\n",
       "      <th>coef_x_11</th>\n",
       "      <th>coef_x_12</th>\n",
       "      <th>coef_x_13</th>\n",
       "      <th>coef_x_14</th>\n",
       "      <th>coef_x_15</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha_1e-15</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00089</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00012</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.4e-09</td>\n",
       "      <td>1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "      <td>-9.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00088</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00012</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.4e-09</td>\n",
       "      <td>1.8e-10</td>\n",
       "      <td>-2e-10</td>\n",
       "      <td>-9.2e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.22</td>\n",
       "      <td>1.1</td>\n",
       "      <td>-0.37</td>\n",
       "      <td>0.00077</td>\n",
       "      <td>0.0016</td>\n",
       "      <td>-0.00011</td>\n",
       "      <td>-6.4e-05</td>\n",
       "      <td>-6.3e-06</td>\n",
       "      <td>1.4e-06</td>\n",
       "      <td>7.8e-07</td>\n",
       "      <td>2.1e-07</td>\n",
       "      <td>4e-08</td>\n",
       "      <td>5.3e-09</td>\n",
       "      <td>2e-10</td>\n",
       "      <td>-1.9e-10</td>\n",
       "      <td>-9.3e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-05</th>\n",
       "      <td>0.96</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.6</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.7e-06</td>\n",
       "      <td>1e-06</td>\n",
       "      <td>7.7e-08</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-7e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>1</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.17</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.048</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.5e-06</td>\n",
       "      <td>5.1e-07</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-4.4e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1.5e-08</td>\n",
       "      <td>7.5e-10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>3.6</td>\n",
       "      <td>1.8</td>\n",
       "      <td>-0.55</td>\n",
       "      <td>-0.00056</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>37</td>\n",
       "      <td>0.038</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "      <td>-0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              rss intercept coef_x_1 coef_x_2 coef_x_3 coef_x_4 coef_x_5  \\\n",
       "alpha_1e-15  0.96      0.22      1.1    -0.37  0.00089   0.0016 -0.00012   \n",
       "alpha_1e-10  0.96      0.22      1.1    -0.37  0.00088   0.0016 -0.00012   \n",
       "alpha_1e-08  0.96      0.22      1.1    -0.37  0.00077   0.0016 -0.00011   \n",
       "alpha_1e-05  0.96       0.5      0.6    -0.13   -0.038       -0        0   \n",
       "alpha_0.0001    1       0.9     0.17       -0   -0.048       -0       -0   \n",
       "alpha_0.001   1.7       1.3       -0    -0.13       -0       -0       -0   \n",
       "alpha_0.01    3.6       1.8    -0.55 -0.00056       -0       -0       -0   \n",
       "alpha_1        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_5        37     0.038       -0       -0       -0       -0       -0   \n",
       "alpha_10       37     0.038       -0       -0       -0       -0       -0   \n",
       "\n",
       "             coef_x_6 coef_x_7 coef_x_8 coef_x_9 coef_x_10 coef_x_11  \\\n",
       "alpha_1e-15  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-10  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-08  -6.4e-05 -6.3e-06  1.4e-06  7.8e-07   2.1e-07     4e-08   \n",
       "alpha_1e-05         0        0  7.7e-06    1e-06   7.7e-08         0   \n",
       "alpha_0.0001        0        0  9.5e-06  5.1e-07         0         0   \n",
       "alpha_0.001         0        0        0        0         0   1.5e-08   \n",
       "alpha_0.01         -0       -0       -0       -0         0         0   \n",
       "alpha_1            -0       -0       -0       -0        -0        -0   \n",
       "alpha_5            -0       -0       -0       -0        -0        -0   \n",
       "alpha_10           -0       -0       -0       -0        -0        -0   \n",
       "\n",
       "             coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15    5.4e-09   1.8e-10    -2e-10  -9.2e-11  \n",
       "alpha_1e-10    5.4e-09   1.8e-10    -2e-10  -9.2e-11  \n",
       "alpha_1e-08    5.3e-09     2e-10  -1.9e-10  -9.3e-11  \n",
       "alpha_1e-05          0         0        -0    -7e-11  \n",
       "alpha_0.0001         0        -0        -0  -4.4e-11  \n",
       "alpha_0.001    7.5e-10         0         0         0  \n",
       "alpha_0.01           0         0         0         0  \n",
       "alpha_1             -0        -0        -0        -0  \n",
       "alpha_5             -0        -0        -0        -0  \n",
       "alpha_10            -0        -0        -0        -0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alpha_1e-15      0\n",
       "alpha_1e-10      0\n",
       "alpha_1e-08      0\n",
       "alpha_1e-05      8\n",
       "alpha_0.0001    10\n",
       "alpha_0.001     12\n",
       "alpha_0.01      13\n",
       "alpha_1         15\n",
       "alpha_5         15\n",
       "alpha_10        15\n",
       "dtype: int64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# amount of zeroes in each row\n",
    "coef_matrix_lasso.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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