Multi-variate LASSO regression with CV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-variate Rregression Metamodel with DOE based on random sampling\n",
    "* Input variable space should be constructed using random sampling, not classical factorial DOE\n",
    "* Linear fit is often inadequate but higher-order polynomial fits often leads to overfitting i.e. learns spurious, flawed relationships between input and output\n",
    "* R-square fit can often be misleding measure in case of high-dimensional regression\n",
    "* Metamodel can be constructed by selectively discovering features (or their combination) which matter and shrinking other high-order terms towards zero\n",
    "\n",
    "#### LASSO: Least Absolute Shrinkage and Selection Operator\n",
    "$$ {\\displaystyle \\min _{\\beta _{0},\\beta }\\left\\{{\\frac {1}{N}}\\sum _{i=1}^{N}(y_{i}-\\beta _{0}-x_{i}^{T}\\beta )^{2}\\right\\}{\\text{ subject to }}\\sum _{j=1}^{p}|\\beta _{j}|\\leq t.} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random (equivalent to Latin Hypercube sampling done in Optislang) feature vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X=np.array(10*np.random.randn(37,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df=pd.DataFrame(X,columns=['Feature'+str(l) for l in range(1,6)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487\n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441\n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619\n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331\n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the random distributions of input features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998dd2550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2299895dd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e98908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b8ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GGdSSJDXMoJYkqWEGtSRJDTOoJUlqmEEtSVLDDGpJkhpmUEuS1DCDWpKkhhnUkiQ1zKCW\nJKlhBrUkSQ0zqCVJaphBLUlSwwxqSZIaZlBLktQwg1qSpIYZ1JIkNcygliSpYQa1JEkNM6glSWqY\nQS1JUsMMakmSGmZQS5LUMINakqSGGdSSJDXMoJYkqWEGtSRJDTOoJUlqmEEtSVLDDGpJkhpmUEuS\n1DCDWpKkhhnUkiQ1zKCWJKlhyxLUSdYkmUlSSVYvxxiSJI2D5dqj/lNgZpnWLUnS2Og8qJM8A3gO\n8K6u1y1J0rhZ1eXKkuwJnA68Fbily3VLkjSOut6jfhXwQOADHa9XkqSxlKrqZkXJw4DvAC+vqnOT\nbAD+O/Dgqvqp89VJNgIbASYmJo7ctGnTwGPNzMywevVoXaPWYk1br7t1yeuY2Btu2NHBZBozinWN\nYk0wmnWNYk3Qdl3r1uy/6L4Lvb+vX7/+4qqa3FX/Lg99vwP4alWdO0jjqjoDOANgcnKypqamBh5o\nenqa3Wk/DFqsacNJm5e8jhPW7eS0rZ2eYWnCKNY1ijXBaNY1ijVB23VtO35q0X2X+v7eyX+RJIcD\nrwCekeQh/cX79H/un+Suqmr07yRJktrV1Z8ujwb2Av5unteuBf4SeGVHY0mSNDa6CuqvAOvnLHsO\n8AbgaOCqjsaRJGmsdBLUVXUTMD17WZK1/X9eON/FZJIkade817ckSQ1btqCuqjOrKu5NS5K0eO5R\nS5LUMINakqSGGdSSJDXMoJYkqWEGtSRJDTOoJUlqmEEtSVLDDGpJkhpmUEuS1DCDWpKkhhnUkiQ1\nzKCWJKlhBrUkSQ0zqCVJaphBLUlSwwxqSZIaZlBLktQwg1qSpIYZ1JIkNcygliSpYQa1JEkNM6gl\nSWqYQS1JUsMMakmSGmZQS5LUMINakqSGGdSSJDXMoJYkqWEGtSRJDTOoJUlqmEEtSVLDDGpJkhpm\nUEuS1DCDWpKkhhnUkiQ1rLOgTvKiJJuT/CDJTJKLk7y0q/VLkjSOVnW4rt8FrgZeC9wEHA18PMmB\nVXV6h+NIkjQ2ugzqY6rqplnPL0hyMPB6wKCWJGkROjv0PSek7/F14OCuxpAkadws98VkTwWuXOYx\nJEkaWamq5Vlx8kzgC8ArqurMeV7fCGwEmJiYOHLTpk0Dr3tmZobVq1d3NNM2tFjT1utuXfI6JvaG\nG3Z0MJnGjGJdo1gTjGZdo1gTtF3XujX7L7rvQu/v69evv7iqJnfVf1mCOsla4GvARVX1H3bVfnJy\nsrZs2TLw+qenp5mamlrs9JrUYk1rT9q85HWcsG4np23t8lKINoxiXaNYE4xmXaNYE7Rd17ZTn7vo\nvgu9vycZKKg7P/Sd5KHAecD3gOO7Xr8kSeOk06BOsg/wOeABwPOq6vYu1y9J0rjp7BhDklXAp4BH\nA0+rqn/uat2SJI2rLk8G/Dm9m5y8FnhYkofNeu3rVXVHh2NJkjQWugzqZ/V/vnee1x4FbOtwLEmS\nxkJnQV1Va7talyRJ6vHbsyRJaphBLUlSwwxqSZIaZlBLktQwg1qSpIYZ1JIkNcygliSpYQa1JEkN\nM6glSWqYQS1JUsMMakmSGmZQS5LUMINakqSGGdSSJDXMoJYkqWEGtSRJDVu10hNYDmtP2rzSU9ht\nJ6zbyYYhnLckaXm5Ry1JUsMMakmSGmZQS5LUMINakqSGGdSSJDXMoJYkqWEGtSRJDTOoJUlqmEEt\nSVLDDGpJkhpmUEuS1DCDWpKkhhnUkiQ1zKCWJKlhBrUkSQ0zqCVJaphBLUlSwzoN6iSPTfLFJLcn\n+X6StybZs8sxJEkaJ6u6WlGSA4DzgW8DLwB+DjiN3h8Db+lqHEmSxklnQQ28Ctgb+I9VdRvwhST7\nAack+ZP+MkmStBu6PPR9FPD5OYG8iV54/3KH40iSNDa6DOrDgMtnL6iqfwJu778mSZJ2U5dBfQBw\nyzzLb+6/JkmSdlOqqpsVJT8GTqyq98xZfi3wV1X1pjnLNwIb+08fA1yxG8MdCNy0hOm2aBRrAusa\nJqNYE4xmXaNYE4xfXYdU1UG76tzlxWQ3A/vPs/yA/mv3UlVnAGcsZqAkW6pqcjF9WzWKNYF1DZNR\nrAlGs65RrAmsayFdHvq+nDnnopM8EtiHOeeuJUnSYLoM6vOAZyd58KxlLwZ2AF/qcBxJksZGl0H9\nQeAO4Owkv9o/B30K8GfL8BnqRR0yb9wo1gTWNUxGsSYYzbpGsSawrnl1djEZ9G4hCrwfeCq9K8A/\nApxSVXd1NogkSWOk06CWJEndGppvz0qyX5K3JbkkyW1Jrk/yN0l+fk67qSQ1z+PUlZr7Qgatqd92\nTf+1HyW5Kcn7k+yzEvMeRJIXJzk7yQ/6//03zNNmaLYVDFZTv91Qbav5JJleYNs8aKXnNohR/IKg\nJBsW2CavWum5DSrJoUk+lOTSJHclmZ6nTZK8Kck1SXYk+XKSJ6zAdAc2YF3b5tl21w+y/i4/nrXc\n/g3wW8BfAl+mdzX5G4GvJXlcVV0zp/3xwFWznl93v8xy9wxUU5K9gM8DdwIvAR4C/Fn/58tXYN6D\nOA5YC3wOeOUu2g7DtoIBahrSbbWQ/wO8ac6yO1ZiIrtjDL4g6FfoXaR7j6sWatigw4Gjga8Cey3Q\n5iTgZOBEep8Yej1wfpIjqmqgYFsBg9QF8HHg9FnP7xxo7VU1FA9gX2DvOcseCswAfzBr2RRQwBEr\nPecOa3opcBfwqFnLXgTcDTx6petYoLY9+j9X97fHhnnaDM222o2ahm5bLVDrNHDWSs9jkXN/I717\nN+w3a9nv0bud8X4rNa8O6trQ//9u9UrPZQk17DHr32cB03NefxBwK/D7s5btC9wIvH2l57/YuvrL\ntwHvWsz6h+bQd1Vtr6odc5b9C/A94OCVmdXS7EZNRwH/r6qunrXsM/T+GnvOsk90Earq7pWeQ9cG\nrGnottUI8guCGjXA79DTgP2AT87qsx04h952bdJyv98NTVDPJ8lBwKHAlfO8fEH/XMG2JG8ZlvNT\nC9Q03xee3Al8l9H4wpOh3FYLGKVt9az+Od7bk3w+yeNWekIDGvUvCPpukp1Jrkjy2ys9mY4dRu+I\n1HfmLL+M0dh2v5XkziS3JjkrySGDdBqmc9TzOY3eYeIzZy27FTgVuJDeXszzgD8EDgJeez/PbzHm\nq2lUv/Bk2LfVfEZlW30J+Cjwj8AhwJuBC5M8vqq2reTEBjAq22CuH9A7d/v3wJ70roH4YJJ9qurd\nKzqz7hwAzNRPf6T3ZmCfJA/o/+E7jD5L7xz2tcAvAH9A73dqXVXdel8dVzSok+wP/Myu2lXVT92C\nNMnv0Ls459iq+uGstl8Hvj6r6flJ7gBen+RtVbWsN3xfjppasJS67qPt0G6rYbO7tVbVH8xafGGS\n8+ntpb4W+N1lmaTuU1V9nt6Fivc4r38V/puTvHcUTzeNkqqavfNxYZKLgG/Qu/bgvffVd6X3qF8I\nfHiAdrnXk+T59K6ce0NV/c0A/c+idzHJOnpXsi6n5ajpvr7w5JuLmeQiLKquRWh+W+1CC9tqPkuq\ntaquT/J/gSd1OqvlsVtfEDTkzqJ3seIhwNW7aDsMbgZWJ9lzzl71AcDtQ7w3/VOq6ltJrmCA36kV\nPUddVR+pquzqMbtPkn9P78KQD1bVnw46VOeTX2ig5alpvi88eQDwb7mfvvBkMXUtdqgO1jHYQMtT\n04pvq/l0VOuw3B1pnL4gaFi2yaAup3dY/9A5y3/quoMRMdD2G6qLyZIcTu/qv/8FvGY3uh4H7AQu\nXY55LcWANZ0HPHnOhQfPBx7Y7zdKmt1WAxrJbZXkEcDTgYtXei4DGKcvCDoO+CG9T4qMgouA2+gd\nAQKgf7OgY+ht15GR5Ah6f4Ds8ndqpQ99DyzJw+m90c0A7wP+XfKvOwC3VdW3++3+gt5FF5cAP6b3\nIfRXA+9p8LzvQDXRO7z1ZnpfeHIyvcN67wY+XlVzr45sQnr3fX8svc9FAkwmmQFurKov9dsMzbaC\nwWpiCLfVXP2ru99B7yMy19K7Mc8b6X0W/D0rOLVBfZDeH71nJ/ljekczTmF5viDofpPkLHoXI32L\n3nv3i/uP1wzL+el+6B7df7oG2C/Jcf3n51bV7endmfDkJDfzkxue7MG9bxTSlF3VBawHXkZvp+x6\neheTvQX4J+594fD8FvPh65V48JObY8z3mJ7V7jX09sZ+RO8uSv8AvI7+fc1begxaU7/tz9L7PO4M\nvb+gPwDss9I13Edtp4zSthq0pmHcVvPUuab/5vIDelfj/xD4NHDYSs9tN2p4LHABvb3oHwBvA/Zc\n6XktsaZ3AlfQ+5jZDnp7Yv9ppee1mzWsvY/3vLX9NqH3x+61/TovBJ640nNfSl3A44Av0rtxy4/p\nhfWZwMGDrN8v5ZAkqWFDdY5akqRxY1BLktQwg1qSpIYZ1JIkNcygliSpYQa1JEkNM6glSWqYQS1J\nUsMMakmSGvb/ARYm5kBZVLh7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d76c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df.columns:\n",
    "    df.hist(i,bins=5,xlabelsize=15,ylabelsize=15,figsize=(8,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate the output variable by analytic function + Gaussian noise (our goal will be to *'learn'* this function)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's construst the ground  truth  or  originating  function  as  follows: \n",
    " \n",
    "$$ y=f(x_1,x_2,x_3,x_4,x_5)= 5x_1^2+13x_2+0.1x_1x_3^2+2x_4x_5+0.1x_5^3+0.8x_1x_4x_5+\\psi(x)\\ :\\ \\psi(x) = {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['y']=5*df['Feature1']**2+13*df['Feature2']+0.1*df['Feature3']**2*df['Feature1'] \\\n",
    "+2*df['Feature4']*df['Feature5']+0.1*df['Feature5']**3+0.8*df['Feature1']*df['Feature4']*df['Feature5'] \\\n",
