Lecture3-Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b6a45fa4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline, make_pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, LassoCV, ElasticNetCV, RidgeCV, Ridge, Lasso\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import cross_val_score, KFold, GridSearchCV\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "import patsy\n",
    "import warnings\n",
    "from sklearn.base import BaseEstimator, clone\n",
    "import statsmodels.api as sm\n",
    "warnings.simplefilter('ignore')\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ec6ec82b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# simple scalar regression \"population\" dgp\n",
    "n = 10000\n",
    "W = np.random.uniform(0, 1, size=(n, 1))\n",
    "y = np.exp(2 * W[:, 0])\n",
    "grid = np.linspace(0, 1, 1000).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e9ff9106",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit BLPs with polynomial features\n",
    "lr_poly = lambda p: make_pipeline(PolynomialFeatures(degree=p, include_bias=False),\n",
    "                                  LinearRegression())\n",
    "pred1 = lr_poly(3).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0eeb4458",
   "metadata": {},
   "outputs": [
    {
     "data": {
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o5jhOVlRFSg+YAI4wu2MVeyoWIiISdI5n5rJswst0c6wh34qg5IBJEFvG7liCioWIiAQZV4GbDz8dw6PuiQB4bngDK+lqm1PJOSoWIiISVN7/ah7D0kYRZhmy6t5JVOsH7I4k/0HFQkREgsbUZdu4ecvTJFjZZJZpTNwdf9NFsIoYFQsREQkK6/afIm7249R1HCQnogzOgVMgooTdseS/qFiIiEiRdyIrlxUTXuRGxyoKCCf6nongTLQ7llyEioWIiBRpeQUePhn7IUMKvgCg4Ma3sKq0sTmVXIqKhYiIFGkffDWLx9LewGEZMhveS4lrNFmzKFOxEBGRImvK4s3cvOUPOK0zpJdtjrPXX+yOJL9DxUJERIqkZbtOUHbe49RwHOV0ZHkSBk6G8Ei7Y8nvULEQEZEiZ//JbDZ9PoLOjnXkWxHE3jsZ4irYHUsug4qFiIgUKVm5+Uz45F0G8xUA5qZ3dWXNIKJiISIiRYbbY/jr+Ck8nfMuANnNHyby6nvsDSVeUbEQEZEi44PvFvHwkZeItvLITOpAbM9RdkcSL6lYiIhIkTB95U46rB1GRSuNrLgaOO/5J4SF2x1LvKRiISIitlu3/ySRPzxGY8decsLjiRv0FZSItzuWFIKKhYiI2OpI+hnWfPY8PRwrKCCcEv0nQenqdseSQlKxEBER25zJc/P5J3/hYfMlAO4ef8FRrb3NqeRKqFiIiIgtPB7DexO+4ImsdwHIbDaEqFb32ZpJrpyKhYiI2OKDGYu4/+CLlLDySU/qhPPm1+2OJD7gVbH44x//iGVZFzwqVqzor2wiIhKivly2jQ7rnqC8lU5mXE0S7hkPjjC7Y4kPeH0eT4MGDZg/f/7552Fh+iKIiMjlW7z9GKVmP0ojxz5ywhNw3v81lHDaHUt8xOtiER4err0UIiJSKDuOZ7Fv0lMMcKwl34okesBkKFXV7ljiQ17Psdi5cyeJiYlUq1aNfv36sWfPHn/kEhGREJOS5eKHMa8wwJp5dsFto7GqtLE3lPicV8WidevWTJgwgTlz5jBmzBiOHTtG27ZtOXny5CXf43K5yMzMvOAhIiLFS26+mzFj/saw/E8ByLnu/4ho3NvmVOIPXhWL7t27c8cdd9CoUSO6dOnCDz/8AMD48eMv+Z5Ro0YRHx9//pGcnHxliUVEJKh4PIZ3J0zhyYy3cFiGzPr9ien4B7tjiZ9c0emmsbGxNGrUiJ07d15ynREjRpCRkXH+cfDgwSv5SBERCTIffbeABw48T4zlIj3xOpx3vA+WZXcs8ZMruruLy+Vi69atXHvttZdcJyoqiqioqCv5GBERCVJfL91M57VDKefIIN1Zm4R7J+rGYiHOqz0WTz/9NAsXLmTv3r2sXLmS3r17k5mZycCBA/2VT0REgtSirYepNOdhajsOkxVZjoQHpuu00mLAq9p46NAh7rrrLlJTUylXrhzXXHMNK1asoEqVKv7KJyIiQWjzoXROTn6E2xy/kOuIpuSgryG+st2xJAC8KhaTJ0/2Vw4REQkRB0/lsPTTZxlsLcSNg7A7P8Oq1MTuWBIguleIiIj4TFp2Hl9+9CqDPVMAyLvhLSLq3mhzKgkkFQsREfGJ3Hw3H378d57MHQ1AVuuniG7zkM2pJNBULERE5Iq5PYb3Pvucp9JfJ8wyZNTtR9yNr9gdS2ygYiEiIlfEGMMHU39g8KERlLDySUvqRHyff+haFcWUioWIiFyRz+et4PYtT5BgZXOqVBNK6VoVxZqKhYiIFNoPq7bScslDVLZOkh5TldIPToPIGLtjiY1ULEREpFCWbT9M2e8HUddxkKyIsiQ8NANiy9gdS2ymYiEiIl77+cBJsiYNorVjK2ccscQOmgaldLFEUbEQEREv7T6RxbZxj3CDtZJ8Igi7axKOxMZ2x5IiQsVCREQu29GMMyz+6EnuNHPwYFFw62gia11vdywpQlQsRETksqRl5zHjgxHc5/4KgJyubxHdrI/NqaSoUbEQEZHflZNXwMQP/8Rg1zgAMtq+QMl2D9ucSooiFQsREflNeQUePvn4PR7JfA+AU02HEN/1WZtTSVGlYiEiIpfk8Rg+/mwsg1POXqo7tXZfSt/6hq6qKZekYiEiIhdljOGTyVMYdPBFoqwCUpJvpGy/0SoV8ptULERE5KI+nzGLO7cPJ9ZycaJ8O8oNnACOMLtjSRGnYiEiIv9j6tzFdFv3CAlWNicSmlD+wakQHmV3LAkCKhYiInKBGQtXcc2SQVSw0kmNqUn5wd9CZKzdsSRIqFiIiMh5s1dsoNGPA0h2pHAqKokyQ76H6FJ2x5IgomIhIiIA/LRuC9Vn3k01xzHSIipS6pFZWM5KdseSIKNiISIiLNu8iwrf3kVtx2HSw8sRP2Q2VsJVdseSIKRiISJSzK3Zvp/YqXdS39pHRlgpSj70A44y1eyOJUFKxUJEpBjbtOcI1qQ7aWLtJsvhJOaB7wmvUMfuWBLEVCxERIqpbQePkzOhD1db28i2Yom871siEhvaHUuCnIqFiEgxtOfYKVI/7UdrNnPGisYx4GuirmpudywJASoWIiLFzL7jaRz4qC/tzTpyicJ91xSiq7exO5aECBULEZFiZP+JNPZ/dCfXm1XkEUFen88pWbuD3bEkhKhYiIgUEwdT0tn34Z108JwtFTl3fI6zQTe7Y0mIUbEQESkGDqaks2f0haUiodGNdseSEBRudwAREfGvwycz2Du6z79Lxe0qFeI/2mMhIhLCjpzMYM8Hvbnu11Jx+vbPSWisUiH+o2IhIhKijp7KYPcHvbnWvQoXkWTd/k9Kq1SIn6lYiIiEoONpmez+R5/zpeL0bRMo07i73bGkGFCxEBEJMcfTMtn59960d6/ERSSZvcZTpolKhQSGJm+KiISQI6lp7B99B+3da3ERScat4ynftIfdsaQYUbEQEQkRh46ncuyj22jj+ZlcIsnsNYHyTbWnQgJLxUJEJAQcOHqMtI970cJsJYcSZPf+gvINO9kdS4ohFQsRkSC39+BBcj7tRROziyxiyes3lXJ129kdS4opFQsRkSC2e+9e3ONvpQH7ybDicPefRpmaLe2OJcWYioWISJDasXMH4RNvozaHOGUl4Bg4g9JVm9gdS4o5FQsRkSC0fdsvRE++jas4ToqjLJGDvic+uZ7dsURULEREgs0vm9dT6qveJJLKMUdFYh76AWelmnbHEgGu8AJZo0aNwrIsnnzySR/FERGR37JxzVLKTb2NRFI5HFaZkkPmqlRIkVLoPRarV6/m448/pnHjxr7MIyIil7B68Wxqz7+feCubA+HVKPPoTGJLJ9odS+QChdpjcfr0afr378+YMWMoVaqUrzOJiMh/WTZnCg3m30u8lc2uqPqUf+JHlQopkgpVLIYOHUrPnj3p0qXL767rcrnIzMy84CEiIpdvyfSPaLHsEWIsF1tjW1HlybmUcJaxO5bIRXl9KGTy5MmsXbuWNWvWXNb6o0aNYuTIkV4HExERWDjpTa7dPgqHZfg5oTMNh36BIyLK7lgil+TVHouDBw8ybNgwJk6cSIkSJS7rPSNGjCAjI+P84+DBg4UKKiJSnBiPh4Vjn6fDjtdxWIb15W+n0eNfqlRIkWcZY8zlrjx9+nRuu+02wsLCzi9zu91YloXD4cDlcl3w2sVkZmYSHx9PRkYGTqez8MlFREKUx+1h2YeP0D5lMgBrqjxIi/v+DJZlczIpzi53++3VoZDOnTuzadOmC5YNGjSIunXr8txzz/1uqRARkd+Wn5/Hur/fS/uMWQCsrfsMLfq9ZHMqkcvnVbGIi4ujYcOGFyyLjY2lTJky/7NcRES8cyY7i21/70PrM8spMA5+vvo1rr5lqN2xRLyiK2+KiBQB6SlHOf5RL5oVbCPXRLD92vdo3qW/3bFEvHbFxWLBggU+iCEiUnwd27+N/M9uo445QgaxHO3xGU1ad7M7lkihaI+FiIiN9m1aRtzXd1GRdI5SFle/qdSt29zuWCKFpmIhImKTbUumkzx/MLHksttRjdj7p1E1qZrdsUSuiIqFiIgNNs38kLorXyDCcrMpsgnJj3xDQqmydscSuWIqFiIigWQMGyb/kabb3wULVsZ2pPFjXxAdHW13MhGfULEQEQkQ4y7g508eoenRLwFYUPYu2g/5O+Hh+lMsoUPfZhGRAMg/k8nOD/rSJGsZHmOxoNpTdBz4MpaupikhRsVCRMTPTqccIPXj26ifv4tcE8HKZqPo1Oshu2OJ+IWKhYiIH6XsXA2T+lLVnCTVxLOv2yd0aKdrVEjoUrEQEfGT/Su+odzsR4ghlz0kkddvMi3qNbI7lohfqViIiPjBzu/+QvU1rxJmGdaFNaHCQ1OoXrGS3bFE/E7FQkTElzxuto9/nDr7J4IFP8XcSPNHxxFfMsbuZCIBoWIhIuIjntwsdn90F3XSFgPwQ/mH6frQG0RGhNmcTCRwVCxERHwgN2UfqZ/cTi3Xblwmgvn1/h89+j6i00ml2FGxEBG5Qqe2LsLx5T0kmQxSjZOf24+mZ9eb7I4lYgsVCxGRK3Dox4+psHgEERSwnSpk3/E5nRo3tjuWiG1ULERECsNdwN4vhlNt13gAFoW3peqDE6hTsZzNwUTspWIhIuIlcyaNAx/fRbW05QBMd95Dp0fewRkdZXMyEfupWIiIeMF1fAfpY2+nSt5BzphIvq/xMrf1H0p4mMPuaCJFgoqFiMhlSts0h4hv7qeCOc1RU5r17T6gT7fudscSKVJULEREfo8xHJ37V8otf5VwPGykFnm9/0mPRvXsTiZS5KhYiIj8lrwcDk54iORD3wMwJ7wjdR4cS9WKZWwOJlI0qViIiFxCQepeUj/tQ3LOTgqMg6mlH6bHQ68SHxNpdzSRIkvFQkTkIrI2z8H6+gEqmixSjZMfG7zJnb3vIsyhK2mK/BYVCxGR/2QMx2eOotzqt3Bg+NnUILXHJ/Rt3dzuZCJBQcVCROQcVxZHx99PpSNzAfg+rAu1Bo2mU1J5m4OJBA8VCxERwJ2yk1Of9qHSmb3kmTA+Lz2U2x98iYRYXfRKxBsqFiJS7GVt+Jawb4dQzuRwzJRiboO3GNi7j+ZTiBSCioWIFF/ufE5Mf4Hymz4GYI2pw8keY7i3dRObg4kELxULESmWTMZhTnzWnwpp6wGYGnEzje57lxaVy9qcTCS4qViISLGTu30++V8+QAV3OpkmmkkVn+XuQY/jLBFhdzSRoKdiISLFh8fNqVl/ImH1O5TAsMVThZ/bvsfgG67HsjSfQsQXVCxEpHjITiVl/L2UO7EUgOlWFxLveZ9+tSvbHEwktKhYiEjIK9i3jJyJ91IuP4UzJpJPEx6nzwPPUt5Zwu5oIiFHxUJEQpfHQ8ZPfyV28Z9w4ma3pxL/avw2D9/Wk4gwh93pREKSioWIhKbTKaR+PoiyxxYDMMu0Jfy293moWS2bg4mENhULEQk5+Tt/IvfLByibf5JcE8HYkg9z06AXqFK2pN3RREKeioWIhA53PhkzRxK39u/EYdjhqcyPDd/kwdt7EBUeZnc6kWJBxUJEQkPafk79815Kn9oAwFd0oVTvv/BI46q2xhIpblQsRCTo5f38De7pj1Pac5pME8OYhCfpN+gJKidE2x1NpNhRsRCR4JV/hoxpTxO/5XMA1nlqsvrqtxl20/WE66wPEVuoWIhIUDJHNpAx6X4STu/GYyw+c/Si1t2vM7huot3RRIo1ryr96NGjady4MU6nE6fTSZs2bZg1a5a/somI/C+Pm+x//Rn3x51JOL2bEyaBt8q9zk3DP+RalQoR23m1xyIpKYk33niDmjVrAjB+/HhuvfVW1q9fT4MGDfwSUETkvPQDpE96gIQTqwCY52nJsQ5v8mzH5jgcuteHSFFgGWPMlfyA0qVL8/bbb/PAAw9c1vqZmZnEx8eTkZGB0+m8ko8WkWIkb/1kPN8Np4Qnm2wTxejoh+kx4BnqV463O5pIsXC52+9Cz7Fwu91MnTqV7Oxs2rRpc8n1XC4XLpfrgmAiIpftTBqZXz+Bc9cM4OwEzUUN/8Rjt3WlRISuTSFS1HhdLDZt2kSbNm3Izc2lZMmSTJs2jfr1619y/VGjRjFy5MgrCikixZNn90JyvnwIp+s4BcbBmLA+1LvzjzxZX3MpRIoqrw+F5OXlceDAAdLT0/n666/55JNPWLhw4SXLxcX2WCQnJ+tQiIhcWn4up2f/kZi1H+LAsNdTgYmVX2JI/76ULRlldzqRYulyD4Vc8RyLLl26UKNGDT766COfBhOR4skcWkvW5Adxnt4DwGRPZ0y3P9GvXV0sSxM0Rezi9zkW5xhjLtgjISJSKAUusueNosTK93DiIcXE83H8MPoNGEyNcrp5mEiw8KpYvPDCC3Tv3p3k5GSysrKYPHkyCxYsYPbs2f7KJyLFwdGNZH7xIM7MHQB872nDsfav8Vzn5rqCpkiQ8apYHD9+nAEDBnD06FHi4+Np3Lgxs2fPpmvXrv7KJyKhzJ3PmX+9ReTSv+DEzUkTx4clh3Jb/6HclKhDpSLByKtiMXbsWH/lEJHi5vgvZE1+kLi0LQDMdrdkT+tXeebG1kSGay+FSLDSvUJEJLDcBeQufIfwxW8SZwpIN7H8PXoIPe96jBurlLY7nYhcIRULEQmcY5vInDIEZ9pmAOa7m7Op2UievrmdLnYlEiJULETE//JzyZk/iqiVf8OJm0wTwz9KPETnvsN4qnoZu9OJiA+pWIiIX5n9yzg99VHiTu8Fzs6l2NHiFZ7q0VZ7KURCkIqFiPhHbibZs14mduM44oATJoGPYh/h1ruHcGNSgt3pRMRPVCxExOfMjjnkfPMEsbnHAJjquZ60ti/zXJdmOuNDJMSpWIiI72Sf5PS3T1NyxzfEAvs95Rlb6kkG3H0vtSrE2Z1ORAJAxUJErpwx5K+fRMHMFyhZkI7bWEwwPbA6vcgr19UnzKF7fIgUFyoWInJlUraT+dXjOI+vJALY5knmi4rPcH/f3lQpE2t3OhEJMBULESmc/DOc+fFNIlb+Dacp4IyJZExYX6rd+gx/bHqV7kQqUkypWIiI18zO+WRPG0bJnEMA/OhuxrqGL/DwLR2Jj46wOZ2I2EnFQkQuX+ZRsr59hrjd31ESOGpK80nsYHrc+TDPVNXluEVExUJELofHTd6KMZgf/x9x7mzcxuKfpgeeDs/z/PUNidCtzUXkVyoWIvKbzMHVZH4zjPi0XwDY4KnO9MrP8ECfXiSXjrE5nYgUNSoWInJxp1PI/P5FnNumEA9kmhg+ihhAo1uf4JWGlTU5U0QuSsVCRC7kLsC1/CPMT6/jdJ8G4BvPdZxo9TyPdbuG6Ejd30NELk3FQkTOM3sXkTVtOM7MnQBs8lTlu8rD6d9b16QQkcujYiEikHGYzBnP4dz9HU4gzZRkbNQAmvd6ghfqJ9qdTkSCiIqFSHFW4CJn0fuEL/kzTk8ubmMx2XQlu+1zPNa5mW5rLiJeU7EQKY6MIX/L9+R8P4L4MwcBWO2pzZyrnua+O24mqZTO9hCRwlGxEClmzNGNpH3zDKVTVhIPnDAJjI99gPa3P8pLNcvaHU9EgpyKhUhxkXWM9O9fxrn9S0pjcJkIJjpuJv6GZxneuq7uQCoiPqFiIRLq8s+QveA9wpe/S4LnDADfe9py6OpnuefGaykZpT8DIuI7+osiEqqMIW/jVFyz/o841zEA1ntq8mOVJ+l72x3cpKtmiogfqFiIhCD3gVWkffMHyqb/TCRw2JThC+f9dLj9EZ6uVsbueCISwlQsREKISdlByvQXKX94LmWBbBPF5xF3UPHGPzC8eQ0cmkchIn6mYiESCrKOkfL9SEpvn0x5PLiNxQzrenKuHcHADi10PQoRCRgVC5FglpvJqfl/JnbtR5QzuQD8y3M1e5r8gT49uhEfHWFzQBEpblQsRIJRQR5ZSz/GsehtSrvTAVjnqcmK6k/Qq9eddEqItjefiBRbKhYiwcTj4fS6qeTPG0kp12EAdnsqMbvCw3S5/UEereS0OaCIFHcqFiLBwBiyt87l9A+vUCF7KwApJp6v4u6hea8nGFqzos0BRUTOUrEQKeJydy3i1Hcvk5ixnljgtCnBN9F3cFWPpxnSqBqWpTM9RKToULEQKaJc+1aROuP/qHxqBYmAy0TwXWR34rs+xz0tGujUUREpklQsRIqY/MMbOf7tyySdWEBlIN+E8UNEVyI7PsttbZrrnh4iUqSpWIgUEXnHtnH021eocnQ2SYDbWMwOu56Ca5+l53XXEBHmsDuiiMjvUrEQsZkrZTeHpo+k6uHvqIIHgLlWW7LaPEPPTh10cSsRCSoqFiI2cR3fyYFvX6Xake+o8WuhWGi15FSrp7mxc1eiI1UoRCT4qFiIBJjr2DYOTn+VasdmUuvXQrHcasqpVk/TuUsP7aEQkaCmYiESIGcOb+bwjNeodnwONX8tFMsczcloNZxOXXoQFa5CISLBT8VCxM+y9m/k2PevUiNlPjUxACx2tCTnmj/QsdMNRIZrUqaIhA4VCxE/Obl7LSnfv0rdtJ+I+3XZorBryG3zBzp27KKzPEQkJKlYiPjYkU0LSJ/7FvWzllLm12WLI9pR0P4PXNu+I+EqFCISwrwqFqNGjeKbb75h27ZtREdH07ZtW958803q1Knjr3wiwcEY9q74FvfCv1Az92cSAY+xWB59HREdn6V9q3a69LaIFAteFYuFCxcydOhQWrZsSUFBAS+++CLdunVjy5YtxMbG+iujSJFl3Pns+OlzSqx8n2r5ewDIM2GsjOtGQtc/0K5JS5sTiogElmWMMYV9c0pKCuXLl2fhwoVcd911l/WezMxM4uPjycjIwOnULZ4lOOW7cvjlh9FU2PwxlTzHAMg2UawucyvJPZ6hRs3aNicUEfGty91+X9Eci4yMDABKly59yXVcLhcul+uCYCLBKiPtFFu/+yu19kygKekApJk41iX2pe7Nw7k+sbK9AUVEbFboYmGMYfjw4bRv356GDRtecr1Ro0YxcuTIwn6MSJFweP8u9v3wDo2OT+MaKweAY5RlR437aHTTY3QuVcrmhCIiRUOhD4UMHTqUH374gSVLlpCUlHTJ9S62xyI5OVmHQqTIM8awdd1iTv/0Ls2yFhBhuQHY70jmeKMhNOnxIFFRJewNKSISIH49FPL4448zY8YMFi1a9JulAiAqKoqoqKjCfIyILfILClj/4xSi13xIo/yfzy60YGtUEzzXPEb9DndQxaGrZIqIXIxXxcIYw+OPP860adNYsGAB1apV81cukYBLTUtj0w8fUn3XBFpxBIB8E8amhE6U6Tqceg3b2pxQRKTo86pYDB06lEmTJvHtt98SFxfHsWNnZ8PHx8cTHR3tl4Ai/rZlxw4Ozf0bLVOm0dHKAiCLGLZV7k31nsNpnqgCLSJyubyaY3GpC/yMGzeO++6777J+hk43laIgr8DD0sXzMSs+ol3uAqKsAgCOOSpwvP791O0+hKjYBHtDiogUIX6ZY3EFl7wQKRKOp2WyZtZ4knb8k45sP7vQgn3R9TFtHqNa+35U1PwJEZFC071CJOQZY1i/ZTtH/zWaFqnT6WmlA5BPOLvLdaFClyeoWqedvSFFREKEioWErIycfBb9NIuY9Z9wbf4SmltusCDNUYoTdfpT/cbHqBtfye6YIiIhRcVCQooxhvV7j7Nt/gQaHp7Mzdbusy9YsD+6IY5rBpPcrh+lwiPtDSoiEqJULCQkZOXmM3/pCvJXjaNz7lyaW1lgQR4RHEzsToVuT1Clqm4IJiLibyoWEtQ2HUhlw/wvqL7/S26z/n0xq/TwcmQ3vo/EToOpUbKcvSFFRIoRFQsJOhln8pm/Yi35q8bRKWc2A6x0sMCDxeEybSl13WASGvYkIUxfbxGRQNNfXgkKHo9hxa4TbF70FbUOTKWXtYEwy4AFmWGlyKrXj8ROg0kurYtZiYjYScVCirQj6WeYtWwdZv0/6Z43l7bWSXCcfe1wqVY42z+Ms8mtODUZU0SkSFCxkCLHVeBm/uaD7F7yNQ2Pz+A+x8bzeyeyw+LJrncn5a4fTOWyteyOKiIi/0XFQoqMrUcz+WnRApxbJ9PdLKKnlQW/XgQztfTVONs/TGyjXsRG6FblIiJFlYqF2OpEVi6z1mwnY/UUrjs9i0cde86+YMHpiLK4G99FfNtBlC1Tw96gIiJyWVQsJODO5LmZ+8sRflk+m3pHp3OnYxXRVh44wE0Yp5I6U/raBylZszPozA4RkaCiv9oSEB6PYcWekyxYsQrnjq+5mUXc6jhx/lBHeskaRLW8j+gWd1Mutqy9YUVEpNBULMSvdhzPYuaqLeRt/JpOeT/xgmPH+bM6XGGx5NW9nbg2g0io3Bwsy96wIiJyxVQsxOdOZOXyw/oDHF49navT5/KIYz1RVgE4wIODrMT2OFvfQ1S9m4mKjLE7roiI+JCKhfhERk4+szYdYcuaf1Hr2A/0ciynlHX6/KGOzPi6RLe4m4imfYmPq2hvWBER8RsVCym0bFcB87ceZ8Xq1VQ88B03W0vo5zh2vkzkRJXDatyX6BZ346zQwN6wIiISECoW4hVXgZsF21NYvGYjJXd/R3eWcqtjz/kyke+IJq92T2Jb9iemWgdwhNkbWEREAkrFQn5XgdvD8j0n+XHNFsK3f0tXz1Jec2w7PwnTQxhnktsT26I/EXV7EhFV0t7AIiJiGxULuSi3x7Bm3yl+XL+D/F9m0DF/MS85fiHc8pwvFKcrtia2+Z046t9KrG5NLiIiqFjIf3B7DCv3nmT+hr3kbvmB6/MW8QfHxrNndPx6RON0mcbENL8TR8PbKRlf2d7AIiJS5KhYFHMFbg8r955i3obd5G2ZSfv8ZTzt2EiM5fp3mYivTXSzPoQ1uoOSurS2iIj8BhWLYijf7WH57pP8tGEHBVtncl3BMkY4NhFl5Z8vE2dKXkVkkz6ENe5NyQr17Q0sIiJBQ8WimMgr8LB0dyoL1m3F2j6T693LecGxmQjL/e/TQ+OqEdX4NsIa3Ep0pSa6EqaIiHhNxSKE5ea7WbQjhWUbfiFi5w9c717B/zm2np2A+WuZyE6oTYnGtxPW4FZiytdTmRARkSuiYhFi0nPy+Ne2E6xfvxrn/nlcz2petnbisMy/50yUbkhMk9twNLiV2LK17A0sIiIhRcUiBBzNOMO8zUfYvX4Bicd/oou1htsdR8+fFgpwulwzYprcjqPBLZQsVdW2rCIiEtpULIKQMYZdJ07z46b9pGycQ620RXQPW0c5K/P8Xgm3FU5OYltKNrkFq04PnRoqIiIBoWIRJDwew/qD6SzeuJW8X2bSNGcZAx2biLbyzv9XdIWXpKB6V2Ib30JYzc7ElYi3N7SIiBQ7KhZFmKvAzYrdJ9m4dglhu+bTqmA1j1s7CfuP+RLZJSph1etJTKObiarSjqiwCHtDi4hIsaZiUcSknnaxePNejq+fTdljC2nPejpYaWdf/HXORHpCfaIb3kxUg5uIrdhIZ3KIiEiRoWJhM2MMO45lsWbdSvK2zqZW5nJ6WtuItNzwa1/Is0qQmdiO+MY9iah7AwnxSfaGFhERuQQVCxvkFXhYvfMwe9fMocS+H2mZv4b+jhNnX/x1r0RaiWQKanSlTNObiKzajrIRJewLLCIicplULALk1GkXa9YsJ3PzbCqkLKcFW2hn5Z190QH5RJBSpgWxDXsQ37gnpXRPDhERCUIqFn5ijGHvvn3sWfUDYXt/ot6ZtXQ7N1fi10Mc6eHlybqqI+Wb30xUrY4kRpW0L7CIiIgPqFj4UF7uGXasmUf6pjmUP7GM2mYP1c+9aIGLSI4kNCeydhcqNetOQsUGJGjipYiIhBAViythDCl7NnBwzUwi9i2gZs4GGp47vPGr/RHVOV35Oio070HZeh2oprkSIiISwlQsvGEMBal7OLh+Nme2L6DiqdWUM2mUO/e6BakksC++NRF1ulDzmpuoUjrRzsQiIiIBpWLxezIOkbXtX5zcNB/nsRWULjhOtf94OddEsDWq0dm9Es16ULNBS8qGOS7540REREKZisV/O30Cz55FnPrlR8L2L6ZU7kHigLhfX84zYWy2anGiTGti63aiQatONIt32plYRESkyFCxOJ0CB5bj2rUA186FOLN24QDK/vqy21hsMtXZGdMMq/p11GjehSbVEwlzaNKliIjIf/O6WCxatIi3336btWvXcvToUaZNm0avXr38EM1P0g/A/uWY/UvJ27OUqPRdAET9+gDY4qnCaqsh2YltqNSoM20bVqepU5MuRUREfo/XxSI7O5smTZowaNAg7rjjDn9k8h1jIHUH7F8G+5fh2b8MR+Yh4OylJM4ViW2eZFZ56rLPeTXOOtfTumFt7q5aigjNlRAREfGK18Wie/fudO/e3R9Zrpy7AI5vgv3LYf9SzIEVWDmp5192AAXGwWZTjVWeumyw6hNR7Rpa1q9FpzrlSCoVY192ERGREOD3ORYulwuXy3X+eWZmpu8/JD8XpvSHAyshL+v8YouzZ22s99RilanDKk9dTiU05pp6VehYpzz3VitNiYgw3+cREREppvxeLEaNGsXIkSP9+hm5RJB3eDvOvCyyTDSrPXVY7anLSk9dtjtq0Lx6BTrWKc9rdctTrWysX7OIiIgUZ34vFiNGjGD48OHnn2dmZpKcnOzTz4gIc/Bk7kAOumLYaq6iUkIs19cpx6N1ytO2ZhliInXyi4iISCD4fYsbFRVFVFTU7694BcIcFg2v7UWzMAd/rVueWuVLYukeHCIiIgEXMv+Uf6xTLbsjiIiIFHteF4vTp0+za9eu88/37t3Lhg0bKF26NFdddZVPw4mIiEhw8bpYrFmzho4dO55/fm7+xMCBA/nss898FkxERESCj9fF4vrrr8cY448sIiIiEuR0aUkRERHxGRULERER8RkVCxEREfEZFQsRERHxGRULERER8RkVCxEREfEZFQsRERHxGRULERER8RkVCxEREfEZFQsRERHxmYDf3fTc5cAzMzMD/dEiIiJSSOe22793W4+AF4usrCwAkpOTA/3RIiIicoWysrKIj4+/5OuWCfAdxTweD0eOHCEuLg7Lsnz2czMzM0lOTubgwYM4nU6f/Vy5kMY5cDTWgaFxDgyNc2D4c5yNMWRlZZGYmIjDcemZFAHfY+FwOEhKSvLbz3c6nfrSBoDGOXA01oGhcQ4MjXNg+Gucf2tPxTmavCkiIiI+o2IhIiIiPhMyxSIqKopXXnmFqKgou6OENI1z4GisA0PjHBga58AoCuMc8MmbIiIiErpCZo+FiIiI2E/FQkRERHxGxUJERER8RsVCREREfCaoisUHH3xAtWrVKFGiBFdffTWLFy/+zfUXLlzI1VdfTYkSJahevToffvhhgJIGN2/G+ZtvvqFr166UK1cOp9NJmzZtmDNnTgDTBi9vv8/nLF26lPDwcJo2berfgCHE27F2uVy8+OKLVKlShaioKGrUqMGnn34aoLTBy9txnjhxIk2aNCEmJoZKlSoxaNAgTp48GaC0wWnRokXcfPPNJCYmYlkW06dP/933BHxbaILE5MmTTUREhBkzZozZsmWLGTZsmImNjTX79++/6Pp79uwxMTExZtiwYWbLli1mzJgxJiIiwnz11VcBTh5cvB3nYcOGmTfffNOsWrXK7Nixw4wYMcJERESYdevWBTh5cPF2nM9JT0831atXN926dTNNmjQJTNggV5ixvuWWW0zr1q3NvHnzzN69e83KlSvN0qVLA5g6+Hg7zosXLzYOh8O89957Zs+ePWbx4sWmQYMGplevXgFOHlxmzpxpXnzxRfP1118bwEybNu0317djWxg0xaJVq1ZmyJAhFyyrW7euef755y+6/rPPPmvq1q17wbLBgweba665xm8ZQ4G343wx9evXNyNHjvR1tJBS2HHu27eveemll8wrr7yiYnGZvB3rWbNmmfj4eHPy5MlAxAsZ3o7z22+/bapXr37Bsvfff98kJSX5LWOouZxiYce2MCgOheTl5bF27Vq6det2wfJu3bqxbNmyi75n+fLl/7P+DTfcwJo1a8jPz/db1mBWmHH+bx6Ph6ysLEqXLu2PiCGhsOM8btw4du/ezSuvvOLviCGjMGM9Y8YMWrRowVtvvUXlypWpXbs2Tz/9NGfOnAlE5KBUmHFu27Ythw4dYubMmRhjOH78OF999RU9e/YMRORiw45tYcBvQlYYqampuN1uKlSocMHyChUqcOzYsYu+59ixYxddv6CggNTUVCpVquS3vMGqMOP83/7yl7+QnZ3NnXfe6Y+IIaEw47xz506ef/55Fi9eTHh4UPxvWyQUZqz37NnDkiVLKFGiBNOmTSM1NZVHH32UU6dOaZ7FJRRmnNu2bcvEiRPp27cvubm5FBQUcMstt/C3v/0tEJGLDTu2hUGxx+Kc/77NujHmN2+9frH1L7ZcLuTtOJ/zxRdf8Mc//pEpU6ZQvnx5f8ULGZc7zm63m7vvvpuRI0dSu3btQMULKd58pz0eD5ZlMXHiRFq1akWPHj145513+Oyzz7TX4nd4M85btmzhiSee4OWXX2bt2rXMnj2bvXv3MmTIkEBELVYCvS0Min/6lC1blrCwsP9pvidOnPifJnZOxYoVL7p+eHg4ZcqU8VvWYFaYcT5nypQpPPDAA0ydOpUuXbr4M2bQ83acs7KyWLNmDevXr+exxx4Dzm78jDGEh4czd+5cOnXqFJDswaYw3+lKlSpRuXLlC24PXa9ePYwxHDp0iFq1avk1czAqzDiPGjWKdu3a8cwzzwDQuHFjYmNjufbaa3nttde0V9lH7NgWBsUei8jISK6++mrmzZt3wfJ58+bRtm3bi76nTZs2/7P+3LlzadGiBREREX7LGswKM85wdk/Ffffdx6RJk3R89DJ4O85Op5NNmzaxYcOG848hQ4ZQp04dNmzYQOvWrQMVPegU5jvdrl07jhw5wunTp88v27FjBw6Hg6SkJL/mDVaFGeecnBwcjgs3QWFhYcC//0UtV86WbaHfpoX62LlTmcaOHWu2bNlinnzySRMbG2v27dtnjDHm+eefNwMGDDi//rlTbJ566imzZcsWM3bsWJ1uehm8HedJkyaZ8PBw849//MMcPXr0/CM9Pd2uXyEoeDvO/01nhVw+b8c6KyvLJCUlmd69e5tffvnFLFy40NSqVcs8+OCDdv0KQcHbcR43bpwJDw83H3zwgdm9e7dZsmSJadGihWnVqpVdv0JQyMrKMuvXrzfr1683gHnnnXfM+vXrz5/WWxS2hUFTLIwx5h//+IepUqWKiYyMNM2bNzcLFy48/9rAgQNNhw4dLlh/wYIFplmzZiYyMtJUrVrVjB49OsCJg5M349yhQwcD/M9j4MCBgQ8eZLz9Pv8nFQvveDvWW7duNV26dDHR0dEmKSnJDB8+3OTk5AQ4dfDxdpzff/99U79+fRMdHW0qVapk+vfvbw4dOhTg1MHlp59++s2/uUVhW6jbpouIiIjPBMUcCxEREQkOKhYiIiLiMyoWIiIi4jMqFiIiIuIzKhYiIiLiMyoWIiIi4jMqFiIiIuIzKhYiIiLiMyoWIiIi4jMqFiIiIuIzKhYiIiLiMyoWIiIi4jP/H0LIfhV1L8IUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# even 3rd degree polynomial is good enough\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4ca961c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now let's go to finite sample and noisy data\n",
