{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression multiple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Une variable quantitative $Y$ dite à expliquer (ou encore, réponse, exogène, dépendante) est mise en relation avec $p$ variables quantitatives $X_1,\\dots,X_p$ dites explicatives.\n",
    "\n",
    "Les données sont supposées provenir de l'observation d'un échantillon statistique de taille $n$, $(n > p + 1)$ de $R^{(p+1)}$ :\n",
    "\n",
    "$$\n",
    "(x^1_i,\\dots,x^j_i,\\dots,x^p_i,y_i ),\\quad i = 1,\\dots,n.\n",
    "$$\n",
    "\n",
    "L'écriture du modèle linéaire dans cette situation conduit à supposer que l'espérance de $Y$ appartient au sous-espace de $R^n$ engendré par $X=\\{1, X^1 ,\\dots , X^p \\}$ où 1 désigne le vecteur de $R^n$. C'est-à-dire que les $(p + 1)$ variables aléatoires vérifient :\n",
    "\n",
    "$$\n",
    "Y_i =\\beta_0 +\\beta_1X_i^1 +\\beta_2X_i^2 +\\dots+\\beta_pX_i^p +\\varepsilon_i, \\quad i = 1,\\dots,n.\n",
    "$$\n",
    "\n",
    "Les $\\varepsilon_i$ sont des termes d'erreur indépendants et identiquement distribués tels que $\\mathbb E(\\varepsilon_i)=0$ et ${\\rm Var}(\\varepsilon_i)=\\sigma^2$.\n",
    "\n",
    "Les données sont rangées dans une matrice $X\\in \\mathbb R^{n\\times(p + 1)}$ de terme général $X_i^j$, dont la première colonne contient le vecteur 1 $(X_0^i = 1)$, et dans un vecteur $Y$ de terme général $Y_i$. En notant les vecteurs $\\varepsilon = [\\varepsilon_1, \\dots, \\varepsilon_n]′$ et $\\beta= [\\beta_0, \\beta_1, \\dots \\beta_p ]′$ , le modèle s'écrit matriciellement :\n",
    "\n",
    "$$\n",
    "Y = X\\beta + \\varepsilon\n",
    "$$\n",
    "\n",
    "Conditionnellement à la connaissance des valeurs des $X_j$, les paramètres inconnus du modèle : le vecteur $\\beta$ et $\\sigma^2$ (paramètre de nuisance), sont estimés par minimisation des carrés des écarts. \n",
    "\n",
    "L'expression à minimiser sur $\\beta\\in \\mathbb R^{p+1}$ s'écrit :\n",
    "\\begin{align*}\n",
    "\\sum_{i=1}^n(Y_i −\\beta_0 −\\beta_1X_i^1 −\\dots−\\beta_pX_i^p)^2&=\\|Y−X\\beta\\|^2_2\\\\\n",
    "&= Y′Y − 2\\beta′X′Y + \\beta′X′X\\beta\n",
    "\\end{align*}\n",
    "\n",
    "Par dérivation matricielle de la dernière équation on obtient les équations normales :\n",
    "$$\n",
    "X′Y − X′X\\beta = 0\n",
    "$$\n",
    "dont la solution correspond bien à un minimum car la matrice hessienne $2X′X$\n",
    "est semi définie-positive.\n",
    "Nous faisons l'hypothèse supplémentaire que la matrice $X′X$ est inversible, c’est-à-dire que la matrice $X$ est de rang $(p + 1)$ et donc qu'il n'existe pas de colinéarité entre ses colonnes. Si cette hypothèse n'est pas vérifiée, il suffit en principe de supprimer des colonnes de X et donc des variables du modèle. Une approche de réduction de dimension (régression ridge, Lasso, PLS ...) est à mettre en œuvre.\n",
    "Alors, l’estimation des paramètres $\\beta_j$ est donnée par :\n",
    "\n",
    "\n",
    "$$\n",
    "\\hat \\beta= (X′X)^{-1}X′Y\n",
    "$$\n",
    "\n",
    "et les valeurs ajustées (ou estimées, prédites) de $Y$ ont pour expression :\n",
    "\n",
    "$$\n",
    "\\hat Y􏰞= X\\hat \\beta􏰞 = X(X′X)^{−1}X′Y = HY\n",
    "$$\n",
    "\n",
    "où $H=X(X′X)^{−1}X′$. Géométriquement, c'est la matrice de projection orthogonale dans $R^n$ sur le sous-espace ${\\rm Vect}(X)$ engendré par les vecteurs colonnes de $X$. On note\n",
    "$$\n",
    "e=Y−\\hat Y􏰞 =Y−X\\hat \\beta􏰞=(I−H)Y\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Régression ridge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit le modèle linéaire :\n",
    "\n",
    "$$\n",
    " Y=\\tilde X {\\tilde{􏰟\\beta}􏰟}+\\varepsilon\n",
    "$$\n",
    "\n",
    "where \n",
    "\n",
    "$$\\tilde X=\n",
    "\\begin{pmatrix} \n",
    "1 & X^1_1 & X^2_1 &\\dots & X^p_1\\\\\n",
    "1 & X^1_2 & X^2_2 &\\dots & X^p_2 \\\\\n",
    "\\vdots & \\vdots & \\vdots & \\vdots \\\\\n",
    "1 & X^1_n & X^2_n &\\dots & X^p_n\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\tilde{\\beta}=\\begin{pmatrix} \n",
    "\\beta_0\\\\\n",
    "\\beta_1\\\\\n",
    "\\vdots \\\\\n",
    "\\beta_p\n",
    "\\end{pmatrix},\n",
    "\\quad\n",
    "{\\beta}=\\begin{pmatrix} \n",
    "\\beta_1\\\\\n",
    "\\beta_2\\\\\n",
    "\\vdots \\\\\n",
    "\\beta_p\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "où $X_0 = (1,1,\\dots,1)′$, et $X$ désigne la matrice $\\tilde X$􏰟 privée de sa première colonne. L'estimateur ridge est défini par un critère des moindres carrés, avec une pénalité de type $L_2$ :\n",
    "\n",
    "L'estimateur ridge de $\\tilde \\beta$ dans le modèle\n",
    "$$\n",
    " Y=\\tilde X {\\tilde{􏰟\\beta}􏰟}+\\varepsilon\n",
    "$$\n",
    "est défini par :\n",
    "\n",
    "$$\n",
    "\\hat{\\beta}_{\\rm ridge}:={\\arg\\min}_{\\beta\\in \\mathbb R^{(p+1)}}\\left(\\sum_{i=1}^n (Y_i- \\sum_{j=0}^pX_i^j\\beta_j)^2+\\lambda\\sum_{j=0}^p \\beta_j^2 \\right)\n",
    "$$\n",
    "où $\\lambda$ est un paramètre positif, à choisir.\n",
    "\n",
    "\n",
    "Cela revient à chercher $${\\arg\\min}_{\\beta\\in \\mathbb R^{(p+1)}}\\left(\\sum_{i=1}^n (Y_i- \\sum_{j=0}^pX_i^j\\beta_j)^2\\right)$$\n",
    "\n",
    "sous la contrainte supplémentaire :\n",
    "\n",
    "$$\n",