    "+30*np.random.normal(loc=5,scale=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>-431.953540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>2072.648112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>1701.292666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>2253.726636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>486.519017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5            y\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  -431.953540\n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  2072.648112\n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  1701.292666\n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  2253.726636\n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   486.519017"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot single-variable scatterplots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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te7U12TvEq1ZfxVlvP4vDTYdrskuiGqT1irPaeg6ionBJoWqb0VJfX8/8Y/M5Ony0/P5X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\nIiKhU7iIiEjo/j9Af/hleNgpbQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998c88a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d9ed68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BR4FHgH9fL7FF+z5PcUbUbuBPYq7DvwOeAB6n+J9raR38u/ZRnCUzBnw+7nhK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\ny2OqKla3YwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e70f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TkcsMufu/uPvB6O5dwHHR8rlAt7sPu/sTwABwWpVje8zdd1TzNadrkthi328J\ndhow4O6/cfcDQDfF/SVjuPsvgP1jms8FNkbLG4H3VDWoyASxxc7dn3H3+6LlHPAY0EKg/abkUpn/\nCmyJlluA3SXrno7akuKE6PD7TjM7I+5gSiRxv30i6vb8TlxdKZEk7ptSDvzMzO41s3VxBzOOZnd/\nJlp+FmiOM5hxJOVzhpktAd4C/IpA+03XcxmHmf0MOHacVZ9191ujx3wWOAjclLTYxvEM8Fp332dm\ny4Afm9nJ7v5CAmKrusniBL4FfInif5xfAv6W4o8IOVS7u+8xs9cAPzWzx6Nf6Ynj7m5mSZoam5jP\nmZk1AjcDF7v7C2Y2uq6S/abkMg53f9dk683sI8A5wFkedUwCe4DFJQ87LmqramwTPGcYGI6W7zWz\nncDrgKCDsOXERpX2W6npxmlmNwCbZzOWKVR938yEu++J/j5nZj+i2I2XpOTyWzNb5O7PmNki4Lm4\nAxrh7r8dWY7zc2ZmR1BMLDe5+y1Rc5D9pm6xGTKzVcClwGp3/0PJqh5gjZk1mNkJQBtwdxwxjmVm\nx5jZYdHyiRRj+028UY1K1H6Lvkwj3gs8PNFjq+AeoM3MTjCzecAaivsrdmaWNrPMyDLFiS5x7qvx\n9AAXRssXAkk6eo79c2bFQ5Qbgcfc/ZqSVWH2W5yzFebijeKA827g/uj2DyXrPktxds8O4L/EENt7\nKfbLDwO/BW6P2t8HPBLFex/w7qTEloT9NibOfwQeAh6MvmSLYo6ng+Isnp0Uuxdji2VMXCdSnL32\nQPTZijU24J8odv++FH3O1gILgTuAfuBnwIIExRb75wxop9gt92DJ/2cdofabztAXEZHg1C0mIiLB\nKbmIiEhwSi4iIhKckouIiASn5CIiIsEpuYhUwMxeLqlse39URmOm2zjazD4WPjows/eZmY+tRC0y\n2zQVWaQCZjbk7o0VbmMJsNndT5nh8w5z95cnWZ8BbqNYUfnj7h5rWXypLzpyEQnMzA6z4nV/7okK\nE/73qL3RzO4ws/ui66CMVDheDyyNjny+amYrzGxzyfa+EZUcGrmGylVmdh/wATNbamY/iYpH/tLM\n3lASypcoXhbi36vyxkVKqLaYSGWOMrP7o+Un3P29FM/A/r27v83MGoB/NbN/oVjZ4b1eLA7YBNxl\nZj0Ur5lxiru/GcDMVkzxmvvc/a3RY+8A/tLd+83s7cA3gXea2VuBxe5+m5n9z8DvWWRKSi4ilXlx\nJCmU+DMRNDITAAABOUlEQVTgTWb2/uj+qynWTHsauNLMzgQKFMvnl1POPAuj1Wz/E/DPJZVsG8ws\nBVwDfKSMbYsEoeQiEp4Bn3D321/RWOzaOgZY5u4vmdmTwJHjPP8gr+yyHvuYfPQ3BfxubHIzs1cD\npwDboqRzLNBjZqs17iLVojEXkfBuB/4qKmeOmb0uqhz8auC5KLGsBI6PHp+jeJnZEU8BJ0WVoo8G\nzhrvRbx4PZ4nzOwD0euYmZ3q7r939yZ3X+LuSyheMVWJRapKyUUkvA3Ao8B9ZvYw8G2KvQQ3AcvN\n7CHgAuBxAHffR3Fc5mEz+6q77wY2USzDvgn4f5O81oeAtWY2Up1Yl0GWRNBUZBERCU5HLiIiEpyS\ni4iIBKfkIiIiwSm5iIhIcEouIiISnJKLiIgEp+QiIiLBKbmIiEhw/x8BwsWLtFy84wAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2299898d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FCPQAq8ys1cwWBjE+GkWMxcTpGE4gdscv+IMz7lLg2Ym2raPHgE4zW2hmM4FV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b87668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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h4qVbW4F/AewK3mokmMhEunMRCW3fvp2uK7oYPTwaPPIqngg56U4FgKXAP6ORYCIlKFxE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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998929198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df.columns:\n",
    "    df.plot.scatter(i,'y', edgecolors=(0,0,0),s=50,c='g',grid=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "linear_model = LinearRegression(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_linear=df.drop('y',axis=1)\n",
    "y_linear=df['y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=True)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_model.fit(X_linear,y_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred_linear = linear_model.predict(X_linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-square of simple linear fit is very bad, coefficients have no meaning i.e. we did not 'learn' the function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "RMSE_linear = np.sqrt(np.sum(np.square(y_pred_linear-y_linear)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of linear model: 4838.87696595\n"
     ]
    }
   ],
   "source": [
    "print(\"Root-mean-square error of linear model:\",RMSE_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear model coefficients</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
       "      <td>9.172156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>-0.945568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3</th>\n",
       "      <td>10.948377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4</th>\n",
       "      <td>45.069370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5</th>\n",
       "      <td>52.445902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Linear model coefficients\n",
       "Feature1                   9.172156\n",
       "Feature2                  -0.945568\n",
       "Feature3                  10.948377\n",
       "Feature4                  45.069370\n",
       "Feature5                  52.445902"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_linear = pd.DataFrame(linear_model.coef_,index=df.drop('y',axis=1).columns, columns=['Linear model coefficients'])\n",
    "coeff_linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 value of linear model: 0.347548929728\n"
     ]
    }
   ],
   "source": [
    "print (\"R2 value of linear model:\",linear_model.score(X_linear,y_linear))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x229989a3d68>]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2UP/JFhERtxgqvH+bQw/vIiIJl52djeM4dO9uYXLu/AHj3a0t4Xlu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\nJKkgTN4lSZKkgjB5lyRJkgri/wOX3gxwzkuAeAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998b91be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel(\"Predicted value with linear fit\",fontsize=20)\n",
    "plt.ylabel(\"Actual y-values\",fontsize=20)\n",
    "plt.grid(1)\n",
    "plt.scatter(y_pred_linear,y_linear,edgecolors=(0,0,0),lw=2,s=80)\n",
    "plt.plot(y_pred_linear,y_pred_linear, 'k--', lw=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create polynomial features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(3,include_bias=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Feature1', 'Feature2', 'Feature3', 'Feature4', 'Feature5', 'Feature1^2', 'Feature1 Feature2', 'Feature1 Feature3', 'Feature1 Feature4', 'Feature1 Feature5', 'Feature2^2', 'Feature2 Feature3', 'Feature2 Feature4', 'Feature2 Feature5', 'Feature3^2', 'Feature3 Feature4', 'Feature3 Feature5', 'Feature4^2', 'Feature4 Feature5', 'Feature5^2', 'Feature1^3', 'Feature1^2 Feature2', 'Feature1^2 Feature3', 'Feature1^2 Feature4', 'Feature1^2 Feature5', 'Feature1 Feature2^2', 'Feature1 Feature2 Feature3', 'Feature1 Feature2 Feature4', 'Feature1 Feature2 Feature5', 'Feature1 Feature3^2', 'Feature1 Feature3 Feature4', 'Feature1 Feature3 Feature5', 'Feature1 Feature4^2', 'Feature1 Feature4 Feature5', 'Feature1 Feature5^2', 'Feature2^3', 'Feature2^2 Feature3', 'Feature2^2 Feature4', 'Feature2^2 Feature5', 'Feature2 Feature3^2', 'Feature2 Feature3 Feature4', 'Feature2 Feature3 Feature5', 'Feature2 Feature4^2', 'Feature2 Feature4 Feature5', 'Feature2 Feature5^2', 'Feature3^3', 'Feature3^2 Feature4', 'Feature3^2 Feature5', 'Feature3 Feature4^2', 'Feature3 Feature4 Feature5', 'Feature3 Feature5^2', 'Feature4^3', 'Feature4^2 Feature5', 'Feature4 Feature5^2', 'Feature5^3']\n",
      "55\n"
     ]
    }
   ],
   "source": [
    "X_poly = poly.fit_transform(X)\n",
    "X_poly_feature_name = poly.get_feature_names(['Feature'+str(l) for l in range(1,6)])\n",
    "print(X_poly_feature_name)\n",
    "print(len(X_poly_feature_name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
       "      <th>Feature1^2</th>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <th>...</th>\n",
       "      <th>Feature3^3</th>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <th>Feature4^3</th>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <th>Feature5^3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>238.813659</td>\n",
       "      <td>275.152347</td>\n",
       "      <td>-371.136432</td>\n",
       "      <td>162.200862</td>\n",
       "      <td>88.433008</td>\n",
       "      <td>...</td>\n",
       "      <td>13851.985264</td>\n",
       "      <td>-6053.849078</td>\n",
       "      <td>-3300.599522</td>\n",
       "      <td>2645.764341</td>\n",
       "      <td>1442.488639</td>\n",
       "      <td>786.454576</td>\n",
       "      <td>-1156.300538</td>\n",
       "      <td>-630.422885</td>\n",
       "      <td>-343.710827</td>\n",
       "      <td>-187.393471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>450.364147</td>\n",