    "n = 500\n",
    "W = np.random.uniform(0, 1, size=(n, 1))\n",
    "y = np.exp(2 * W[:, 0]) + np.random.normal(0, 5, size=n)\n",
    "grid = np.linspace(0, 1, 1000).reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "01b46d81",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit a 10 degree polynomial\n",
    "lr_poly = lambda p: make_pipeline(PolynomialFeatures(degree=p, include_bias=False),\n",
    "                                  LinearRegression())\n",
    "pred1 = lr_poly(10).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2a343ccf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# It is very noisy!\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "db99afe8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# What if we use Lasso with cross-validated penalty\n",
    "lr_poly = lambda p: make_pipeline(PolynomialFeatures(degree=p, include_bias=False),\n",
    "                                  StandardScaler(),\n",
    "                                  LassoCV(cv=5))\n",
    "pred1 = lr_poly(10).fit(W, y).predict(grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ccef6f53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Much more stable\n",
    "plt.plot(grid, pred1)\n",
    "plt.plot(grid, np.exp(2 * grid))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "791bd981",
   "metadata": {},
   "source": [
    "# A more complex DGP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2dfe0181",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's go to a real high-dimensional dgp\n",
    "def gen_data(n, p, *, sparse=True):\n",
    "    if sparse:\n",
    "        beta = (1 / np.arange(1, p)) ** 2\n",
    "    else:\n",
    "        beta = ((np.random.normal(0, 1, p - 1)) * 0.2)\n",
    "    true_fn = lambda x: np.exp(2 * x[:, 0]) + (x[:, 1:] @ beta)\n",
    "    X = np.random.uniform(-.5, .5, size=(n, p))\n",
    "    gX = true_fn(X) \n",
    "    y = gX + np.random.normal(0, 1, n)\n",
    "    Xtest = np.random.uniform(-.5, .5, size=(n, p))\n",
    "    gXtest = true_fn(Xtest)\n",
    "    ytest = gXtest + np.random.normal(0, 1, n)\n",
    "    Xpop = np.random.uniform(-.5, .5, size=(10000, p)) # almost population limit\n",
    "    gXpop = true_fn(Xpop)\n",
    "    ypop = gXpop + np.random.normal(0, 1, 10000) # almost population limit\n",
    "    return X, y, gX, Xtest, ytest, gXtest, Xpop, ypop, gXpop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "da0e4296",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "X, y, gX, Xtest, ytest, gXtest, Xpop, ypop, gXpop = gen_data(100, 400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "89f926b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33641445133307446"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, gXpop) # The best r-squared we can hope for"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1b69c1e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression().fit(X, y) # what does OLS do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "13de2ef2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.10973075049794656"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, lr.predict(Xpop)) # negative out-of-sample R^2! Worse than a constant prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "eef91661",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()), (&#x27;lassocv&#x27;, LassoCV())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" ><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()), (&#x27;lassocv&#x27;, LassoCV())])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">StandardScaler</label><div class=\"sk-toggleable__content\"><pre>StandardScaler()</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LassoCV</label><div class=\"sk-toggleable__content\"><pre>LassoCV()</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('standardscaler', StandardScaler()), ('lassocv', LassoCV())])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcv = make_pipeline(StandardScaler(), LassoCV()) # let's use LassoCV\n",
    "lcv.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bea64c21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23844851136266676"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, lcv.predict(Xpop)) # a positive R-square close to the best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "dcf34002",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's look at the distribution of coefficients of the differnt models\n",
    "lrcoefs = np.abs(lr.coef_)\n",
    "plt.plot(lrcoefs[np.argsort(lrcoefs)[::-1]], label='lr')\n",
    "lcvcoefs = np.abs(lcv[-1].coef_)\n",
    "plt.plot(lcvcoefs[np.argsort(lcvcoefs)[::-1]], label='lcv')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "13c58930",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's verify the inutition behind the lasso and the marginal predictive abilit\n",
    "ulcv = LassoCV().fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "131dbb2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "score = X.T @ (y - ulcv.predict(X)) / X.shape[0]\n",
    "plt.scatter(ulcv.coef_, score)\n",
    "plt.axhline(ulcv.alpha_)\n",
    "plt.axhline(-ulcv.alpha_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "84042ae0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# What if we chose the penalty based on theory, not cross-validation\n",
    "# We wrap the package so that it has the familiar sklearn API\n",
    "import hdmpy\n",
    "\n",
    "class RLasso(BaseEstimator):\n",
    "    \n",
    "    def __init__(self, *, post=False):\n",
    "        self.post = post\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        self.rlasso_ = hdmpy.rlasso(X, y, post=self.post)\n",
    "        return self\n",