    "\\|\\beta\\|_2^2=\\sum_{j=0}^p \\beta_j^2 \\leq \\frac{1}{\\lambda}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          x         y\n",
      "0  1.047198  0.795794\n",
      "1  1.117011  0.775370\n",
      "2  1.186824  0.917377\n",
      "3  1.256637  0.844052\n",
      "4  1.326450  1.106248\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a456a491d0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from matplotlib.pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 10 #dimension fenetre du plot\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",
    "#print(x)\n",
    "np.random.seed(777)  #Jackpot\n",
    "y = np.sin(x) + np.random.normal(0,0.15,len(x))\n",
    "#print(np.random.normal(0,0.15,len(x)))\n",
    "#plt.hist(np.random.normal(0,0.15,len(x)),50)\n",
    "data = pd.DataFrame(np.column_stack([x,y]),columns=['x','y'])\n",
    "print(data.head())\n",
    "\n",
    "\n",
    "#faites plot de x Vs Y\n",
    "\n",
    "plt.plot(x, y,'.', color='b')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          x         y       x_2       x_3       x_4       x_5       x_6  \\\n",
      "0  1.047198  0.795794  1.096623  1.148381  1.202581  1.259340  1.318778   \n",
      "1  1.117011  0.775370  1.247713  1.393709  1.556788  1.738948  1.942424   \n",
      "2  1.186824  0.917377  1.408551  1.671702  1.984016  2.354677  2.794587   \n",
      "3  1.256637  0.844052  1.579137  1.984402  2.493673  3.133642  3.937850   \n",
      "4  1.326450  1.106248  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",
      "0    1.096623\n",
      "1    1.247713\n",
      "2    1.408551\n",
      "3    1.579137\n",
      "4    1.759470\n",
      "Name: x_2, dtype: float64\n",
      "          x       x_2\n",
      "0  1.047198  1.096623\n",
      "1  1.117011  1.247713\n",
      "2  1.186824  1.408551\n",
      "3  1.256637  1.579137\n",
      "4  1.326450  1.759470\n"
     ]
    }
   ],
   "source": [
    "print(data.head())\n",
    "print(data['x_2'].head())\n",
    "print(data[['x', 'x_2']].head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60, 16)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$X$ : la matrice des données ou caractéristiques (features) (nrow: $N$, ncol: $M+1$)\n",
    "$Y$ : la variable de sortie  (length:$N$)\n",
    "$\\hat Y$:les valeurs prédites de $Y$ (length:$N$)\n",
    "$W$: les poids ou coefficients de régréssion (length: $M+1$).\n",
    "\n",
    "Ici, $N$ est le nombre total des points données dont on dispose et $M$ est le nombre total de caractéristiques. $X$ a $M+1$ colonnes  car  elle a $M$ features et 1 intercept (constante).\n",
    "\n",
    "Pour chaque point $i$ la prédiction est \n",
    "\n",
    "$$\n",
    "\\hat y_i=\\sum_{j=0}^M w_j x_i^j\n",
    "$$\n",
    "\n",
    "L'expression à minimiser pour la régréssion est ${\\rm RSS}$ (Residual Sum of Squares) définie par :\n",
    "\n",
    "$$\n",
    "{\\rm RSS}(w):=\\sum_{i=1}^N\\left(y_i-\\hat y_i\\right)^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import Linear Regression model from scikit-learn.\n",
    "# pip install sklearn \n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "def linear_regression(data, power, models_to_plot):\n",
    "    #initialize predictors:\n",
    "    predictors=['x'] # label\n",
    "    \n",
    "    if power>=2:\n",
    "        predictors.extend(['x_%d'%i for i in range(2,power+1)])\n",
    "    \n",
    "    if power>=16:\n",
    "       print('Powers larger than 16 not defined on the database')\n",
    "    #print(predictors)\n",
    "    \n",
    "    \n",
    "    # Fit the model\n",
    "    linreg = LinearRegression() #In theory, normalising the predictors \n",
    "                                             #will not affect the predictions made by linear regression. \n",
    "                                            #However, there are some practical reasons for doing so.\n",
    "    \n",
    "    # data[predictors] = data[predictors] - np.mean(data[predictors]) / np.sqrt(np.var(data[predictors]))\n",
    "    \n",
    "    linreg.fit(data[predictors], data['y']) # find optimal weights w\n",
    "\n",
    "    y_pred = linreg.predict(data[predictors])  # \\hat y   compute  ΣwX\n",
    "    \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, linewidth=4, color = 'r')\n",
    "        plt.plot(data['x'],data['y'],'.',color = 'b')\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",
    "\n",
    "    ret = [rss]\n",
    "    #Reminder\n",
    "    #x = [1, 2, 3] x.append([4, 5]) print (x) [1, 2, 3, [4, 5]]\n",
    "    #x = [1, 2, 3] x.extend([4, 5]) print (x) [1, 2, 3, 4, 5]\n",
    "    \n",
    "    ret.extend([linreg.intercept_]) # constante de regression w0\n",
    "    ret.extend(linreg.coef_) # les autres coefficients w1,... wpower\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "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",
    "#print(coef_matrix_simple)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x1000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rcParams['figure.figsize'] = 12, 10\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} #dictionnary where 1, 3, 6, 9, 12 and 15 are \n",
    "                                                        #the powers to be plot\n",
    "\n",