       "      <td>242.927223</td>\n",
       "      <td>-79.783161</td>\n",
       "      <td>-7.401034</td>\n",
       "      <td>269.419924</td>\n",
       "      <td>...</td>\n",
       "      <td>53.135896</td>\n",
       "      <td>4.929117</td>\n",
       "      <td>-179.434718</td>\n",
       "      <td>0.457246</td>\n",
       "      <td>-16.645146</td>\n",
       "      <td>605.933472</td>\n",
       "      <td>0.042416</td>\n",
       "      <td>-1.544076</td>\n",
       "      <td>56.209028</td>\n",
       "      <td>-2046.178007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>187.553677</td>\n",
       "      <td>98.312514</td>\n",
       "      <td>263.630971</td>\n",
       "      <td>-133.846016</td>\n",
       "      <td>-2.679000</td>\n",
       "      <td>...</td>\n",
       "      <td>7133.471192</td>\n",
       "      <td>-3621.678794</td>\n",
       "      <td>-72.489856</td>\n",
       "      <td>1838.734178</td>\n",
       "      <td>36.803257</td>\n",
       "      <td>0.736637</td>\n",
       "      <td>-933.529330</td>\n",
       "      <td>-18.685094</td>\n",
       "      <td>-0.373992</td>\n",
       "      <td>-0.007486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>390.726434</td>\n",
       "      <td>218.878557</td>\n",
       "      <td>20.456610</td>\n",
       "      <td>195.477657</td>\n",
       "      <td>1.805316</td>\n",
       "      <td>...</td>\n",
       "      <td>1.108388</td>\n",
       "      <td>10.591446</td>\n",
       "      <td>0.097816</td>\n",
       "      <td>101.208905</td>\n",
       "      <td>0.934705</td>\n",
       "      <td>0.008632</td>\n",
       "      <td>967.124046</td>\n",
       "      <td>8.931784</td>\n",
       "      <td>0.082489</td>\n",
       "      <td>0.000762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>28.496841</td>\n",
       "      <td>-71.163840</td>\n",
       "      <td>26.038690</td>\n",
       "      <td>-3.066398</td>\n",
       "      <td>-44.069336</td>\n",
       "      <td>...</td>\n",
       "      <td>-116.054593</td>\n",
       "      <td>13.666955</td>\n",
       "      <td>196.417286</td>\n",
       "      <td>-1.609464</td>\n",
       "      <td>-23.130719</td>\n",
       "      <td>-332.427601</td>\n",
       "      <td>0.189536</td>\n",
       "      <td>2.723946</td>\n",
       "      <td>39.147722</td>\n",
       "      <td>562.619066</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 55 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5  Feature1^2  \\\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  238.813659   \n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  450.364147   \n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  187.553677   \n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  390.726434   \n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   28.496841   \n",
       "\n",
       "   Feature1 Feature2  Feature1 Feature3  Feature1 Feature4  Feature1 Feature5  \\\n",
       "0         275.152347        -371.136432         162.200862          88.433008   \n",
       "1         242.927223         -79.783161          -7.401034         269.419924   \n",
       "2          98.312514         263.630971        -133.846016          -2.679000   \n",
       "3         218.878557          20.456610         195.477657           1.805316   \n",
       "4         -71.163840          26.038690          -3.066398         -44.069336   \n",
       "\n",
       "      ...         Feature3^3  Feature3^2 Feature4  Feature3^2 Feature5  \\\n",
       "0     ...       13851.985264         -6053.849078         -3300.599522   \n",
       "1     ...          53.135896             4.929117          -179.434718   \n",
       "2     ...        7133.471192         -3621.678794           -72.489856   \n",
       "3     ...           1.108388            10.591446             0.097816   \n",
       "4     ...        -116.054593            13.666955           196.417286   \n",
       "\n",
       "   Feature3 Feature4^2  Feature3 Feature4 Feature5  Feature3 Feature5^2  \\\n",
       "0          2645.764341                 1442.488639           786.454576   \n",
       "1             0.457246                  -16.645146           605.933472   \n",
       "2          1838.734178                   36.803257             0.736637   \n",
       "3           101.208905                    0.934705             0.008632   \n",
       "4            -1.609464                  -23.130719          -332.427601   \n",
       "\n",
       "    Feature4^3  Feature4^2 Feature5  Feature4 Feature5^2   Feature5^3  \n",
       "0 -1156.300538          -630.422885          -343.710827  -187.393471  \n",
       "1     0.042416            -1.544076            56.209028 -2046.178007  \n",
       "2  -933.529330           -18.685094            -0.373992    -0.007486  \n",
       "3   967.124046             8.931784             0.082489     0.000762  \n",
       "4     0.189536             2.723946            39.147722   562.619066  \n",
       "\n",
       "[5 rows x 55 columns]"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_poly = pd.DataFrame(X_poly, columns=X_poly_feature_name)\n",
    "df_poly.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature1</th>\n",
       "      <th>Feature2</th>\n",
       "      <th>Feature3</th>\n",
       "      <th>Feature4</th>\n",
       "      <th>Feature5</th>\n",
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       "      <th>Feature1 Feature2</th>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <th>...</th>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <th>Feature4^3</th>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <th>Feature5^3</th>\n",
       "      <th>y</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-15.453597</td>\n",
       "      <td>-17.805068</td>\n",
       "      <td>24.016184</td>\n",
       "      <td>-10.495994</td>\n",
       "      <td>-5.722487</td>\n",
       "      <td>238.813659</td>\n",
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       "      <td>-371.136432</td>\n",
       "      <td>162.200862</td>\n",
       "      <td>88.433008</td>\n",
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       "      <td>-6053.849078</td>\n",
       "      <td>-3300.599522</td>\n",
       "      <td>2645.764341</td>\n",
       "      <td>1442.488639</td>\n",
       "      <td>786.454576</td>\n",
       "      <td>-1156.300538</td>\n",
       "      <td>-630.422885</td>\n",
       "      <td>-343.710827</td>\n",
       "      <td>-187.393471</td>\n",
       "      <td>-431.953540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-21.221785</td>\n",
       "      <td>-11.447068</td>\n",
       "      <td>3.759493</td>\n",
       "      <td>0.348747</td>\n",
       "      <td>-12.695441</td>\n",
       "      <td>450.364147</td>\n",
       "      <td>242.927223</td>\n",
       "      <td>-79.783161</td>\n",
       "      <td>-7.401034</td>\n",
       "      <td>269.419924</td>\n",
       "      <td>...</td>\n",
       "      <td>4.929117</td>\n",
       "      <td>-179.434718</td>\n",
       "      <td>0.457246</td>\n",
       "      <td>-16.645146</td>\n",
       "      <td>605.933472</td>\n",
       "      <td>0.042416</td>\n",
       "      <td>-1.544076</td>\n",
       "      <td>56.209028</td>\n",
       "      <td>-2046.178007</td>\n",
       "      <td>2072.648112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.695024</td>\n",
       "      <td>7.178703</td>\n",
       "      <td>19.250129</td>\n",
       "      <td>-9.773332</td>\n",
       "      <td>-0.195619</td>\n",
       "      <td>187.553677</td>\n",
       "      <td>98.312514</td>\n",
       "      <td>263.630971</td>\n",
       "      <td>-133.846016</td>\n",
       "      <td>-2.679000</td>\n",
       "      <td>...</td>\n",
       "      <td>-3621.678794</td>\n",
       "      <td>-72.489856</td>\n",
       "      <td>1838.734178</td>\n",
       "      <td>36.803257</td>\n",
       "      <td>0.736637</td>\n",
       "      <td>-933.529330</td>\n",
       "      <td>-18.685094</td>\n",
       "      <td>-0.373992</td>\n",
       "      <td>-0.007486</td>\n",
       "      <td>1701.292666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>19.766801</td>\n",
       "      <td>11.073039</td>\n",
       "      <td>1.034897</td>\n",