    "\n",
    "    @property\n",
    "    def coef_(self):\n",
    "        return self.rlasso_.est['beta'].values.flatten()\n",
    "\n",
    "    def predict(self, X):\n",
    "        return X @ self.coef_ + self.rlasso_.est['intercept'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "89ed8e4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "rlasso = RLasso().fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "af556950",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.21842174729732677"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, rlasso.predict(Xpop)) # pretty good!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "316ee37c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrcoefs = np.abs(lr.coef_)\n",
    "plt.plot(lrcoefs[np.argsort(lrcoefs)[::-1]], label='lr')\n",
    "lcvcoefs = np.abs(lcv[-1].coef_)\n",
    "plt.plot(lcvcoefs[np.argsort(lcvcoefs)[::-1]], label='lcv')\n",
    "rlassocoefs = np.abs(rlasso.coef_)\n",
    "plt.plot(rlassocoefs[np.argsort(rlassocoefs)[::-1]], label='rlasso')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "338c3d5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's try post lasso OLS\n",
    "class PostLassoOLS(BaseEstimator):\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        # We train LassoCV\n",
    "        lasso = LassoCV().fit(X, y)\n",
    "        # We find the non-zero coefficients\n",
    "        self.feats_ = np.abs(lasso.coef_) > 1e-6\n",
    "        # We train OLS on them\n",
    "        self.lr_ = LinearRegression().fit(X[:, self.feats_], y)\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        return self.lr_.predict(X[:, self.feats_])\n",
    "\n",
    "    @property\n",
    "    def coef_(self):\n",
    "        return self.lr_.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d218afce",
   "metadata": {},
   "outputs": [],
   "source": [
    "plasso = PostLassoOLS().fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "66281a50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.050489240477440855"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, plasso.predict(Xpop))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bacc7931",
   "metadata": {},
   "source": [
    "Very Poor! Post (LassoCV) OLS is not the same as CV-ing the whole Post-Lasso-OLS process. Post (LassoCV) OLS is wrong! Let's CV the whole process!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2154db88",
   "metadata": {},
   "outputs": [],
   "source": [
    "class PostLassoOLS(BaseEstimator):\n",
    "    \n",
    "    def __init__(self, *, alpha=1):\n",
    "        self.alpha = alpha\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        lasso = Lasso(self.alpha).fit(X, y)\n",
    "        self.feats_ = np.abs(lasso.coef_) > 1e-6\n",
    "        self.lr_ = LinearRegression().fit(X[:, self.feats_], y)\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        return self.lr_.predict(X[:, self.feats_])\n",
    "\n",
    "    @property\n",
    "    def coef_(self):\n",
    "        return self.lr_.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "dff6bf62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),\n",
       "                (&#x27;gridsearchcv&#x27;,\n",
       "                 GridSearchCV(estimator=PostLassoOLS(),\n",
       "                              param_grid={&#x27;alpha&#x27;: array([1.00000000e-04, 7.74263683e-04, 5.99484250e-03, 4.64158883e-02,\n",
       "       3.59381366e-01, 2.78255940e+00, 2.15443469e+01, 1.66810054e+02,\n",
       "       1.29154967e+03, 1.00000000e+04])},\n",
       "                              scoring=&#x27;r2&#x27;))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),\n",
       "                (&#x27;gridsearchcv&#x27;,\n",
       "                 GridSearchCV(estimator=PostLassoOLS(),\n",
       "                              param_grid={&#x27;alpha&#x27;: array([1.00000000e-04, 7.74263683e-04, 5.99484250e-03, 4.64158883e-02,\n",
       "       3.59381366e-01, 2.78255940e+00, 2.15443469e+01, 1.66810054e+02,\n",
       "       1.29154967e+03, 1.00000000e+04])},\n",
       "                              scoring=&#x27;r2&#x27;))])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">StandardScaler</label><div class=\"sk-toggleable__content\"><pre>StandardScaler()</pre></div></div></div><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">gridsearchcv: GridSearchCV</label><div class=\"sk-toggleable__content\"><pre>GridSearchCV(estimator=PostLassoOLS(),\n",
       "             param_grid={&#x27;alpha&#x27;: array([1.00000000e-04, 7.74263683e-04, 5.99484250e-03, 4.64158883e-02,\n",
       "       3.59381366e-01, 2.78255940e+00, 2.15443469e+01, 1.66810054e+02,\n",
       "       1.29154967e+03, 1.00000000e+04])},\n",
       "             scoring=&#x27;r2&#x27;)</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">estimator: PostLassoOLS</label><div class=\"sk-toggleable__content\"><pre>PostLassoOLS()</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" ><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PostLassoOLS</label><div class=\"sk-toggleable__content\"><pre>PostLassoOLS()</pre></div></div></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('standardscaler', StandardScaler()),\n",
       "                ('gridsearchcv',\n",
       "                 GridSearchCV(estimator=PostLassoOLS(),\n",
       "                              param_grid={'alpha': array([1.00000000e-04, 7.74263683e-04, 5.99484250e-03, 4.64158883e-02,\n",
       "       3.59381366e-01, 2.78255940e+00, 2.15443469e+01, 1.66810054e+02,\n",
       "       1.29154967e+03, 1.00000000e+04])},\n",
       "                              scoring='r2'))])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcv = GridSearchCV(PostLassoOLS(), {'alpha': np.logspace(-4, 4, 10)},\n",