    "# 23 veut dire que les plots seront sur 2 lignes et 3 colonnes.\n",
    "\n",
    "#for power in models_to_plot:\n",
    "#    print(power)\n",
    "#    print(models_to_plot[power])\n",
    "\n",
    "\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)\n",
    "#pour i=1\n",
    "#ret=[rss,intecept, coef_1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>3.00292</td>\n",
       "      <td>1.948944</td>\n",
       "      <td>-0.624285</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>2.889391</td>\n",
       "      <td>1.676354</td>\n",
       "      <td>-0.417477</td>\n",
       "      <td>-0.033284</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>1.234969</td>\n",
       "      <td>-0.936539</td>\n",
       "      <td>2.735806</td>\n",
       "      <td>-1.149697</td>\n",
       "      <td>0.119786</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>1.225881</td>\n",
       "      <td>-0.442955</td>\n",
       "      <td>1.921448</td>\n",
       "      <td>-0.693187</td>\n",
       "      <td>0.01503</td>\n",
       "      <td>0.00843</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>1.202404</td>\n",
       "      <td>-2.480399</td>\n",
       "      <td>6.177905</td>\n",
       "      <td>-3.981141</td>\n",
       "      <td>1.199064</td>\n",
       "      <td>-0.192247</td>\n",
       "      <td>0.012919</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>1.198729</td>\n",
       "      <td>-4.560663</td>\n",
       "      <td>11.433066</td>\n",
       "      <td>-9.165706</td>\n",
       "      <td>3.768272</td>\n",
       "      <td>-0.870805</td>\n",
       "      <td>0.104041</td>\n",
       "      <td>-0.004888</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>1.198552</td>\n",
       "      <td>-5.743244</td>\n",
       "      <td>14.935767</td>\n",
       "      <td>-13.37465</td>\n",
       "      <td>6.435759</td>\n",
       "      <td>-1.837566</td>\n",
       "      <td>0.305273</td>\n",
       "      <td>-0.027259</td>\n",
       "      <td>0.001029</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>1.185251</td>\n",
       "      <td>-32.40843</td>\n",
       "      <td>105.505347</td>\n",
       "      <td>-141.718996</td>\n",
       "      <td>105.728104</td>\n",
       "      <td>-47.828053</td>\n",
       "      <td>13.405183</td>\n",
       "      <td>-2.275321</td>\n",
       "      <td>0.214202</td>\n",
       "      <td>-0.008577</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>1.161835</td>\n",
       "      <td>59.943316</td>\n",
       "      <td>-248.219785</td>\n",
       "      <td>435.780117</td>\n",
       "      <td>-422.404898</td>\n",
       "      <td>250.877226</td>\n",
       "      <td>-95.19084</td>\n",
       "      <td>23.16412</td>\n",
       "      <td>-3.497711</td>\n",
       "      <td>0.298274</td>\n",
       "      <td>-0.010975</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>1.154293</td>\n",
       "      <td>197.307628</td>\n",
       "      <td>-833.78369</td>\n",
       "      <td>1517.941701</td>\n",
       "      <td>-1565.161331</td>\n",
       "      <td>1015.506701</td>\n",
       "      <td>-434.48543</td>\n",
       "      <td>124.468668</td>\n",
       "      <td>-23.632801</td>\n",
       "      <td>2.852857</td>\n",
       "      <td>-0.198144</td>\n",
       "      <td>0.006025</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>1.147219</td>\n",
       "      <td>-152.824808</td>\n",
       "      <td>809.908438</td>\n",
       "      <td>-1873.473949</td>\n",
       "      <td>2497.097228</td>\n",
       "      <td>-2126.207672</td>\n",
       "      <td>1214.859753</td>\n",
       "      <td>-476.148847</td>\n",
       "      <td>128.314394</td>\n",
       "      <td>-23.359477</td>\n",
       "      <td>2.74308</td>\n",
       "      <td>-0.187468</td>\n",
       "      <td>0.005662</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>1.14905</td>\n",
       "      <td>37.304014</td>\n",
       "      <td>-111.433208</td>\n",
       "      <td>103.755435</td>\n",
       "      <td>10.488315</td>\n",
       "      <td>-83.04651</td>\n",
       "      <td>57.923207</td>\n",
       "      <td>-12.589408</td>\n",
       "      <td>-4.296982</td>\n",
       "      <td>3.559872</td>\n",
       "      <td>-1.043563</td>\n",
       "      <td>0.163339</td>\n",
       "      <td>-0.013579</td>\n",
       "      <td>0.000473</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>1.145641</td>\n",
       "      <td>45.095204</td>\n",
       "      <td>-115.95217</td>\n",
       "      <td>65.334769</td>\n",
       "      <td>69.990038</td>\n",
       "      <td>-75.702388</td>\n",
       "      <td>-36.945916</td>\n",
       "      <td>99.473795</td>\n",
       "      <td>-75.218763</td>\n",
       "      <td>32.004549</td>\n",
       "      <td>-8.62197</td>\n",
       "      <td>1.505889</td>\n",
       "      <td>-0.165941</td>\n",
       "      <td>0.010514</td>\n",
       "      <td>-0.000292</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_14</th>\n",
       "      <td>1.130364</td>\n",
       "      <td>25.096132</td>\n",
       "      <td>-47.938824</td>\n",
       "      <td>2.275035</td>\n",
       "      <td>38.099401</td>\n",
       "      <td>5.08899</td>\n",
       "      <td>-36.644464</td>\n",