       "      <td>9.889190</td>\n",
       "      <td>0.091331</td>\n",
       "      <td>390.726434</td>\n",
       "      <td>218.878557</td>\n",
       "      <td>20.456610</td>\n",
       "      <td>195.477657</td>\n",
       "      <td>1.805316</td>\n",
       "      <td>...</td>\n",
       "      <td>10.591446</td>\n",
       "      <td>0.097816</td>\n",
       "      <td>101.208905</td>\n",
       "      <td>0.934705</td>\n",
       "      <td>0.008632</td>\n",
       "      <td>967.124046</td>\n",
       "      <td>8.931784</td>\n",
       "      <td>0.082489</td>\n",
       "      <td>0.000762</td>\n",
       "      <td>2253.726636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-5.338243</td>\n",
       "      <td>13.330948</td>\n",
       "      <td>-4.877764</td>\n",
       "      <td>0.574421</td>\n",
       "      <td>8.255401</td>\n",
       "      <td>28.496841</td>\n",
       "      <td>-71.163840</td>\n",
       "      <td>26.038690</td>\n",
       "      <td>-3.066398</td>\n",
       "      <td>-44.069336</td>\n",
       "      <td>...</td>\n",
       "      <td>13.666955</td>\n",
       "      <td>196.417286</td>\n",
       "      <td>-1.609464</td>\n",
       "      <td>-23.130719</td>\n",
       "      <td>-332.427601</td>\n",
       "      <td>0.189536</td>\n",
       "      <td>2.723946</td>\n",
       "      <td>39.147722</td>\n",
       "      <td>562.619066</td>\n",
       "      <td>486.519017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 56 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Feature1   Feature2   Feature3   Feature4   Feature5  Feature1^2  \\\n",
       "0 -15.453597 -17.805068  24.016184 -10.495994  -5.722487  238.813659   \n",
       "1 -21.221785 -11.447068   3.759493   0.348747 -12.695441  450.364147   \n",
       "2  13.695024   7.178703  19.250129  -9.773332  -0.195619  187.553677   \n",
       "3  19.766801  11.073039   1.034897   9.889190   0.091331  390.726434   \n",
       "4  -5.338243  13.330948  -4.877764   0.574421   8.255401   28.496841   \n",
       "\n",
       "   Feature1 Feature2  Feature1 Feature3  Feature1 Feature4  Feature1 Feature5  \\\n",
       "0         275.152347        -371.136432         162.200862          88.433008   \n",
       "1         242.927223         -79.783161          -7.401034         269.419924   \n",
       "2          98.312514         263.630971        -133.846016          -2.679000   \n",
       "3         218.878557          20.456610         195.477657           1.805316   \n",
       "4         -71.163840          26.038690          -3.066398         -44.069336   \n",
       "\n",
       "      ...       Feature3^2 Feature4  Feature3^2 Feature5  Feature3 Feature4^2  \\\n",
       "0     ...              -6053.849078         -3300.599522          2645.764341   \n",
       "1     ...                  4.929117          -179.434718             0.457246   \n",
       "2     ...              -3621.678794           -72.489856          1838.734178   \n",
       "3     ...                 10.591446             0.097816           101.208905   \n",
       "4     ...                 13.666955           196.417286            -1.609464   \n",
       "\n",
       "   Feature3 Feature4 Feature5  Feature3 Feature5^2   Feature4^3  \\\n",
       "0                 1442.488639           786.454576 -1156.300538   \n",
       "1                  -16.645146           605.933472     0.042416   \n",
       "2                   36.803257             0.736637  -933.529330   \n",
       "3                    0.934705             0.008632   967.124046   \n",
       "4                  -23.130719          -332.427601     0.189536   \n",
       "\n",
       "   Feature4^2 Feature5  Feature4 Feature5^2   Feature5^3            y  \n",
       "0          -630.422885          -343.710827  -187.393471  -431.953540  \n",
       "1            -1.544076            56.209028 -2046.178007  2072.648112  \n",
       "2           -18.685094            -0.373992    -0.007486  1701.292666  \n",
       "3             8.931784             0.082489     0.000762  2253.726636  \n",
       "4             2.723946            39.147722   562.619066   486.519017  \n",
       "\n",
       "[5 rows x 56 columns]"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_poly['y']=df['y']\n",
    "df_poly.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train=df_poly.drop('y',axis=1)\n",
    "y_train=df_poly['y']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model without regularization and cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "poly = LinearRegression(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of simple polynomial model: 1.89910302223e-11\n"
     ]
    }
   ],
   "source": [
    "model_poly=poly.fit(X_train,y_train)\n",
    "y_poly = poly.predict(X_train)\n",
    "RMSE_poly=np.sqrt(np.sum(np.square(y_poly-y_train)))\n",
    "print(\"Root-mean-square error of simple polynomial model:\",RMSE_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Coefficients polynomial model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
       "      <td>1.393774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>11.469286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3</th>\n",
       "      <td>-7.258182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4</th>\n",
       "      <td>4.967388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5</th>\n",
       "      <td>0.428594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2</th>\n",
       "      <td>4.610796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2</th>\n",
       "      <td>0.130565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3</th>\n",
       "      <td>0.168512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4</th>\n",
       "      <td>1.652596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5</th>\n",
       "      <td>0.850184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2</th>\n",
       "      <td>-0.063637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3</th>\n",
       "      <td>1.015700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4</th>\n",
       "      <td>0.112208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5</th>\n",
       "      <td>1.075431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2</th>\n",
       "      <td>-0.174379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4</th>\n",
       "      <td>0.097619</td>\n",
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       "    <tr>\n",
       "      <th>Feature3 Feature5</th>\n",
       "      <td>0.247009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2</th>\n",
       "      <td>-0.361048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.699143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^2</th>\n",
       "      <td>-0.329357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^3</th>\n",
       "      <td>0.004918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature2</th>\n",
       "      <td>0.009731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature3</th>\n",
       "      <td>-0.041778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature4</th>\n",
       "      <td>-0.037414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2 Feature5</th>\n",
       "      <td>0.037574</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2^2</th>\n",
       "      <td>0.002429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature3</th>\n",
       "      <td>0.038951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature4</th>\n",
       "      <td>-0.016154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature5</th>\n",
       "      <td>-0.003858</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.101864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature4</th>\n",
       "      <td>-0.054881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3 Feature5</th>\n",
       "      <td>0.002807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>-0.054250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.500361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature5^2</th>\n",
       "      <td>-0.053616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^3</th>\n",
       "      <td>0.025803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature3</th>\n",