    "                   scoring='r2')\n",
    "lcv = make_pipeline(StandardScaler(), lcv)\n",
    "lcv.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8a4bf6f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.166286782831505"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, lcv.predict(Xpop)) # much better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "b14b4354",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.abs(lcv[-1].best_estimator_.coef_)[np.argsort(np.abs(lcv[-1].best_estimator_.coef_))[::-1]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e9c5e8fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# The theoretical driven approach also supports post lasso OLS\n",
    "# choses a penalty appropriate for the post-lasso-ols model\n",
    "lcv = make_pipeline(StandardScaler(), RLasso(post=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0db08ff1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),\n",
       "                (&#x27;rlasso&#x27;, RLasso(post=True))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" ><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Pipeline</label><div class=\"sk-toggleable__content\"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),\n",
       "                (&#x27;rlasso&#x27;, RLasso(post=True))])</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-10\" type=\"checkbox\" ><label for=\"sk-estimator-id-10\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">StandardScaler</label><div class=\"sk-toggleable__content\"><pre>StandardScaler()</pre></div></div></div><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-11\" type=\"checkbox\" ><label for=\"sk-estimator-id-11\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RLasso</label><div class=\"sk-toggleable__content\"><pre>RLasso(post=True)</pre></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "Pipeline(steps=[('standardscaler', StandardScaler()),\n",
       "                ('rlasso', RLasso(post=True))])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lcv.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4899d3b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.23040048026438686"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, lcv.predict(Xpop))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ca9c4de5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BALAv6WGaqqoqLV++XMXFxSopKdGWLVsUDodVUVEh6eMhlqNHj2rHjh2SpLq6Ol144YVasGCB+vv79eMf/1i7du3Srl27xrclY3BiAisAALAl6TBSXl6u7u5ubdiwQZFIREVFRWpqalJ+fr4kKRKJJOw50t/fr/vvv19Hjx7VtGnTtGDBAj333HO64YYbxq8VYxSf50IaAQDAGo9JgTGKaDQqn8+nnp6ecZ0/8t9v/U7feOwXKsjJ0ov3f2ncPhcAAIz+7zfPphFzRgAAsMnpMBJDFAEAwB6nw8gIW6MAAIBPkNNhJDZQwygNAAD2OB1GTiymIY0AAGCL22Fk8JWeEQAA7HE7jHgYpgEAwDa3w4jtCgAAALfDSAz7jAAAYI/TYYTd4AEAsM/tMMJADQAA1rkdRmI9I3SNAABgjdNhJIZ9RgAAsMfpMELPCAAA9rkdRmLbwVuuBwAALnM6jMTQMwIAgD1Oh5ETT+0ljQAAYAthBAAAWOV2GBHPpgEAwDa3wwg7sAIAYJ3bYWTwlWfTAABgj9thhJ4RAACsczqMxNAxAgCAPY6HkdgEVtIIAAC2OB1GWNoLAIB9boeRwVf6RQAAsMftMMIMVgAArHM7jAy+kkUAALDH7TAS6xhhAisAANY4HUZiiCIAANjjdBjh2TQAANjndhhhaS8AANY5HUZiDAM1AABYM6YwUl9fr4KCAmVmZioQCKi5uXlU173yyitKT0/XX/zFX4zla8fdiQmsdusBAIDLkg4jjY2NqqysVE1Njdra2rR48WKVlZUpHA6f9rqenh6tWLFCS5cuHXNlx1tsnxGyCAAA9iQdRjZt2qRVq1Zp9erVKiwsVF1dnfLy8tTQ0HDa6+644w7deuutKikpGXNlx1t8yghpBAAAa5IKI/39/WptbVUwGEw4HwwG1dLSMuJ1Tz75pH77299q3bp1o/qevr4+RaPRhGMinNiAlTQCAIAtSYWRrq4uDQwMyO/3J5z3+/3q6OgY9ppDhw7pgQce0FNPPaX09PRRfU9tba18Pl/8yMvLS6aaSWPOCAAA9oxpAqvnlDWxxpgh5yRpYGBAt956q773ve/pkksuGfXnV1dXq6enJ360t7ePpZpnFN9nZEI+HQAAjMbouioG5eTkKC0tbUgvSGdn55DeEknq7e3Vq6++qra2Nq1du1aSdPz4cRljlJ6erhdeeEFLliwZcp3X65XX602mamPCPiMAANiXVM9IRkaGAoGAQqFQwvlQKKTS0tIh5bOzs7V//37t27cvflRUVGj+/Pnat2+fFi5ceHa1P0vxB+UxTgMAgDVJ9YxIUlVVlZYvX67i4mKVlJRoy5YtCofDqqiokPTxEMvRo0e1Y8cOTZkyRUVFRQnXz5o1S5mZmUPOWxGfwAoAAGxJOoyUl5eru7tbGzZsUCQSUVFRkZqampSfny9JikQiZ9xz5FzBs2kAALDPY1JgjCIajcrn86mnp0fZ2dnj9rldH/ap+KGfS5LeevjGcftcAAAw+r/fPJtmUApkMgAAJiWnw8jJi2nIIgAA2OF2GGFtLwAA1rkdRk76mY4RAADscDuMnJRGmDMCAIAdboeRk/pGiCIAANjhdBhRQs+IvWoAAOAyt8PISQx9IwAAWOF0GPHQMwIAgHVuhxHbFQAAAI6HEfYZAQDAOrfDyEk/M0wDAIAdboeRk+eMMIEVAAAr3A4jJ+8zQhYBAMAKp8PIycgiAADY4XQYYTt4AADsczqMnIwoAgCAHU6HEVb2AgBgn9thhAmsAABY53YYSdhoxFo1AABwmtth5KSf2WcEAAA7nA4jJ2OYBgAAO5wOIyc/m4YsAgCAHW6HkZN+Zp8RAADscDuMsLQXAADrHA8jDNMAAGCb02HkZIzSAABgh/NhJNY5wtJeAADscD6MxJFFAACwwvkwEps1QhYBAMAOwsjgOA1zRgAAsIMwYrsCAAA4bkxhpL6+XgUFBcrMzFQgEFBzc/OIZV9++WUtWrRIM2fO1LRp03TppZfqn/7pn8Zc4fHGBFYAAOxKT/aCxsZGVVZWqr6+XosWLdLjjz+usrIyHThwQPPmzRtSPisrS2vXrtUVV1yhrKwsvfzyy7rjjjuUlZWlv/u7vxuXRpwNjzySDMM0AABY4jFJ7oO+cOFCXXXVVWpoaIifKyws1LJly1RbWzuqz7j55puVlZWlf/3Xfx1V+Wg0Kp/Pp56eHmVnZydT3TO65P/8VP3HjuuVB5bogvOmjetnAwDgstH+/U5qmKa/v1+tra0KBoMJ54PBoFpaWkb1GW1tbWppadG1116bzFdPmPhqGrpGAACwIqlhmq6uLg0MDMjv9yec9/v96ujoOO21c+fO1fvvv69jx45p/fr1Wr169Yhl+/r61NfXF/89Go0mU80xIYsAAGDHmCawek55wpwxZsi5UzU3N+vVV1/VY489prq6Oj399NMjlq2trZXP54sfeXl5Y6nmqPCwPAAA7EqqZyQnJ0dpaWlDekE6OzuH9JacqqCgQJJ0+eWX67333tP69ev1zW9+c9iy1dXVqqqqiv8ejUYnLJB4xD4jAADYlFTPSEZGhgKBgEKhUML5UCik0tLSUX+OMSZhGOZUXq9X2dnZCcdEoWcEAAC7kl7aW1VVpeXLl6u4uFglJSXasmWLwuGwKioqJH3cq3H06FHt2LFDkvToo49q3rx5uvTSSyV9vO/Ixo0bddddd41jM8buxHbwdI0AAGBD0mGkvLxc3d3d2rBhgyKRiIqKitTU1KT8/HxJUiQSUTgcjpc/fvy4qqurdeTIEaWnp+uiiy7Sww8/rDvuuGP8WnEW2A4eAAC7kt5nxIaJ3Gfk8nU/U2/fMb14/5dUkJM1rp8NAIDLJmSfkcksBTIZAACTEmEk/mwaAABgg/Nh5MQOrFarAQCAswgjrO0FAMAqwkg8i9A1AgCADYSRwVeGaQAAsIMwEttnxHI9AABwlfNhJIaeEQAA7HA+jLAdPAAAdhFGYvuMkEUAALDC+TByom8EAADY4HwYoWcEAAC7CCODr8wZAQDADsIIPSMAAFjlfBgBAAB2OR9GPIMDNfSMAABgB2EkNkzDnBEAAKwgjNiuAAAAjiOMeBimAQDAJufDSAxZBAAAO5wPIyeW9hJHAACwwfkwEkMUAQDADufDCJueAQBgF2HkpA3hAQDAJ48wQs8IAABWEUZsVwAAAMcRRmL7jFiuBwAAriKMDL4yTAMAgB3Oh5EY9hkBAMAOwkj8QXkAAMAG58MIwzQAANhFGIlPYCWNAABgA2HEdgUAAHDcmMJIfX