       "      <td>-0.624898</td>\n",
       "      <td>38.513343</td>\n",
       "      <td>-36.057266</td>\n",
       "      <td>17.213916</td>\n",
       "      <td>-5.034803</td>\n",
       "      <td>0.939958</td>\n",
       "      <td>-0.109773</td>\n",
       "      <td>0.007333</td>\n",
       "      <td>-0.000214</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>model_pow_15</th>\n",
       "      <td>1.104655</td>\n",
       "      <td>10.729048</td>\n",
       "      <td>-14.41147</td>\n",
       "      <td>-5.868767</td>\n",
       "      <td>8.521389</td>\n",
       "      <td>10.285739</td>\n",
       "      <td>-3.40661</td>\n",
       "      <td>-11.727599</td>\n",
       "      <td>2.892694</td>\n",
       "      <td>11.780032</td>\n",
       "      <td>-12.913967</td>\n",
       "      <td>6.612437</td>\n",
       "      <td>-2.019619</td>\n",
       "      <td>0.38868</td>\n",
       "      <td>-0.046442</td>\n",
       "      <td>0.003159</td>\n",
       "      <td>-0.000094</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   rss   intercept    coef_x_1     coef_x_2     coef_x_3  \\\n",
       "model_pow_1    3.00292    1.948944   -0.624285          NaN          NaN   \n",
       "model_pow_2   2.889391    1.676354   -0.417477    -0.033284          NaN   \n",
       "model_pow_3   1.234969   -0.936539    2.735806    -1.149697     0.119786   \n",
       "model_pow_4   1.225881   -0.442955    1.921448    -0.693187      0.01503   \n",
       "model_pow_5   1.202404   -2.480399    6.177905    -3.981141     1.199064   \n",
       "model_pow_6   1.198729   -4.560663   11.433066    -9.165706     3.768272   \n",
       "model_pow_7   1.198552   -5.743244   14.935767    -13.37465     6.435759   \n",
       "model_pow_8   1.185251   -32.40843  105.505347  -141.718996   105.728104   \n",
       "model_pow_9   1.161835   59.943316 -248.219785   435.780117  -422.404898   \n",
       "model_pow_10  1.154293  197.307628  -833.78369  1517.941701 -1565.161331   \n",
       "model_pow_11  1.147219 -152.824808  809.908438 -1873.473949  2497.097228   \n",
       "model_pow_12   1.14905   37.304014 -111.433208   103.755435    10.488315   \n",
       "model_pow_13  1.145641   45.095204  -115.95217    65.334769    69.990038   \n",
       "model_pow_14  1.130364   25.096132  -47.938824     2.275035    38.099401   \n",
       "model_pow_15  1.104655   10.729048   -14.41147    -5.868767     8.521389   \n",
       "\n",
       "                 coef_x_4     coef_x_5    coef_x_6    coef_x_7   coef_x_8  \\\n",
       "model_pow_1           NaN          NaN         NaN         NaN        NaN   \n",
       "model_pow_2           NaN          NaN         NaN         NaN        NaN   \n",
       "model_pow_3           NaN          NaN         NaN         NaN        NaN   \n",
       "model_pow_4       0.00843          NaN         NaN         NaN        NaN   \n",
       "model_pow_5     -0.192247     0.012919         NaN         NaN        NaN   \n",
       "model_pow_6     -0.870805     0.104041   -0.004888         NaN        NaN   \n",
       "model_pow_7     -1.837566     0.305273   -0.027259    0.001029        NaN   \n",
       "model_pow_8    -47.828053    13.405183   -2.275321    0.214202  -0.008577   \n",
       "model_pow_9    250.877226    -95.19084    23.16412   -3.497711   0.298274   \n",
       "model_pow_10  1015.506701   -434.48543  124.468668  -23.632801   2.852857   \n",
       "model_pow_11 -2126.207672  1214.859753 -476.148847  128.314394 -23.359477   \n",
       "model_pow_12    -83.04651    57.923207  -12.589408   -4.296982   3.559872   \n",
       "model_pow_13   -75.702388   -36.945916   99.473795  -75.218763  32.004549   \n",
       "model_pow_14      5.08899   -36.644464   -0.624898   38.513343 -36.057266   \n",
       "model_pow_15    10.285739     -3.40661  -11.727599    2.892694  11.780032   \n",
       "\n",
       "               coef_x_9 coef_x_10 coef_x_11 coef_x_12 coef_x_13 coef_x_14  \\\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         NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "model_pow_7         NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "model_pow_8         NaN       NaN       NaN       NaN       NaN       NaN   \n",
       "model_pow_9   -0.010975       NaN       NaN       NaN       NaN       NaN   \n",
       "model_pow_10  -0.198144  0.006025       NaN       NaN       NaN       NaN   \n",
       "model_pow_11    2.74308 -0.187468  0.005662       NaN       NaN       NaN   \n",
       "model_pow_12  -1.043563  0.163339 -0.013579  0.000473       NaN       NaN   \n",
       "model_pow_13   -8.62197  1.505889 -0.165941  0.010514 -0.000292       NaN   \n",
       "model_pow_14  17.213916 -5.034803  0.939958 -0.109773  0.007333 -0.000214   \n",
       "model_pow_15 -12.913967  6.612437 -2.019619   0.38868 -0.046442  0.003159   \n",
       "\n",
       "             coef_x_15  \n",
       "model_pow_1        NaN  \n",
       "model_pow_2        NaN  \n",
       "model_pow_3        NaN  \n",
       "model_pow_4        NaN  \n",
       "model_pow_5        NaN  \n",
       "model_pow_6        NaN  \n",
       "model_pow_7        NaN  \n",
       "model_pow_8        NaN  \n",
       "model_pow_9        NaN  \n",
       "model_pow_10       NaN  \n",