       "      <td>0.013705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature4</th>\n",
       "      <td>0.015238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature5</th>\n",
       "      <td>-0.023577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3^2</th>\n",
       "      <td>0.017878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature4</th>\n",
       "      <td>-0.049529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature3 Feature5</th>\n",
       "      <td>0.046253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4^2</th>\n",
       "      <td>-0.086538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature4 Feature5</th>\n",
       "      <td>-0.096008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2 Feature5^2</th>\n",
       "      <td>0.002131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^3</th>\n",
       "      <td>0.012258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <td>-0.036247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>-0.001195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <td>0.007787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <td>0.055605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <td>-0.010458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^3</th>\n",
       "      <td>0.011201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <td>0.120465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <td>0.040685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.049927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients polynomial model\n",
       "Feature1                                         1.393774\n",
       "Feature2                                        11.469286\n",
       "Feature3                                        -7.258182\n",
       "Feature4                                         4.967388\n",
       "Feature5                                         0.428594\n",
       "Feature1^2                                       4.610796\n",
       "Feature1 Feature2                                0.130565\n",
       "Feature1 Feature3                                0.168512\n",
       "Feature1 Feature4                                1.652596\n",
       "Feature1 Feature5                                0.850184\n",
       "Feature2^2                                      -0.063637\n",
       "Feature2 Feature3                                1.015700\n",
       "Feature2 Feature4                                0.112208\n",
       "Feature2 Feature5                                1.075431\n",
       "Feature3^2                                      -0.174379\n",
       "Feature3 Feature4                                0.097619\n",
       "Feature3 Feature5                                0.247009\n",
       "Feature4^2                                      -0.361048\n",
       "Feature4 Feature5                                1.699143\n",
       "Feature5^2                                      -0.329357\n",
       "Feature1^3                                       0.004918\n",
       "Feature1^2 Feature2                              0.009731\n",
       "Feature1^2 Feature3                             -0.041778\n",
       "Feature1^2 Feature4                             -0.037414\n",
       "Feature1^2 Feature5                              0.037574\n",
       "Feature1 Feature2^2                              0.002429\n",
       "Feature1 Feature2 Feature3                       0.038951\n",
       "Feature1 Feature2 Feature4                      -0.016154\n",
       "Feature1 Feature2 Feature5                      -0.003858\n",
       "Feature1 Feature3^2                              0.101864\n",
       "Feature1 Feature3 Feature4                      -0.054881\n",
       "Feature1 Feature3 Feature5                       0.002807\n",
       "Feature1 Feature4^2                             -0.054250\n",
       "Feature1 Feature4 Feature5                       0.500361\n",
       "Feature1 Feature5^2                             -0.053616\n",
       "Feature2^3                                       0.025803\n",
       "Feature2^2 Feature3                              0.013705\n",
       "Feature2^2 Feature4                              0.015238\n",
       "Feature2^2 Feature5                             -0.023577\n",
       "Feature2 Feature3^2                              0.017878\n",
       "Feature2 Feature3 Feature4                      -0.049529\n",
       "Feature2 Feature3 Feature5                       0.046253\n",
       "Feature2 Feature4^2                             -0.086538\n",
       "Feature2 Feature4 Feature5                      -0.096008\n",
       "Feature2 Feature5^2                              0.002131\n",
       "Feature3^3                                       0.012258\n",
       "Feature3^2 Feature4                             -0.036247\n",
       "Feature3^2 Feature5                             -0.001195\n",
       "Feature3 Feature4^2                              0.007787\n",
       "Feature3 Feature4 Feature5                       0.055605\n",
       "Feature3 Feature5^2                             -0.010458\n",
       "Feature4^3                                       0.011201\n",
       "Feature4^2 Feature5                              0.120465\n",
       "Feature4 Feature5^2                              0.040685\n",
       "Feature5^3                                       0.049927"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff_poly = pd.DataFrame(model_poly.coef_,index=df_poly.drop('y',axis=1).columns, \n",
    "                          columns=['Coefficients polynomial model'])\n",
    "coeff_poly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### R-square value of the simple polynomial model is perfect but the model is flawed as shown above i.e. it learned wrong coefficients and overfitted the to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 value of simple polynomial model: 1.0\n"
     ]
    }
   ],
   "source": [
    "print (\"R2 value of simple polynomial model:\",model_poly.score(X_train,y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metamodel (Optislang style :) - polynomial model with cross-validation and LASSO regularization\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LassoCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model1 = LassoCV(cv=10,verbose=0,normalize=True,eps=0.001,n_alphas=100, tol=0.0001,max_iter=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=None, copy_X=True, cv=10, eps=0.001, fit_intercept=True,\n",
       "    max_iter=5000, n_alphas=100, n_jobs=1, normalize=True, positive=False,\n",
       "    precompute='auto', random_state=None, selection='cyclic', tol=0.0001,\n",
       "    verbose=0)"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred1 = np.array(model1.predict(X_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root-mean-square error of Metamodel: 10.6254345131\n"
     ]
    }
   ],
   "source": [
    "RMSE_1=np.sqrt(np.sum(np.square(y_pred1-y_train)))\n",
    "print(\"Root-mean-square error of Metamodel:\",RMSE_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients Metamodel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature1</th>\n",
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       "      <th>Feature2</th>\n",
       "      <td>12.891291</td>\n",
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       "      <th>Feature3</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature1^2</th>\n",
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       "      <th>Feature1 Feature2</th>\n",
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       "      <th>Feature2 Feature5</th>\n",
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       "      <th>Feature3^2</th>\n",
       "      <td>-0.000000</td>\n",
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       "      <th>Feature3 Feature4</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature3 Feature5</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.995183</td>\n",
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       "      <th>Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