29CgoKlJmZqUAgoObm5hHL7t69W1/5yld0/vnnKzs7WyUlJfrZz3425gqPNw8bsAIAYFXSYaSxsVGVlZWqqalRW1ubFi9erLKyMoXD4WHL7927V1/5ylfU1NSk1tZWffnLX9ZNN92ktra2s678eIhtB08WAQDADo9Jck3rwoULddVVV6mhoSF+rrCwUMuWLVNtbe2oPmPBggUqLy/Xd7/73VGVj0aj8vl86unpUXZ2djLVPaPr6/bq1x29+vGqhfrCxTnj+tkAALhstH+/k+oZ6e/vV2trq4LBYML5YDColpaWUX3G8ePH1dvbqxkzZoxYpq+vT9FoNOGYaExgBQDAjqTCSFdXlwYGBuT3+xPO+/1+dXR0jOoz/vEf/1F/+MMfdMstt4xYpra2Vj6fL37k5eUlU80xYWkvAAB2jGkCq8eTuAbFGDPk3HCefvpprV+/Xo2NjZo1a9aI5aqrq9XT0xM/2tvbx1LNUeHZNAAA2JWeTOGcnBylpaUN6QXp7Owc0ltyqsbGRq1atUr/9m//puuuu+60Zb1er7xebzJVGzOW9gIAYFdSPSMZGRkKBAIKhUIJ50OhkEpLS0e87umnn9Ztt92mn/zkJ7rxxhvHVtMJEuvQ4dk0AADYkVTPiCRVVVVp+fLlKi4uVklJibZs2aJwOKyKigpJHw+xHD16VDt27JD0cRBZsWKFNm/erGuuuSbeqzJt2jT5fL5xbMrYeHg2DQAAViUdRsrLy9Xd3a0NGzYoEomoqKhITU1Nys/PlyRFIpGEPUcef/xxHTt2THfeeafuvPPO+PmVK1dq+/btZ9+Cs+ThSXkAAFiV9D4jNkzkPiM3/fBl7T/ao223FWvJpaef9wIAAEZvQvYZmYxOzBmxWw8AAFxFGBl8JYwAAGCH82FE7DMCAIBVzocR9hkBAMAuwgj7jAAAYBVhZPCVKAIAgB3Oh5EYOkYAALDD+TBy4gF/pBEAAGwgjAy+0jMCAIAdhBF2gwcAwCrCCIt7AQCwyvkwIraDBwDAKufDyInpq6QRAABscD6MxNAzAgCAHc6HESawAgBgF2FkcKCG7eABALCDMMJiGgAArCKMEEYAALCKMBIfprFcEQAAHEUYiU9gJY0AAGCD82Ekhp4RAADsIIwMIowAAGCH82HEMzhOQxYBAMAOwsjgK/uMAABgB2GEHVgBALCKMGK7AgAAOI4wQtcIAABWOR9GYthnBAAAO5wPIycmsFqtBgAAziKMMEoDAIBVzocR8WwaAACscj6M8GwaAADsIozYrgAAAI4bUxipr69XQUGBMjMzFQgE1NzcPGLZSCSiW2+9VfPnz9eUKVNUWVk51rpOiHjPCB0jAABYkXQYaWxsVGVlpWpqatTW1qbFixerrKxM4XB42PJ9fX06//zzVVNToyuvvPKsKzzePOLZNAAA2JR0GNm0aZNWrVql1atXq7CwUHV1dcrLy1NDQ8Ow5S+88EJt3rxZK1askM/nO+sKTxi6RgAAsCKpMNLf36/W1lYFg8GE88FgUC0tLeNWqb6+PkWj0YRjorC0FwAAu5IKI11dXRoYGJDf70847/f71dHRMW6Vqq2tlc/nix95eXnj9tmnYs4IAAB2jWkCa/x5LoOMMUPOnY3q6mr19PTEj/b29nH77FPF54yQRgAAsCI9mcI5OTlKS0sb0gvS2dk5pLfkbHi9Xnm93nH7vNNibS8AAFYl1TOSkZGhQCCgUCiUcD4UCqm0tHRcK/ZJiT+bxmotAABwV1I9I5JUVVWl5cuXq7i4WCUlJdqyZYvC4bAqKiokfTzEcvToUe3YsSN+zb59+yRJH374od5//33t27dPGRkZuuyyy8anFWchNrzEKA0AAHYkHUbKy8vV3d2tDRs2KBKJqKioSE1NTcrPz5f08SZnp+458rnPfS7+c2trq37yk58oPz9fb7311tnVfhyRRQAAsCPpMCJJa9as0Zo1a4Z9b/v27UPOncuTQ+PDNOdwHQEAmMx4Ng0TWAEAsIowMvhKxwgAAHYQRmITWJk1AgCAFYQR2xUAAMBxzocRsR08AABWEUYGkUUAALDD+TBy4tk0lisCAICjCCOxYRr6RgAAsIIwMvhKzwgAAHYQRlhOAwCAVYQRFvcCAGAVYSS+tJdxGgAAbHA+jMSQRQAAsMP5MHJiNQ0AALDB+TAi9hkBAMAq58MI+4wAAGAXYWTwlZ4RAADsIIywshcAAKsII7E5I5brAQCAq5wPI3GM0wAAYIXzYYSlvQAA2EUYGXylYwQAADsII57YnBHSCAAANjgfRmLoGQEAwA7nwwhLewEAsIswwtJeAACscj6MxDBMAwCAHc6HEZ5NAwCAXYSR2A9kEQAArCCMsOkZAABWEUZi+4wwaQQAACsII4OvZBEAAOwYUxipr69XQUGBMjMzFQgE1NzcfNrye/bsUSAQUGZmpj7zmc/oscceG1NlJwT7jAAAYFXSYaSxsVGVlZWqqalRW1ubFi9erLKyMoXD4WHLHzlyRDfccIMWL16strY2Pfjgg7r77ru1a9eus678eGCfEQAA7Eo6jGzatEmrVq3S6tWrVVhYqLq6OuXl5amhoWHY8o899pjmzZunuro6FRYWavXq1br99tu1cePGs678eGKYBgAAO9KTKdzf36/W1lY98MADCeeDwaBaWlqGveYXv/iFgsFgwrmvfvWr2rp1q/785z9r6tSpQ67p6+tTX19f/PdoNJpMNZMSW03zy8Pd+t7/e2PCvgcAgHPZ16+aq6ILfFa+O6kw0tXVpYGBAfn9/oTzfr9fHR0dw17T0dExbPljx46pq6tLubm5Q66pra3V9773vWSqNmbZmR+HoQORqA5EJi70AABwLvvcvE+nRhiJ8ZzydDljzJBzZyo/3PmY6upqVVVVxX+PRqPKy8sbS1XP6Nar50mSPuz784R8PgAAqeDiWZ+y9t1JhZGcnBylpaUN6QXp7Owc0vsRM3v27GHLp6ena+bMmcNe4/V65fV6k6namPn+11R9+0sXfSLfBQAAhkpqAmtGRoYCgYBCoVDC+VAopNLS0mGvKSkpGVL+hRdeUHFx8bDzRQAAgFuSXk1TVVWlJ554Qtu2bdPBgwd17733KhwOq6KiQtLHQywrVqyIl6+oqNDbb7+tqqoqHTx4UNu2bdPWrVt1//33j18rAABAykp6zkh5ebm6u7u1YcMGRSIRFRUVqampSfn5+ZKkSCSSsOdIQUGBmpqadO+99+rRRx/VnDlz9IMf/EBf//rXx68VAAAgZXlMCjyUJRqNyufzqaenR9nZ2barAwAARmG0f7+dfzYNAACwizACAACsIowAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsCrp7eBtiG0SG41GLdcEAACMVuzv9pk2e0+JMNLb2ytJysvLs1wTAACQrN7eXvl8vhHfT4ln0xw/flzvvvuupk+fLo/HM26fG41GlZeXp/b29kn7zJvJ3sbJ3j5p8rdxsrdPmvxtnOztkyZ/GyeqfcYY9fb2as6cOZoyZeSZISnRMzJlyhTNnTt3wj4/Ozt7Uv7HdbLJ3sbJ3j5p8rdxsrdPmvxtnOztkyZ/GyeifafrEYlhAisAALCKMAIAAKxyOox4vV6tW7dOXq/XdlUmzGRv42RvnzT52zjZ2ydN/jZO9vZJk7+NttuXEhNYAQDA5OV0zwgAALCPMAIAAKwijAAAAKsIIwAAwCqnw0h9fb0KCgqUmZmpQCCg5uZm21Uak/Xr18vj8SQcs2fPjr9vjNH69es1Z84cTZs2TV/60pf0xhtvWKzxme3du1c33XST5syZI4/Ho//4j/9IeH80berr69Ndd92lnJwcZWVl6S//8i/1zjvvfIKtGNmZ2nfbbbcNuafXXHNNQplzuX21tbX6/Oc/r+nTp2vWrFlatmyZ3nzzzYQyqX4PR9PGVL6PDQ0NuuKKK+KbYJWUlOinP/1p/P1Uv3/SmduYyvdvOLW1tfJ4PKqsrIyfO2fuo3HUzp07zdSpU82PfvQjc+DAAXPPPfeYrKws8/bbb9uuWtLWrVtnFixYYCKRSPzo7OyMv//www+b6dOnm127dpn9+/eb8vJyk5uba6LRqMVan15TU5Opqakxu3btMpLMM888k/D+aNpUUVFhLrjgAhMKhcyvfvUr8+Uvf9lceeWV5tixY59wa4Y6U/tWrlxprr/++oR72t3dnVDmXG7fV7/6VfPkk0+a119/3ezbt8/ceOONZt68eebDDz+Ml0n1eziaNqbyfXz22WfNc889Z958803z5ptvmgcffNBMnTrVvP7668aY1L9/xpy5jal8/071X//1X+bCCy80V1xxhbnnnnvi58+V++hsGLn66qtNRUVFwrlLL73UPPDAA5ZqNHbr1q0zV1555bDvHT9+3MyePds8/PDD8XN/+tOfjM/nM4899tgnVMOzc+of69G06YMPPjBTp041O3fujJc5evSomTJlinn++ec/sbqPxkhh5K/+6q9GvCaV2meMMZ2dnUaS2bNnjzFm8t1DY4a20ZjJdx8//elPmyeeeGJS3r+YWBuNmTz3r7e311x88cUmFAqZa6+9Nh5GzqX76OQwTX9/v1pbWxUMBhPOB4NBtbS0WKrV2Tl06JDmzJmjgoIC/fVf/7UOHz4sSTpy5Ig6OjoS2ur1enXttdembFtH06bW1lb9+c9/TigzZ84cFRUVpUy7X3rpJc2aNUuXXHKJ/vZv/1adnZ3x91KtfT09PZKkGTNmSJqc9/DUNsZMhvs4MDCgnTt36g9/+INKSkom5f07tY0xk+H+3Xnnnbrxxht13XXXJZw/l+5jSjwob7x1dXVpYGBAfr8/4bzf71dHR4elWo3dwoULtWPHDl1yySV677339NBDD6m0tFRvvPFGvD3DtfXtt9+2Ud2zNpo2dXR0KCMjQ5/+9KeHlEmFe1xWVqZvfOMbys/P15EjR/T3f//3WrJkiVpbW+X1elOqfcYYVVVV6Qtf+IKKiookTb57OFwbpdS/j/v371dJSYn+9Kc/6VOf+pSeeeYZXXbZZfE/QpPh/o3URin1758k7dy5U62trXr11VeHvHcu/Tt0MozEeDyehN+NMUPOpYKysrL4z5dffrlKSkp00UUX6V/+5V/ik60mS1tPNpY2pUq7y8vL4z8XFRWpuLhY+fn5eu6553TzzTePeN252L61a9fqtdde08svvzzkvclyD0dqY6rfx/nz52vfvn364IMPtGvXLq1cuVJ79uyJvz8Z7t9IbbzssstS/v61t7frnnvu0QsvvKDMzMwRy50L99HJYZqcnBylpaUNSXWdnZ1DEmIqysrK0uWXX65Dhw7FV9VMpraOpk2zZ89Wf3+/fv/7349YJpXk5uYqPz9fhw4dkpQ67bvrrrv07LPP6sUXX9TcuXPj5yfTPRypjcNJtfuYkZGhz372syouLlZtba2uvPJKbd68eVLdv5HaOJxUu3+tra3q7OxUIBBQenq60tPTtWfPHv3gBz9Qenp6vI7nwn10MoxkZGQoEAgoFAolnA+FQiotLbVUq/HT19engwcPKjc3VwUFBZo9e3ZCW/v7+7Vnz56Ubeto2hQIBDR16tSEMpFIRK+//npKtru7u1vt7e3Kzc2VdO63zxijtWvXavfu3frP//xPFRQUJLw/Ge7hmdo4nFS7j6cyxqivr29S3L+RxNo4nFS7f0uXLtX+/fu1b9+++FFcXKy/+Zu/0b59