       "model_pow_11       NaN  \n",
       "model_pow_12       NaN  \n",
       "model_pow_13       NaN  \n",
       "model_pow_14       NaN  \n",
       "model_pow_15 -0.000094  "
      ]
     },
     "execution_count": 30,
     "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 régression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "{\\rm RSS}(w):=\\sum_{i=1}^N\\left(y_i-\\sum_{j=0}^Mw_jx_i^j\\right)^2+\\lambda \\sum_{j=0}^M w_j^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "def ridge_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    ridgereg = Ridge(alpha=alpha) #alpha c'est lambda\n",
    "    ridgereg.fit(X=data[predictors], y= 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, linewidth=4, color = 'r')\n",
    "        plt.plot(data['x'],data['y'],'.',color = 'b')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((data['y']-y_pred)**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([ridgereg.intercept_])\n",
    "    ret.extend(ridgereg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=4.04792e-26): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=2.41282e-25): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=7.89039e-23): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=3.69428e-22): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=7.79194e-22): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\scipy\\_lib\\_util.py:1226: LinAlgWarning: Ill-conditioned matrix (rcond=1.60716e-21): result may not be accurate.\n",
      "  return f(*arrays, *other_args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "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": 26,
   "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>1.657239</td>\n",
       "      <td>5566.306821</td>\n",
       "      <td>-32099.576379</td>\n",
       "      <td>84138.807323</td>\n",
       "      <td>-133368.451006</td>\n",
       "      <td>143548.540442</td>\n",
       "      <td>-111692.479616</td>\n",
       "      <td>65281.735001</td>\n",
       "      <td>-29364.108054</td>\n",
       "      <td>10304.116586</td>\n",
       "      <td>-2831.234536</td>\n",
       "      <td>604.890628</td>\n",
       "      <td>-98.548971</td>\n",
       "      <td>11.812318</td>\n",
       "      <td>-0.979181</td>\n",
       "      <td>0.049979</td>\n",
       "      <td>-0.00118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>1.04612</td>\n",
       "      <td>443.361898</td>\n",
       "      <td>-1660.871046</td>\n",
       "      <td>2131.081009</td>\n",
       "      <td>-437.863795</td>\n",
       "      <td>-1478.078351</td>\n",
       "      <td>1153.364846</td>\n",
       "      <td>563.661724</td>\n",
       "      <td>-1497.812924</td>\n",
       "      <td>1219.585917</td>\n",
       "      <td>-588.816366</td>\n",
       "      <td>189.294593</td>\n",
       "      <td>-41.788553</td>\n",
       "      <td>6.288634</td>\n",
       "      <td>-0.618283</td>\n",
       "      <td>0.035868</td>\n",
       "      <td>-0.000932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>1.063834</td>\n",
       "      <td>-5.824372</td>\n",
       "      <td>-51.761144</td>\n",
       "      <td>177.226647</td>\n",
       "      <td>-110.598164</td>\n",
       "      <td>-161.558859</td>\n",
       "      <td>212.818823</td>\n",
       "      <td>73.684331</td>\n",
       "      <td>-324.101429</td>\n",
       "      <td>314.144009</td>\n",
       "      <td>-171.987131</td>\n",
       "      <td>61.11938</td>\n",
       "      <td>-14.658028</td>\n",
       "      <td>2.365352</td>\n",
       "      <td>-0.246839</td>\n",
       "      <td>0.015075</td>\n",
       "      <td>-0.00041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>1.123989</td>\n",
       "      <td>1.899961</td>\n",
       "      <td>-3.011585</td>\n",
       "      <td>-0.884479</td>\n",
       "      <td>2.68291</td>\n",
       "      <td>2.869041</td>\n",
       "      <td>-1.393128</td>\n",
       "      <td>-3.934758</td>\n",
       "      <td>1.173689</td>\n",
       "      <td>4.326436</td>\n",
       "      <td>-4.980546</td>\n",
       "      <td>2.627671</td>\n",
       "      <td>-0.820144</td>\n",
       "      <td>0.160448</td>\n",
       "      <td>-0.019415</td>\n",
       "      <td>0.001334</td>\n",
       "      <td>-0.00004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1.153834</td>\n",
       "      <td>-1.288152</td>\n",
       "      <td>0.974034</td>\n",
       "      <td>1.426745</td>\n",
       "      <td>0.80312</td>\n",
       "      <td>-0.653851</td>\n",
       "      <td>-1.422474</td>\n",
       "      <td>0.07845</td>\n",
       "      <td>1.910582</td>\n",
       "      <td>-1.687913</td>\n",
       "      <td>0.643055</td>\n",
       "      <td>-0.104628</td>\n",
       "      <td>-0.005432</td>\n",
       "      <td>0.005493</td>\n",
       "      <td>-0.000998</td>\n",
       "      <td>0.000083</td>\n",
       "      <td>-0.000003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>1.16639</td>\n",
       "      <td>-0.029764</td>\n",
       "      <td>0.137325</td>\n",
       "      <td>0.298685</td>\n",
       "      <td>0.415879</td>\n",
       "      <td>0.349237</td>\n",
       "      <td>-0.045173</td>\n",
       "      <td>-0.619716</td>\n",