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       "      <th>Feature1^3</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature1^2 Feature2</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature1^2 Feature3</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature1^2 Feature4</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature1^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature1 Feature2^2</th>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature1 Feature2 Feature3</th>\n",
       "      <td>-0.000000</td>\n",
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       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.099441</td>\n",
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       "      <th>Feature1 Feature3 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
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       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>0.000024</td>\n",
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       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.799360</td>\n",
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       "      <th>Feature1 Feature5^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature2^2 Feature3</th>\n",
       "      <td>-0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature2^2 Feature4</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature2^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature2 Feature3^2</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature2 Feature3 Feature4</th>\n",
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       "      <th>Feature2 Feature3 Feature5</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature2 Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>Feature2 Feature4 Feature5</th>\n",
       "      <td>-0.000000</td>\n",
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       "    <tr>\n",
       "      <th>Feature2 Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^3</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature4</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>0.001067</td>\n",
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       "    <tr>\n",
       "      <th>Feature3 Feature4^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature4 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3 Feature5^2</th>\n",
       "      <td>-0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^3</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4^2 Feature5</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5^2</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.099169</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients Metamodel\n",
       "Feature1                                  0.000000\n",
       "Feature2                                 12.891291\n",
       "Feature3                                  0.000000\n",
       "Feature4                                  0.000000\n",
       "Feature5                                  0.000000\n",
       "Feature1^2                                4.991474\n",
       "Feature1 Feature2                        -0.000000\n",
       "Feature1 Feature3                         0.000000\n",
       "Feature1 Feature4                         0.000000\n",
       "Feature1 Feature5                         0.000000\n",
       "Feature2^2                                0.000000\n",
       "Feature2 Feature3                         0.000000\n",
       "Feature2 Feature4                        -0.000000\n",
       "Feature2 Feature5                        -0.000000\n",
       "Feature3^2                               -0.000000\n",
       "Feature3 Feature4                         0.000000\n",
       "Feature3 Feature5                         0.000000\n",
       "Feature4^2                                0.000000\n",
       "Feature4 Feature5                         1.995183\n",
       "Feature5^2                               -0.000000\n",
       "Feature1^3                                0.000000\n",
       "Feature1^2 Feature2                       0.000000\n",
       "Feature1^2 Feature3                       0.000000\n",
       "Feature1^2 Feature4                       0.000000\n",
       "Feature1^2 Feature5                       0.000000\n",
       "Feature1 Feature2^2                       0.000000\n",
       "Feature1 Feature2 Feature3               -0.000000\n",
       "Feature1 Feature2 Feature4               -0.000000\n",
       "Feature1 Feature2 Feature5               -0.000000\n",
       "Feature1 Feature3^2                       0.099441\n",
       "Feature1 Feature3 Feature4               -0.000000\n",
       "Feature1 Feature3 Feature5                0.000000\n",
       "Feature1 Feature4^2                       0.000024\n",
       "Feature1 Feature4 Feature5                0.799360\n",
       "Feature1 Feature5^2                       0.000000\n",
       "Feature2^3                                0.000000\n",
       "Feature2^2 Feature3                      -0.000000\n",
       "Feature2^2 Feature4                       0.000000\n",
       "Feature2^2 Feature5                       0.000000\n",
       "Feature2 Feature3^2                       0.000000\n",
       "Feature2 Feature3 Feature4               -0.000000\n",
       "Feature2 Feature3 Feature5                0.000000\n",
       "Feature2 Feature4^2                       0.000000\n",
       "Feature2 Feature4 Feature5               -0.000000\n",
       "Feature2 Feature5^2                      -0.000000\n",
       "Feature3^3                               -0.000000\n",
       "Feature3^2 Feature4                      -0.000000\n",
       "Feature3^2 Feature5                       0.001067\n",
       "Feature3 Feature4^2                       0.000000\n",
       "Feature3 Feature4 Feature5                0.000000\n",
       "Feature3 Feature5^2                      -0.000000\n",
       "Feature4^3                                0.000000\n",
       "Feature4^2 Feature5                       0.000000\n",
       "Feature4 Feature5^2                       0.000000\n",
       "Feature5^3                                0.099169"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff1 = pd.DataFrame(model1.coef_,index=df_poly.drop('y',axis=1).columns, columns=['Coefficients Metamodel'])\n",
    "coeff1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999685404731742"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.score(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11791796322572394"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.alpha_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Recall that the ground  truth  or  originating  function  is  as  follows: \n",
    " \n",
    "$$ y=f(x_1,x_2,x_3,x_4,x_5)= 5x_1^2+13x_2+0.1x_1x_3^2+2x_4x_5+0.1x_5^3+0.8x_1x_4x_5+\\psi(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Printing only the non-zero coefficients of the *metamodel*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Coefficients Metamodel</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Feature2</th>\n",
       "      <td>12.891291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1^2</th>\n",
       "      <td>4.991474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature4 Feature5</th>\n",
       "      <td>1.995183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature3^2</th>\n",
       "      <td>0.099441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4^2</th>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature1 Feature4 Feature5</th>\n",
       "      <td>0.799360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature3^2 Feature5</th>\n",
       "      <td>0.001067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Feature5^3</th>\n",
       "      <td>0.099169</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            Coefficients Metamodel\n",
       "Feature2                                 12.891291\n",
       "Feature1^2                                4.991474\n",
       "Feature4 Feature5                         1.995183\n",
       "Feature1 Feature3^2                       0.099441\n",
       "Feature1 Feature4^2                       0.000024\n",
       "Feature1 Feature4 Feature5                0.799360\n",
       "Feature3^2 Feature5                       0.001067\n",