       "      <td>-0.535627</td>\n",
       "      <td>1.599345</td>\n",
       "      <td>-1.272829</td>\n",
       "      <td>0.531608</td>\n",
       "      <td>-0.131927</td>\n",
       "      <td>0.019774</td>\n",
       "      <td>-0.001693</td>\n",
       "      <td>0.000069</td>\n",
       "      <td>-0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>1.216545</td>\n",
       "      <td>0.741574</td>\n",
       "      <td>0.028452</td>\n",
       "      <td>0.049047</td>\n",
       "      <td>0.052405</td>\n",
       "      <td>0.032838</td>\n",
       "      <td>-0.002714</td>\n",
       "      <td>-0.029437</td>\n",
       "      <td>-0.019478</td>\n",
       "      <td>0.016356</td>\n",
       "      <td>0.013717</td>\n",
       "      <td>-0.017939</td>\n",
       "      <td>0.008305</td>\n",
       "      <td>-0.002091</td>\n",
       "      <td>0.000305</td>\n",
       "      <td>-0.000024</td>\n",
       "      <td>0.000001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>1.232404</td>\n",
       "      <td>0.847114</td>\n",
       "      <td>0.008334</td>\n",
       "      <td>0.015435</td>\n",
       "      <td>0.018656</td>\n",
       "      <td>0.01555</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.004894</td>\n",
       "      <td>-0.008739</td>\n",
       "      <td>-0.001619</td>\n",
       "      <td>0.005196</td>\n",
       "      <td>-0.001312</td>\n",
       "      <td>-0.000396</td>\n",
       "      <td>0.000264</td>\n",
       "      <td>-0.000056</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>1.236434</td>\n",
       "      <td>0.873096</td>\n",
       "      <td>0.004912</td>\n",
       "      <td>0.009424</td>\n",
       "      <td>0.01204</td>\n",
       "      <td>0.011129</td>\n",
       "      <td>0.006058</td>\n",
       "      <td>-0.001214</td>\n",
       "      <td>-0.005753</td>\n",
       "      <td>-0.003315</td>\n",
       "      <td>0.002553</td>\n",
       "      <td>0.00136</td>\n",
       "      <td>-0.001454</td>\n",
       "      <td>0.000488</td>\n",
       "      <td>-0.000082</td>\n",
       "      <td>0.000007</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_20</th>\n",
       "      <td>1.239944</td>\n",
       "      <td>0.893524</td>\n",
       "      <td>0.002876</td>\n",
       "      <td>0.005706</td>\n",
       "      <td>0.007666</td>\n",
       "      <td>0.007719</td>\n",
       "      <td>0.005155</td>\n",
       "      <td>0.00056</td>\n",
       "      <td>-0.00347</td>\n",
       "      <td>-0.003489</td>\n",
       "      <td>0.000605</td>\n",
       "      <td>0.002525</td>\n",
       "      <td>-0.001681</td>\n",
       "      <td>0.000478</td>\n",
       "      <td>-0.000071</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   rss    intercept      coef_x_1      coef_x_2  \\\n",
       "alpha_1e-15   1.657239  5566.306821 -32099.576379  84138.807323   \n",
       "alpha_1e-10    1.04612   443.361898  -1660.871046   2131.081009   \n",
       "alpha_1e-08   1.063834    -5.824372    -51.761144    177.226647   \n",
       "alpha_0.0001  1.123989     1.899961     -3.011585     -0.884479   \n",
       "alpha_0.001   1.153834    -1.288152      0.974034      1.426745   \n",
       "alpha_0.01     1.16639    -0.029764      0.137325      0.298685   \n",
       "alpha_1       1.216545     0.741574      0.028452      0.049047   \n",
       "alpha_5       1.232404     0.847114      0.008334      0.015435   \n",
       "alpha_10      1.236434     0.873096      0.004912      0.009424   \n",
       "alpha_20      1.239944     0.893524      0.002876      0.005706   \n",
       "\n",
       "                   coef_x_3       coef_x_4       coef_x_5      coef_x_6  \\\n",
       "alpha_1e-15  -133368.451006  143548.540442 -111692.479616  65281.735001   \n",
       "alpha_1e-10     -437.863795   -1478.078351    1153.364846    563.661724   \n",
       "alpha_1e-08     -110.598164    -161.558859     212.818823     73.684331   \n",
       "alpha_0.0001        2.68291       2.869041      -1.393128     -3.934758   \n",
       "alpha_0.001         0.80312      -0.653851      -1.422474       0.07845   \n",
       "alpha_0.01         0.415879       0.349237      -0.045173     -0.619716   \n",
       "alpha_1            0.052405       0.032838      -0.002714     -0.029437   \n",
       "alpha_5            0.018656        0.01555       0.006092     -0.004894   \n",
       "alpha_10            0.01204       0.011129       0.006058     -0.001214   \n",
       "alpha_20           0.007666       0.007719       0.005155       0.00056   \n",
       "\n",
       "                  coef_x_7      coef_x_8     coef_x_9   coef_x_10  coef_x_11  \\\n",
       "alpha_1e-15  -29364.108054  10304.116586 -2831.234536  604.890628 -98.548971   \n",
       "alpha_1e-10   -1497.812924   1219.585917  -588.816366  189.294593 -41.788553   \n",
       "alpha_1e-08    -324.101429    314.144009  -171.987131    61.11938 -14.658028   \n",
       "alpha_0.0001      1.173689      4.326436    -4.980546    2.627671  -0.820144   \n",
       "alpha_0.001       1.910582     -1.687913     0.643055   -0.104628  -0.005432   \n",
       "alpha_0.01       -0.535627      1.599345    -1.272829    0.531608  -0.131927   \n",
       "alpha_1          -0.019478      0.016356     0.013717   -0.017939   0.008305   \n",
       "alpha_5          -0.008739     -0.001619     0.005196   -0.001312  -0.000396   \n",
       "alpha_10         -0.005753     -0.003315     0.002553     0.00136  -0.001454   \n",
       "alpha_20          -0.00347     -0.003489     0.000605    0.002525  -0.001681   \n",
       "\n",
       "              coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15   11.812318 -0.979181  0.049979  -0.00118  \n",
       "alpha_1e-10    6.288634 -0.618283  0.035868 -0.000932  \n",
       "alpha_1e-08    2.365352 -0.246839  0.015075  -0.00041  \n",
       "alpha_0.0001   0.160448 -0.019415  0.001334  -0.00004  \n",
       "alpha_0.001    0.005493 -0.000998  0.000083 -0.000003  \n",
       "alpha_0.01     0.019774 -0.001693  0.000069 -0.000001  \n",
       "alpha_1       -0.002091  0.000305 -0.000024  0.000001  \n",
       "alpha_5        0.000264 -0.000056  0.000005      -0.0  \n",
       "alpha_10       0.000488 -0.000082  0.000007      -0.0  \n",
       "alpha_20       0.000478 -0.000071  0.000006      -0.0  "
      ]
     },
     "execution_count": 26,
     "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": 32,
   "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": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# determining the number of zeros in each row of the coefficients data set:\n",
    "coef_matrix_ridge.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Régression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "{\\rm RSS}(w):=\\sum_{i=1}^N\\left(y_i-\\sum_{j=0}^Mw_jx_i^j\\right)^2+\\lambda \\sum_{j=0}^M |w_j|\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "def lasso_regression(data, predictors, alpha, models_to_plot={}):\n",
    "    #Fit the model\n",
    "    lassoreg = Lasso(alpha=alpha, max_iter=int(1e5))\n",
    "    #Fit the model\n",
    "    lassoreg.fit(X=data[predictors], y= 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, linewidth=4, color = 'r')\n",
    "        plt.plot(data['x'],data['y'],'.',color = 'b')\n",
    "        plt.title('Plot for alpha: %.3g'%alpha)\n",
    "    \n",
    "    #Return the result in pre-defined format\n",
    "    rss = sum((data['y']-y_pred)**2)\n",
    "    ret = [rss]\n",
    "    ret.extend([lassoreg.intercept_])\n",
    "    ret.extend(lassoreg.coef_)\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Initialize predictors to all 15 powers of x\n",
    "#complétez\n",
    "\n",
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.030e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.030e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.030e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.054e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.224e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.586e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 6.726e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 8.485e-01, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 1.124e+00, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "c:\\Users\\lione\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:695: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 1.204e+00, tolerance: 3.718e-03\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x1000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Initialize predictors to all 15 powers of x\n",
    "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": 42,
   "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>1.206075</td>\n",
       "      <td>-0.784268</td>\n",
       "      <td>2.527844</td>\n",
       "      <td>-1.021511</td>\n",
       "      <td>0.061823</td>\n",
       "      <td>0.012459</td>\n",
       "      <td>0.000475</td>\n",
       "      <td>-0.000161</td>\n",
       "      <td>-0.000042</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-10</th>\n",
       "      <td>1.206075</td>\n",
       "      <td>-0.784268</td>\n",
       "      <td>2.527844</td>\n",
       "      <td>-1.021511</td>\n",
       "      <td>0.061823</td>\n",
       "      <td>0.012459</td>\n",
       "      <td>0.000475</td>\n",
       "      <td>-0.000161</td>\n",
       "      <td>-0.000042</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-08</th>\n",
       "      <td>1.206076</td>\n",
       "      <td>-0.784234</td>\n",
       "      <td>2.527785</td>\n",
       "      <td>-1.021476</td>\n",
       "      <td>0.061815</td>\n",
       "      <td>0.012459</td>\n",
       "      <td>0.000475</td>\n",
       "      <td>-0.000161</td>\n",
       "      <td>-0.000042</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1e-05</th>\n",
       "      <td>1.206642</td>\n",
       "      <td>-0.749947</td>\n",
       "      <td>2.468236</td>\n",
       "      <td>-0.986587</td>\n",
       "      <td>0.054199</td>\n",
       "      <td>0.012677</td>\n",
       "      <td>0.000534</td>\n",
       "      <td>-0.000154</td>\n",
       "      <td>-0.000042</td>\n",
       "      <td>-0.000005</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.0001</th>\n",
       "      <td>1.212692</td>\n",
       "      <td>-0.451278</td>\n",
       "      <td>1.958392</td>\n",
       "      <td>-0.697252</td>\n",
       "      <td>-0.003956</td>\n",
       "      <td>0.012793</td>\n",
       "      <td>0.001122</td>\n",