       "Feature5^3                                0.099169"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeff1[coeff1['Coefficients Metamodel']!=0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22998d25588>]"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IklSQPvOZz3D77ben1P74xz9y9NFH56kjSf2ZN5dKkrQbFi9ezMSJE9PqzrZL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\neRcRERERyRFK3kVEREREcsT/BzdZBixnBH5DAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998e798d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.xlabel(\"Predicted value with Metamodel\",fontsize=20)\n",
    "plt.ylabel(\"Actual y-values\",fontsize=20)\n",
    "plt.grid(1)\n",
    "plt.scatter(y_pred1,y_train,edgecolors=(0,0,0),lw=2,s=80)\n",
    "plt.plot(y_pred1,y_pred1, 'k--', lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.2215799690947899,\n",
       " 1.0784200309052099,\n",
       " -117815.4824067771,\n",
       " 2474147.0440959162)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eTXR09E3XlZyQzoH150i/loFYLHbonVVANXfuaeWPh4teAFXTtD9NnDiRiRMn\nlktbRQYipZQCWoiIg4hUERFvEfESEe/iKlZKfaeUilNKHcqT9qZS6rxSap/xuifPuYlKqUil1HGl\nVN886aFKqYPGuc+NPqGUclFKzTPSdyqlgvKUGa6UOmm8hudJr2/kjTTKlumyAteuXePq1atkZWXd\ndF2XL6Sy4cfVTBvzGPHRUTffuTxikzJYeSjWrnVqmnZr2759O9u3by+Xtop7RiTAb6WsexbQr4D0\nT0QkxHgtB1BKNQeGAi2MMl8ppXLWtPkaGIl1wESjPHU+DVwRkYbAJ8D7Rl2+wBtAB6A98IZSqppR\n5n2j/YbAFaOOMlO9enXGjh1Lw4YNATh27BjJyaW7mKzbtBoP/6svrXr2xtnFxZ7dZNEfMTz7YwRX\nUm8+YGqappWULbfm/lBKlXgCq4hsAi7bmH0gMNcYFHEGiATaK6X8AW8R2WEExR+AB/KU+d54vxDo\naVwt9QVWi8hlEbkCrAb6GefuNvJilM2pq8w4OlrjaVZWFsuWLeP3338vVT3OVRypVb8uPZ98lmr+\nde3ZRQa3DWDluK746OdEmqZVAFseDHQAHlNKnQVSsc4lEhEJLmWbLyilngD2AOONYFEX2JEnT4yR\nZjLe35iO8fUc1s5kK6WSgOp5028oUx24KiLZBdRV5qpUqcIzzzyDk5P1W56cnExqair+/v4213F6\nXzwpVzIIauWCt5/9Vsyu7eNKbR9Xu9WnaZpWErZcEfUF7sR6NXE/cJ/xtTS+xrp9RAhwEfiolPWU\nOaXUKKXUHqXUnvj4eLvU6evri7e39fHapk2bmDFjBmlpaTaXP70vnh2//I9vnnuK5IQ4u/Qpx97o\nK8zeHmXXOjVNu3UFBAQQEBBQLm3Zsg3EWaVUF6CRiMxUStUASjW9X0Qu5bxXSn0D/GocngcC82QN\nMNLOG+9vTM9bJkYp5QT4AIlGevgNZTYY56oqpZyMq6K8dRXU1+nAdICwsDC7D1vv2bMnjRs3xt3d\nHYCIiAgaNmyIj0/hE0u7DW1MaN+qRB24A2cX+17BrDsWxzebT/O30EDcqth3ywlN0249P/74Y7m1\nVewVkVLqDeB1IGccnzNQqh4az3xyPAjkjKhbBgw1RsLVxzooYZeIXASSlVIdjWc8TwBL85TJGRH3\nN2Cd8RxpFdBHKVXNGKTQB1hlnFtv5MUom1NXuXNzc6Nx48aAdXTd8uXLiYiIKLJMFVcnqvnXoU3f\n+3DzKnZnH7lAAAAgAElEQVTgYok83aU+Ef/qrYOQpmnlzpZnRA8CbYA/AETkglLKq7hCSqk5WK9M\n/JRSMVhHsoUrpUKw7vAahXWOEiJyWCk1HzgCZAPPiUjOwqpjsY7AcwNWGC+AGcBspVQk1kERQ426\nLiul3gZ2G/neEpGcQROvA3OVUu8Ae406KpyXlxcvvPACLsZoOIvFgoND/r8RsrPM7P7tDLWC3HBw\nuES94DYoO620UFVvkKdpWh7jxo0D4NNPPy3ztmwJRFkiIkopAVBKedhSsYg8UkByob/4ReRd4N0C\n0vcA+RZXE5EMYEghdX0HfFdA+mmsQ7ornapVrZvexcXFsWDBAgYNGpRvIIOjkwOHN18g/mw0J7fP\nZcTHX1O9bmBB1ZXK+mNx/H7kEpMGtbJbnZqm3Zr27dtXbm3ZEojmK6WmYX2+MhJ4CrD/ngQaAJ6e\nnri6upKdnZ3vnHJQPPVhV9KTrxJ8dwt8atSya9tRialsPhlPUpoJH3c9lFvTtPKhbFk+TinVG+uz\nFoX1ecvqsu5YZRIWFiZ79uwpt/ZExG633Eoi22zB0UFVSNuaplUu4eHhAGzYsKHUdSilIkQkrLh8\nNi0wZgSe2yr4VCSlFBaLhR07dtCgQQNq166de+5i5FX2rztH276+xByJIKTPvTg42meAgZOjLaP5\nNU3T7Ev/5qmksrKy2LRpE4cPH74+PdNMwrkUog8dYf2s6cSfPWPXdpfuO88DU7ZituiF1jXtdta4\ncePckb1lzaZbc7e78r41lyMpKQlvb+8Cb5VlZaSTkXLNrissAKw8FMvPu6L5+KHW+Hnad007TdNu\nL3a9NaeUcgPuEJHjN90zzWY5k1szMjJwcXG5LiBVcXWjiqub3dvs17I2/VrWLj6jpmmandgyofV+\nYB+w0jgOUUotK+uOaVaxsbF8+umnnDx5Mjdt7+poVn17iPizZ1jz7VeYMjPs3q7JbL89jzRNu/WM\nGjWKUaNGlUtbtjwjehPr3JurACKyD6hfhn3S8qhRowbNmze/bukfsQhmk4WUK5c5umU9l8/HFFFD\nyc3fc442b60mKc1k13o1Tbt1nDhxghMnTpRLW7bcmjOJSNINzyn0g6Vy4ujoyIABA65La9u3HgAW\ns5mx387B0cm+u6s29/fmb6EBZJrNWFd00jRNKzu2/AY7rJR6FHBUSjUCXgS2lW23tBulpaWxdetW\nunbtiqurdcFTew3bvlHLuj60rFv44quapmn2ZMutuRew7pyaCfwMJAHjyrJTWn5Xr15l+/btnD59\nGoD/fb6Pbb9EEn/2DPP+O4HEmGi7txkZl0Jmtrn4jJqmaTehyCsiY7vut0TkFeCf5dMlrSB16tRh\n3LhxufsZ+dR0x6OqC66ebmSmpJBeyi3IC7MtMoFHv93JzCfb0aOJfYeIa5pW+YWEhJRbW8XOI1JK\n7RCRjuXUn0qpouYRFebq1av4+PiU6VI8GSYzC/aco19Lf2p46flEmqaVnK3ziGy5NbdXKbVMKTVM\nKTUo52WHPmqlEBUVxeeff87x48cRESzGCghisWAx2+82mquzI8M6BekgpGlambMlELli3d00Z6vw\nnO3CtQoQGBhIly5dqOZRg5mvbSEy4hLJCXFMGzuCY9s22bWtzGwzq49c4kxCql3r1TSt8nv88cd5\n/PHHy6UtW7YKf7I8OqLZxtHRkbvvvhuz2UJQsB9e1Vzx8vWmfkgoXtX97NpWRpaFZ3+MYGz4nYzv\n08SudWuaVrnFxNh3fmJRig1ESilX4GmsI+dcc9JF5Kky7JdWjNTUFGId99LcsxrKoSp9n33J7m34\nuDuzeGxnmta277bkmqZpedlya242UBvoC2wEAoBrZdkprXhOTk7Ex8dz6WIcOQNOMlJSSL16xa7t\nBAdUpYqTXqRd07SyY8tvmIYi8m8gVUS+B+4FOpRtt7TiuLu707vd39gyLYFrlzPINpmY/tyT7Fqy\nwO5tzdp6hh93nLV7vZqmaWDjEj/G16tKqZZALKAnllQC/g2q0vGBBpw7f5Z6LgH0fOpZatSz/zKA\nG07EU8XRgcc71rN73ZqmVU6dOnUqt7ZsmUf0DLAICAZmAp7Af0Rkatl3r3KobPOI8kpOTubTTz+l\nU6dO9O7du0zayDCZcXUum+WENE3767LbfkQi8q3xdiPQ4GY7ptmXh5snA+8ZQouQRgBcOh1JVkY6\ngc1b2a2NnCAkImU6iVbTtNuTLaPm/lNQuoi8Zf/uaABppjTcnd1tyrttcSRHtlyiVZsmmM1m1nz3\nNVgsPPbeJ3bt08KIGL7aEMnKl7rpwQuadhsYPHgwAIsWLSrztmz5jZKa52UG+gNBZdin29KmmE1M\n3DyRk1dOMmDJABafXGxTuaYd/en1ZHMyMjKZNm0a1dp15cEJb9q9fzW9XGjm701Sut6jSNNuB4mJ\niSQmJpZLW7bcmvso77FS6kNgVZn16DZ17to5Tl09RV3PunT070jz6s1tKlfjDi9q3OEFQIMGDWjQ\noAHu3vbfwqFb4xp0a1zD7vVqmqaVZkc1d6xziTQ7eqzZYzzU5CGcHZx5p8s7uenRydHc4X1HkWWT\n4tNIvZpFv379ADizdw9xUafp8OBDdu9nXHIGHi5OeLjYdzM+TdNuX8XemlNKHVRKHTBeh4HjwKdl\n37Xbwx+X/uBQwiEAnB2u3w117dm1DFgygJ0XdxZZx7ZfTrH2+yO5xzu2bWPL1m2Ys7Pt2tezial0\n/r91/PJH+S39oWnaX58tf9bmXeA0G7gkIvb9DXcbm35wOtHJ0fz64K84qOv/LuhUpxOjg0fTtmbb\nIutof9/1c4dc/QOo6VUV5WDfQQV3+Lrzer+m+hadpt0GevbsWW5t2TKPyLeo8yJy2a49qoTKch5R\nqimVc9fO0dS3aZH50kxpbL+wnZ71iv/hMJlMODo64mDnQKRpmlYS9tyP6A8gHjgBnDTeRxivyjnL\n8xbi4exRbBACmHl4JuM3jic6ueAtwaMPJxJ92DrCxdnZmVMRO/n5zQls2byZ4v7YKKnDF5JYGKFv\nz2maZh+2BKLVwP0i4ici1bHeqvtdROqLiJ7gWkqxqbE8s+oZjl8+blP+ka1GMr339EIHLuz69QwR\nK69fDy7Joli3fj0XL1686f7m9fPOaN757QiZ2fbbiE/TtMqlf//+9O/fv1zasuUZUUcRGZlzICIr\nlFIflGGfbgsx12I4n3IezyqeNuWv4liF9v7tATiUcIikzCTuqntX7vk+T7fAzbtK7nGjdp1oGNaR\n+Ph4ata079KAL/VqxGv9muLipJf90bS/qvT09HJry5ZAdEEp9S/gR+P4MeBC2XXp9hBWO4zfBv2W\nb4BCcUSESbsmYTKb6FSnU255bz+3fHmVUlT39UVEiI6OxtfXFy8vr5vue00v1+IzaZqm2ciW34KP\nADWAxcarhpFWJKXUd0qpOKXUoTxpvkqp1Uqpk8bXannOTVRKRSqljiul+uZJDzWGkEcqpT5XxmJn\nSikXpdQ8I32nUiooT5nhRhsnlVLD86TXN/JGGmX/vIQoR9HJ0VjEUuIgBNbg8mG3D/mmzzfXlbdY\nhL2ro4k6mJCbFrX/D74e+RixUaeZM2cOv//+u136D3D+ajrDv9vF1siE4jNrmqYVodjfhCJyWURe\nEpE2QBjWlbdtGSk3C+h3Q9oEYK2INALWGscopZoDQ7HuAtsP+EoplXPf52tgJNDIeOXU+TRwRUQa\nAp8A7xt1+QJvYN0zqT3wRp6A9z7wiVHmilFHuUozpfHEiid4a3vpl+rz9/THx8UHi1iIuBQBgIOD\n4tDGGKIO/rkkh2/dABq274SLiytDhw7lnnvuuen+5/DzrEJCSiZX0rLsVqemabcnW4Zv/ww8i3Wd\nud2AN/CZiEwutnLrVcqvItLSOD4OhIvIRaWUP7BBRJoopSYCiMgkI98q4E0gClgvIk2N9EeM8qNz\n8ojIdqWUE9Z9kmpgDWjhIjLaKDMN2ADMxTrir7aIZCulOhnlc6++ClPa4dtffvklrq6u+Pv7U7t2\nbdLT09m1axfLNixDmRSD7hnEvffeS4MGpRvzMfvIbCbvnszCAQtpXK0xWenZVHEr+m6rxWIhKiqq\n1G3mpVfj1rS/rg8//BCAV155pdR12G0bCKC5iCQrpR4DVmC9iokAig1EBaglIjlDuGKBWsb7usCO\nPPlijDST8f7G9Jwy5wCMwJIEVM+bfkOZ6sDVPJNx89ZldyLC66+/TlpaWqF5NqzcwIsvvkhISAhz\n5syhadPih3HnNbjRYHxcfGhU1boFRGFB6FpiAi4eHlRxdWPnzp2sWrWKUaNGUadOnRK1dyOlFCLC\n8UvXaFrb+6bq0jStcrmZAFRStgQiZ6WUM/AA8KWImJRSNz0xRUTEHvWUFaXUKGAUwB13FL3WW0HM\nZjMvvvgisbGxXLx4kdjYWC5nXqZZcDMG9xxMlSpVWLFiBatWrWLfvn1069aNNWvWEBwcbHMb7s7u\nDLhzAACXUi/h7uhBxKIYatX3oVlnfwDio6P44dXn6f/8eJp37UG7du3w9va+6SCU45vNp3l/5XE2\nvBJOoK9tW1domqblZUsgmob1Ftl+YJNSqh6QXMr2Liml/PPcmosz0s8DgXnyBRhp57l+gdWc9Lxl\nYoxbcz5AopEefkOZDca5qkopJ+OqKG9d+YjIdGA6WG/NlfSDOjk5MWnSJBLSE3BxdMHNyY0nVz5J\ns+rNGNVhFAAjRowgLS2NBx98kN9//53w8HBWrlxJ+/btS9RWmimNx5Y/RljtMMJi/oa7j0vuOb+A\nOwh/4hnqNmme268WLVoAcPnyZdLS0ggIKP0atve3roOPmzM1vV2Kz6xp2i0jPDwcgA0bNpR9YyJS\nohegACcb8wYBh/IcTwYmGO8nAB8Y71tgDXQuQH3gNOBonNsFdDTaXQHcY6Q/B0w13g8F5hvvfYEz\nQDXjdQbwNc4tAIYa76cCY235HKGhoVJaobND5aPdH4mIiMVikXRTer48GRkZMnDgQAHEy8tL9u3b\nV+J2lpxcIicunxCLxWJTfovFIjNmzJDPPvtMsrOzS9yepml/bd27d5fu3bvfVB3AHrElVtiSqTQv\nYA5wkT+f8zyN9TnNWqxLBa3JCRBG/n8Cp7Cu7t0/T3oYcMg49yV/DrBwNQJLpBGsGuQp85SRHgk8\nmSe9gZE30ijrYstnuZlAtOjEItkXV3xgycrKkoceekgAadKkiVy7dq3UbZ65eua6Y4vZLNGH9suF\nE8euS79y5YrExsaWup28fjtwQb7ZdMoudWmaVvHKMxAVO2pOK9tFT/NKT0+nXbt2HD58mBEjRjBz\n5swS17Hq9O9snHaaju1aMuBvXQAQi4VvXniaWvXvZOAr/yqwXEREBLVr16Zu3dKN33h5/j4i41JY\nPPYuHB30SDpNu9XZ49acPUfNaeXEzc2NefPmERYWxqxZs+jduzePPvpoierodkdXTtVMI6jGnwMs\nlIMDD7z6b6rVLniAQlZWFps3byYoKKjUgei/A1rgXsVJByFN00rMpisipVRnrM97cgOXiPxQdt2q\nXMrriijH9OnTGT16NJ6enuzdu5eGDRuWqp40Uxrnrp2jiW+TYvMmJyfj5uaGs7MzFoul1FtIZGab\nScs0U82jQhat0DTNTr766isAxo4dW+o67LYNhFJqNvAh0AVoZ7yKrVgrvZEjRzJkyBBSUlIYNmwY\n2aXYaVVEeGvrO4z8fSQpWSkAnNy5jU0/zyowv7e3N87OzphMJn744Qf27t1b4jbNFuG+z7fwxrLD\nJS6raVrlMnbs2JsKQiVhy5+9YcBdIjJWRF4wXi+WdcduZ0oppk2bRt26ddmxYweTJk0qUXmz2cIP\n/9xGz7iH+W/n/+au8B0XdYpTu3eQbTIVWtZiseDh4YHZXPItHhwdFE/eVZ8hYaUfDq5pWuWQlpZW\n5IR8e7JliZ8FwIvy54oIt53yvjWXY82aNfTu3RtHR0e2b99Ou3btbC67c9lpagZ5Uz/YD4Ddsbtx\nsjgQ4t9WL8ujaVqxynOwgi1XRH7AEaXUKqXUspxXqXum2axXr1689NJLmM1mhg0bVqK/TjoMaJAb\nhCxiYfLuyUze+xFgHUVXHBHh6NGjxMbGlrjf6Vlmpm86xYlL10pcVtO0248tgehNrMv7vAd8lOel\nlYNJkybRvHlzjh8/zrhx40pUNiPVRFJ8Gg7Kga96fcUn4Z9w8eRxvn3hGRKio4osm5WVxbJly9i5\nc2eJ+5xhMvPZmpOsPnKpxGU1Tbv9FDt8W0Q2lkdHtIK5ubnx888/06FDB7755ht69uzJww8/bFPZ\nXyZH4O3nxn3Pt8bPzXp1lFbLhSueWSw+/gsj73i50LIuLi6MGDECPz+/Eve5mkcV1o4Pp7aP3kBP\n07Ti2TJqrqNSardSKkUplaWUMiulSrvWnFYKrVu35uOPPwasI+pOnTplU7nOgxsSdm/QdWlVvDyJ\nu6c213yLL1+rVi0cHUu3HXhOEMowlXzQg6Zptxdbbs19iXVH1pOAG/AMMKUsO6XlN2bMGAYPHsy1\na9d4+OGHyczMLLZMUCs/atf3uS7NycGJD7p9wJimo7gae5GzyWdJTE8spAY4f/48X375ZameFW04\nHkf7d9dwOj6lxGU1TatYI0aMYMSIEeXSlk0rK4hIpFLKUUTMwEyl1F5gYtl2TctLKcW3335LREQE\nERERvPzyy0yZUvzfAwkx17h2OTN34AKAg3Jg3n9ew6OaL/NbH8dBOTD33rkFjqbz8fHBy8urVHOZ\nWtTxoVvjGjg7lm5yrKZpFae8ghDYNnx7E9AL+BbrZnYXgREi0rrsu1c5VNTw7YLs2rWLrl27kpWV\nxfTp0xk5cmSR+VdOP0js6WSGT+p8XaA5/cdu3Ly8SaoupJnSaFurbc7CsHp4t6ZpJCQkAJTqOXEO\nW4dv2xKI6gGXgCrA37Hu+/OViESWune3mMoUiABmzZrFk08+ibOzM+vWraNLly6F5k2KT8PZxQl3\n7+KX3Jl7bC5bzm/hg24f4O58/SZ3JpMJi8WCi0vJ9x2Ku5bBgj0xjA2/Uwc5TbtFVKp5RCJyFute\nQP4i8l8Refl2CkKV0YgRIxg3bhwmk4nBgwcTHR1daF6fGu6FBqFrlxPYOv/H3JUWFApH5Yibk9t1\n+dLT05k8eTK7d+8uVX83HI/nk9UnOHJRj3HRNC0/W0bN3Q/sA1YaxyF6QmvFmzx5Mr169SIuLo77\n7ruPq1evFpr3/IkrbFlwMl96Ysw5di6ez4XjRwF4uOnDfNrjU5RSXM24yvu73ic5y7oYapcuXahX\nr16p+jq4bQDrxofToo5P8Zk1Tbvt2DqhtT1wFUBE9mHdRVWrQE5OTsybN4+mTZty8OBBHnzwwUJH\n0l2+kMqJXbGkJWddl16vVQjPfDGDO1oG56bl3DrbGbuTBScWcDHFurJTt27dCAwMpDQcHRR3VLfe\n6ktIKX60n6ZptxdbApFJRJJuSNO76VUCvr6+rFy5En9/fzZs2MATTzyBpYDle5rd5c+I/7sr3y06\npRTefjWA/Mv+9A3qy8rBK3O3kFh8cjFHY45y4cKFUvd3YUQMXd9fr4dza5p2HVsC0WGl1KOAo1Kq\nkVLqC2BbGfdLs1G9evVYvnw5Xl5ezJ8/n5dffpkbB6A4OTviUMQQ6g0/fMOyj9/Ll56zGkNyVjKT\nd09m/rz5rFy5stR97dbIj8c63EFNb73igqZVdmPGjGHMmDHl0pYto+bcgX8CfbAOWlgFvC0iGWXf\nvcqhso2aK8jatWvp378/JpOJ999/n9dee+2684nnU1gz6wjhjzWlVpD3def2/O8Xrl1OJHzY06hC\nNsSLTY3lSuwVavvW5rK6zP74/Qy8cyCODqVbeUHTtL8+e46aSxORf4pIOxEJM97fNkHoVtGzZ09+\n+MG6ae7rr7/O999/f915z2ouOFdxxFzAkjth9w+ix/CRhQYhgNoetWl2ZzOqVavG0silfLj7Q65l\nlW517aiEVJ6cuYvYJP1jpGmV1blz5zh37ly5tFXoygrFjYwTkQH27452M4YOHUpcXBwvvfQSTz/9\nNDVr1qR///4AuLg7M+jV0CLLx0Wdxt2nKp7VCl+I7sKFC7S60opB9w6iqmtVACbtnES3gG7cVfcu\nm/t6+EIyUYmpemFUTaukhg0bBtzcPCJbFXVF1AkIADZj3Sr8I/Q2EJXeiy++yMSJEzGbzQwfPjzf\nsG5ztoWM1Pw7tKYlJ/HTP15mz/8WFVn/hQsX2L17N1XFGoSSMpPYcn4LkVetU8tEBJOl8B1gAYL8\nPNj0Wg86Nqheko+madpfVKHPiJRSjkBvrAueBgO/AXNE5HD5da9yuBWeEeUlInTv3p3Nmzfz4osv\n8tlnnwFgMVuY/a/t1GvlR/ijTfKVi9yzk4BmLXD18Cy0bpPJhIhQpcqfI/CyLdmICM6OzmyK2cTb\nO95meu/p1PcpfpT/sv0XqOPjSliQDcuBa5pWbirFygoiYhaRlSIyHOgIRAIblFLPl7pXWrlQSvHF\nF1/g4ODAlClTOHjwIAAOjg606XMHDUNrFliuYViHIoMQgLOz83VBCKwrejs7OgPgXcWbVn6tCPAK\nAKxblB9KOFRgXRkmMx+uOs7MbVEl+Xiapv3FFDlYQSnlopQaBPwIPAd8Diwuj45pN6d169aMGTMG\ns9nMCy+8kDukO7hHIAFNqhVaLvH8ORa99x+SE+IKzZOcnMzMmTM5evRovnMhNUP4OPxjnB2sgemT\niE94a/tbuedN5j9v27k6O/LzyA58+nAIQL5h55qm3R4KDURKqR+A7UBb4L/GqLm3ReR8ufVOuylv\nvfUWfn5+bNy4kfnz5+empyVncWzHxQLLOLu4kBhzjisXC5+46uHhAVDg5NkbTes9jfe6WOcomcwm\n+v3Sjx8O/5B7PqCaO86ODmRlWxg6fQdL9+kfL02rDMaPH8/48ePLpa2inhFZgFTjMG8mBYiIeOcv\n9dd0qz0jyuubb75h1KhR+Pv7c+jQIXx9fdm7OpptiyJ5/O2O+NRwz1fGYjHjUAbzg5Kzkvl639d0\nD+xOR/+OJGUmsf7ceu5rcB/X0i089/MfDO8cRN8WtTFbBAelt6TQtFuZ3baB0G7tQGQ2m+nevTtb\nt27l8ccfZ/bs2WSkmkhLzsLX36PQciJCYkw0foGFL3RqsVg4duwYzZo1K1XA+Pnoz0zaNYlFAxbR\nuFpjRCS3nllbz7B473lmP9MBb1fnEtetadrNOX78OABNmuQf2GQru01o1W5tjo6OzJw5Ezc3N378\n8UeWLFmCq4dzkUEIYNeSBcx+/SWSE+ILzXP8+HHmz5+f+wNbUo80fYSf7/mZxtUaA7AyamXuIqvV\nPV1oUMMzNwitO3aJqITUQuvSNM2+Ro8ezejRo8ulLR2IbgONGjXi/fffB6w/XAkJCZgyzWyac5zI\niIIHJTTrGk6vZ8biUbXwgQ1NmzblkUceKfVfTEopWtVoBUBKVgrv7HiHr/d/DcD9revwiTGIIdts\n4bWFB/jw9z8DXkpmybcu1zStctKB6Dbx3HPPER4eTlxcHGPGjMHRWXEh8irJCekF5vf2q0mru/vg\n6FTo4hsopWjSpAlKKdLT020avFAYzyqezL9/PuNCxwFwPuU8285b19Z1cnTg1xe6Mr6PNeDFX8uk\n7Vurmb+7fJYf0TStbOlAVImkZpvLbAizg4MD3333HZ6enixcuJCvv/6aIf9oR9u+RW92d3z7FnYt\nXVhknqtXrzJlyhQ2bdp0U32s61kXX1frxNZZh2YxbsM4rmZYV4ao7eNKfb8/byc+270BbetZV3eI\nOHuZXh9v5KjeAVbTbkk6EFUSe5JSCd52mB1JZfccpH79+nz77bcA/P3vf2fPHuvW3zdumJdX9MF9\nnNixBYsl/2KpOXx8fGjbti3Nmze3W19fbfcq03tPz13P7qejP3E+xTq0u4aXCy/3aULDml65+f19\nXKnjY93ifMGecwz6aitX06yfy2zRA3I0rVITkXJ/AVHAQaxbkO8x0nyB1cBJ42u1PPknYl3Z4TjQ\nN096qFFPJNbJtjmjAF2AeUb6TiAoT5nhRhsngeG29Dc0NFTszWyxyMr4q7L5crKIiKRmm+WVY9Fy\nIiVdRET2JqWKxWKxe7siIi+88IIAEhgYKDvXHJGvxqyTxPMpBebNTEsVszm7RPUnJyfbo5u5LqZc\nlNDZoTJ9/3Sb8v+6/4I8OXNX7vfvnV8PS5+PN+YeRyemSvy1DLv2UdP+alavXi2rV6++qTpyfr8X\n96rIQOR3Q9oHwATj/QTgfeN9c2C/EVzqA6cAR+PcLqzLDylgBdDfSB8LTDXeDwXmyZ/B7rTxtZrx\nvlpx/S2LQJRtsUjH7YflyQOn8507kJwq/uv2yrfn4uzerohIZmamdOzYUQDp1bOXbFpwTFKTMoss\nY8rKktSkq8XWHRERIe+++67Exdm37xdTLkpKljVY7rywUyZsmiCX0y/bVHbJ3hj5vxVHc4+fmrlL\n+ny8Mfd4xcGLsvN0ol37q2ma7YGoMt2aGwjkbKLzPfBAnvS5IpIpImewXuW0V0r5A94issP4wD/c\nUCanroVAT2WdoNIXWC0il0XkCtYrr35l/cFyLIu7yqC9kWRbBEelmNP6Tqa3CMqXr6WnG5MaBzC0\ndtksBFqlShXmz5+Pn58fa9au4ee1n+LmVfhcHYvFzI8TXmL9rOnF1t2oUSPatm2Lr699+17bozYe\nztZnRFHJURyIP4Cns3VdvGtZ14p8tjYwpC6v92uaezwm/E4m9P/z+IOVx/h28+ncYz0iT9Ng3759\n7Nu3r1zaqqhAJMAapVSEUmqUkVZLRHLWnYkFahnv6wJ5h0fFGGl1jfc3pl9XRkSygSSgehF1lZmU\nbDMZZutoMicFgpBosv6iC3Jzwckh/0RQpRTD6/rh4eSIySKMPxbNqTT7biIXGBjI0qVLcXFxYerU\nqfqBcLkAACAASURBVPx74lsc3xlbYF4HB0fa9h9Ai/Bexdbr5eVFv379cHR0JDMzk4SEBLv2G+Ch\nJg+x7IFlODs6k5GdwRMrnuCD3R/YXD4syJceTf9c+HXZC114Y0ALAGKTMuj03loW740prLim3RbG\njRvHuHHjyqWtigpEXUQkBOgPPKeU6pb3pHGFU6FPmJVSo5RSe5RSe+LjC5/UWZQLGVm0236Eny4m\nAtDfz4fFbRpRy8X2lQLOZmSyMiGZfclppepDUTp37sxPP/2EUop333+TT9+bhtlc8BDs4F79CApu\nU6L6lyxZwg8//IDJVPT+RKWRs0W5s4Mzfer1KdGmfDfydHGiblU3o17FgJA6hNWzXtFdSs7gUrLe\nSVbTylKFBCIxFk4VkTisq3m3By4Zt9swvubMtDwPBOYpHmCknTfe35h+XRmllBPgAyQWUVdBfZwu\n1q3Rw2rUqFGqz+nv4szjdaoT5mO9pVSaZXAauruyrUNTBhu36fYlp5FWSLAojcGDB/PRR9Z9Dmes\neJcVK5YXmtecbWLnkgXEHCl4W4cb9ezZk/79++PsXHZL9Dg6ODImZAxd6nYBYMGJBUzdPxVzEaP8\nilLDy4V3H2xFoK91Db4PVx2n76ebyChgi3VN0+yj3AORUspDKeWV8x7oAxwClmEd0Ybxdanxfhkw\n1NiSoj7QCNhl3MZLVkp1NJ7/PHFDmZy6/gasM66yVgF9lFLVlFLVjLZXleFn5Z931qG1V/6FRUvC\nx9k6qTQl28wj+0/x2nH7TuQcN24c48ePx2QyMXjwYJYtKXiXeIvZzIE1Kzn1xy6b6vXz86NZs2YA\nnD59msjISLv1uTCHEw7zx6U/cFD2+dF+4e5G/HdAC1ydrVdgX22IZG/0FbvUrWmaVeHT5stOLWCx\ncXXgBPwsIiuVUruB+Uqpp4GzwEMAInJYKTUfOAL8f3vnHSZVkS3wX3WanpxzYGZgGPLAkBEJggom\nxMWIimtaXdMan67PNb41uywKrgExLJIWEFwFBSUPOSN5YHLOqXs61fujmyFImNyD1u/77je37q1b\ndepWT5+uU6dO2YCHpJQnfp7+Gfgc8MTpNbfMdX0m8JUQ4ihQhtNzDillmRDiVWCrK98rUsqytmxs\na+Kj0/KvnvF08nRuTFdjsyMAb13LImULIXj77bexWq1MmzaNSTdO4psl33DVVVedlk/vYeT21/+B\np2/TAq9LKVm9ejVWq5XExEQ0mrb7/fPSsJeot9cjhKDCXMFrm1/jkX6P0Mnv/At3z0VcsBdxwc4f\nEpV1Vj5eewyrTdIvLhApJbUWOz4e7vg3Uih+O6jo242go0bffvZwDitLK1neP5kQQ8u/DKWUTL7h\nHuZ8MwuDwcA333zD+PHjz5q3tqIcIQRe/gGNKttkMmGz2fD19cVutyOEaFOFBLAlfwtPrnmSz678\njKTApNOiezeXOosNu0Pia9Sz6Vgpd83awlf3DGag2upc8RsjLc0ZYmvYsGHNLkNF3/4dcENYAI91\nCm8VJQTOkdHsRTN59NFHsVgsTJw4kR9++LXl0lpv5ounH2bt7FmNLtvT0xNfX2ckhGXLljFv3jzs\n9raddxkUOYgVk1aQFJgEwFtb3+KVja+0KIySl0GHrysieIiPBzcNiKVnlHOE+N2efF7+9hc1n6T4\nTTBs2LAWKaGmoBTRRcygAB/uiAoB4HCtuVU864QQTJ06lTtuvpv6+nomTJjAihUrTsuj9zAy6s57\nGXT9TU0uX0pJaGgooaGhaLVOk2JBQUGbxdgz6owN53qtHr1G3zAqyq5q2VxblzAfXpnQCy/XD4Gj\nRTWkHS3FQ+f8t/puTz6rD517y3WFoiOTlpbWMCpqcxqz6vX3frRFZIXWxOFwyKu3HZLDN+2XtlYI\nC2S3O+TXr2yS4y65UQLSaDTKVatWnSd/00IAnUphYaF88cUX5a5du6SUUpaXl8sFCxbIvLw8KaWU\ndXV18ujRo7Kurq7ZdZyNzMpM2fvz3nL+ofmtWq7NfvL9X/XPtXLKZ5sb0t/szJGHClo3/JFC0VaM\nHDlSjhw5skVlcBFGVlA0EyEEH/aMZ2avBLStsLW2RiO45qEUlq76mvvuuw+z2cw111zDpk2bfpX3\n51kfsXz6P5pdV0BAANdffz0xMU5P/Lq6OnJzc7FYnAFL8/Pz+eqrrygsLAQgPT2dN998k7y8PABy\ncnJYsGAB5eVOTza73d6odUvBnsE8OeBJRsWMAmBP8R4+3PUhNZaaZrcFnOuQTrD4z5fwxg19AKi3\n2XnmP3uY59q6QkrJp+uOcbSoukX1KRS/BZQi+o0QazTQ1dtphvoqr4TjdfUtKs83yIher2P6+zO4\n5aZbqa2tZfz48b8K+eHlH4B3YNB5o3OfD4PBQN+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ycjL19fUNG+7NmTOH0NBQxo4d26T3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\nkUKhUCjcilJECoVCoXAr/w8hMoPpETmzrgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22998d34080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display results\n",
    "m_log_alphas = -np.log10(model1.alphas_)\n",
    "\n",
    "plt.figure()\n",
    "ymin, ymax = 2300, 3800\n",
    "plt.plot(m_log_alphas, model1.mse_path_, ':')\n",
    "plt.plot(m_log_alphas, model1.mse_path_.mean(axis=-1), 'k',\n",
    "         label='Average across the folds', linewidth=2)\n",
    "plt.axvline(-np.log10(model1.alpha_), linestyle='--', color='k',\n",
    "            label='alpha: CV estimate')\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel('-log(alpha)')\n",
    "plt.ylabel('Mean square error')\n",
    "plt.axis('tight')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}