       "      <td>-0.000086</td>\n",
       "      <td>-0.000038</td>\n",
       "      <td>-0.000006</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.001</th>\n",
       "      <td>1.265313</td>\n",
       "      <td>0.711026</td>\n",
       "      <td>0.155153</td>\n",
       "      <td>0.163525</td>\n",
       "      <td>-0.103184</td>\n",
       "      <td>-0.007</td>\n",
       "      <td>0.002889</td>\n",
       "      <td>0.000342</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>-0.000006</td>\n",
       "      <td>-0.000001</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_0.01</th>\n",
       "      <td>1.330416</td>\n",
       "      <td>1.00913</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.008997</td>\n",
       "      <td>-0.002765</td>\n",
       "      <td>0.000564</td>\n",
       "      <td>0.000087</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>-0.000001</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <td>1.387253</td>\n",
       "      <td>0.925302</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.002291</td>\n",
       "      <td>0.00019</td>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>-0.000001</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_5</th>\n",
       "      <td>1.605066</td>\n",
       "      <td>0.867163</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.000528</td>\n",
       "      <td>-0.000449</td>\n",
       "      <td>0.000075</td>\n",
       "      <td>0.00002</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_10</th>\n",
       "      <td>1.747649</td>\n",
       "      <td>0.843496</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.000516</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.000035</td>\n",
       "      <td>0.000001</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>-0.0</td>\n",
       "      <td>0.0</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  \\\n",
       "alpha_1e-15   1.206075 -0.784268  2.527844 -1.021511  0.061823  0.012459   \n",
       "alpha_1e-10   1.206075 -0.784268  2.527844 -1.021511  0.061823  0.012459   \n",
       "alpha_1e-08   1.206076 -0.784234  2.527785 -1.021476  0.061815  0.012459   \n",
       "alpha_1e-05   1.206642 -0.749947  2.468236 -0.986587  0.054199  0.012677   \n",
       "alpha_0.0001  1.212692 -0.451278  1.958392 -0.697252 -0.003956  0.012793   \n",
       "alpha_0.001   1.265313  0.711026  0.155153  0.163525 -0.103184    -0.007   \n",
       "alpha_0.01    1.330416   1.00913       0.0       0.0       0.0 -0.008997   \n",
       "alpha_1       1.387253  0.925302      -0.0      -0.0      -0.0      -0.0   \n",
       "alpha_5       1.605066  0.867163      -0.0      -0.0      -0.0      -0.0   \n",
       "alpha_10      1.747649  0.843496      -0.0      -0.0      -0.0      -0.0   \n",
       "\n",
       "              coef_x_5  coef_x_6  coef_x_7  coef_x_8  coef_x_9 coef_x_10  \\\n",
       "alpha_1e-15   0.000475 -0.000161 -0.000042 -0.000005      -0.0       0.0   \n",
       "alpha_1e-10   0.000475 -0.000161 -0.000042 -0.000005      -0.0       0.0   \n",
       "alpha_1e-08   0.000475 -0.000161 -0.000042 -0.000005      -0.0       0.0   \n",
       "alpha_1e-05   0.000534 -0.000154 -0.000042 -0.000005      -0.0       0.0   \n",
       "alpha_0.0001  0.001122 -0.000086 -0.000038 -0.000006      -0.0       0.0   \n",
       "alpha_0.001   0.002889  0.000342  0.000001 -0.000006 -0.000001      -0.0   \n",
       "alpha_0.01   -0.002765  0.000564  0.000087  0.000003 -0.000001      -0.0   \n",
       "alpha_1           -0.0 -0.002291   0.00019    0.0001  0.000001 -0.000001   \n",
       "alpha_5           -0.0 -0.000528 -0.000449  0.000075   0.00002      -0.0   \n",
       "alpha_10          -0.0      -0.0 -0.000516      -0.0  0.000035  0.000001   \n",
       "\n",
       "             coef_x_11 coef_x_12 coef_x_13 coef_x_14 coef_x_15  \n",
       "alpha_1e-15        0.0       0.0       0.0      -0.0      -0.0  \n",
       "alpha_1e-10        0.0       0.0       0.0      -0.0      -0.0  \n",
       "alpha_1e-08        0.0       0.0       0.0      -0.0      -0.0  \n",
       "alpha_1e-05        0.0       0.0       0.0      -0.0      -0.0  \n",
       "alpha_0.0001       0.0       0.0       0.0      -0.0      -0.0  \n",
       "alpha_0.001        0.0       0.0       0.0       0.0      -0.0  \n",
       "alpha_0.01        -0.0      -0.0       0.0       0.0       0.0  \n",
       "alpha_1           -0.0      -0.0      -0.0       0.0       0.0  \n",
       "alpha_5           -0.0      -0.0      -0.0       0.0       0.0  \n",
       "alpha_10          -0.0      -0.0      -0.0      -0.0       0.0  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#pd.options.display.float_format = '{:,.2g}'.format\n",
    "coef_matrix_lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "alpha_1e-15     0\n",
       "alpha_1e-10     0\n",
       "alpha_1e-08     0\n",
       "alpha_1e-05     0\n",
       "alpha_0.0001    0\n",
       "alpha_0.001     0\n",
       "alpha_0.01      3\n",
       "alpha_1         5\n",
       "alpha_5         5\n",
       "alpha_10        7\n",
       "dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef_matrix_lasso.apply(lambda x: sum(x.values==0),axis=1)"
   ]
  }
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