+/SZz3zm3LmP4zYVNsXElvZu3brVHDhwwFRWVpqsrCzz1ltv2a5a0u677z7z0ksvmcOHD5tf/vKX5mtf+5qZPn16vC0PP/yw8fl8Zvfu3Wb//v3mm9/85jm/tLe3t9e0tbWZtrY2I8ls2rTJtLW1xZdej6ZNFRUVZu7cuebnP/+5+dWvfmWWLFlyziy5O137ent7zX333WdaWlrMkSNHzIsvvmhKSkrMBRdckDLt+/a3v218Pp956aWXEpZFfvTRR/EyqX4Pz9TGVL+P1dXVZu/evebIkSPmtddeMw8++KCZMmWKeeGFF4wxqX//jDl9G1P9/o3k5NU0xpw799HZMGKMMY8++qjJz883GRkZ5qqrrkpYkpdKYuvCp06daubMmWNuvvlm88Ybb8TfP378uFm3bp2ZPXu28Xq95otf/KLZv3+/xRqf2YsvvmgkDTlWrlxpjBldm/74xz+atWvXmhkzZphp06aZr33tayYcDltozVCna99HH31kgsGgOf/8883UqVPNvHnzzMqVK4fU/Vxu33Btk2SefPLJeJlUv4dnamOq38fbb789/v/H888/3yxdujQeRIxJ/ftnzOnbmOr3bySnhpFz5T56jDFm/PpZAAAAkuPknBEAAHDuIIwAAACrCCMAAMAqwggAALCKMAIAAKwijAAAAKsIIwAAwCrCCAAAsIowAgAArCKMAAAAqwgjAADAKsIIAACw6v8D+iqUk7AiQmQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.abs(lcv[-1].coef_)[np.argsort(np.abs(lcv[-1].coef_))[::-1]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "805819b4",
   "metadata": {},
   "source": [
    "Let's try other penalty approaches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5a637031",
   "metadata": {},
   "outputs": [],
   "source": [
    "ridge = make_pipeline(StandardScaler(), RidgeCV()).fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ab6c046a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.08645559239393896"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(ypop, ridge.predict(Xpop))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "084ac239",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrcoefs = np.abs(lr.coef_)\n",
    "plt.plot(lrcoefs[np.argsort(lrcoefs)[::-1]], label='lr')\n",
    "lcvcoefs = np.abs(lcv[-1].coef_)\n",
    "plt.plot(lcvcoefs[np.argsort(lcvcoefs)[::-1]], label='lcv')\n",
    "rlassocoefs = np.abs(rlasso.coef_)\n",
    "plt.plot(rlassocoefs[np.argsort(rlassocoefs)[::-1]], label='rlasso')\n",
    "ridgecoefs = np.abs(ridge[-1].coef_)\n",
    "plt.plot(ridgecoefs[np.argsort(ridgecoefs)[::-1]], label='ridge')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "66c888a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "enet = make_pipeline(StandardScaler(), ElasticNetCV()).fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ab31fcb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrcoefs = np.abs(lr.coef_)\n",
    "plt.plot(lrcoefs[np.argsort(lrcoefs)[::-1]], label='lr')\n",
    "lcvcoefs = np.abs(lcv[-1].coef_)\n",
    "plt.plot(lcvcoefs[np.argsort(lcvcoefs)[::-1]], label='lcv')\n",
    "rlassocoefs = np.abs(rlasso.coef_)\n",
    "plt.plot(rlassocoefs[np.argsort(rlassocoefs)[::-1]], label='rlasso')\n",
    "ridgecoefs = np.abs(ridge[-1].coef_)\n",
    "plt.plot(ridgecoefs[np.argsort(ridgecoefs)[::-1]], label='ridge')\n",
    "enetcoefs = np.abs(enet[-1].coef_)\n",
    "plt.plot(enetcoefs[np.argsort(enetcoefs)[::-1]], label='enet')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9de95050",
   "metadata": {},
   "source": [
    "## Wage Prediction\n",
    "\n",
    "Let's try all these approaches for wage prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "b9026c1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "file = \"https://raw.githubusercontent.com/CausalAIBook/MetricsMLNotebooks/main/data/wage2015_subsample_inference.csv\"\n",
    "data = pd.read_csv(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "77235e3e",
   "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>wage</th>\n",
       "      <th>lwage</th>\n",
       "      <th>sex</th>\n",
       "      <th>shs</th>\n",
       "      <th>hsg</th>\n",
       "      <th>scl</th>\n",
       "      <th>clg</th>\n",
       "      <th>ad</th>\n",
       "      <th>mw</th>\n",
       "      <th>so</th>\n",
       "      <th>we</th>\n",
       "      <th>ne</th>\n",
       "      <th>exp1</th>\n",
       "      <th>exp2</th>\n",
       "      <th>exp3</th>\n",
       "      <th>exp4</th>\n",
       "      <th>occ</th>\n",
       "      <th>occ2</th>\n",
       "      <th>ind</th>\n",
       "      <th>ind2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "      <td>5150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>23.410410</td>\n",
       "      <td>2.970787</td>\n",
       "      <td>0.444466</td>\n",
       "      <td>0.023301</td>\n",
       "      <td>0.243883</td>\n",
       "      <td>0.278058</td>\n",
       "      <td>0.317670</td>\n",
       "      <td>0.137087</td>\n",
       "      <td>0.259612</td>\n",
       "      <td>0.296505</td>\n",
       "      <td>0.216117</td>\n",
       "      <td>0.227767</td>\n",
       "      <td>13.760583</td>\n",
       "      <td>3.018925</td>\n",
       "      <td>8.235867</td>\n",
       "      <td>25.118038</td>\n",
       "      <td>5310.737476</td>\n",
       "      <td>11.670874</td>\n",
       "      <td>6629.154951</td>\n",
       "      <td>13.316893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>21.003016</td>\n",
       "      <td>0.570385</td>\n",
       "      <td>0.496955</td>\n",
       "      <td>0.150872</td>\n",
       "      <td>0.429465</td>\n",
       "      <td>0.448086</td>\n",
       "      <td>0.465616</td>\n",
       "      <td>0.343973</td>\n",
       "      <td>0.438464</td>\n",
       "      <td>0.456761</td>\n",
       "      <td>0.411635</td>\n",
       "      <td>0.419432</td>\n",
       "      <td>10.609465</td>\n",
       "      <td>4.000904</td>\n",
       "      <td>14.488962</td>\n",
       "      <td>53.530225</td>\n",
       "      <td>11874.356080</td>\n",
       "      <td>6.966684</td>\n",
       "      <td>5333.443992</td>\n",
       "      <td>5.701019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>3.021978</td>\n",
       "      <td>1.105912</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>370.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>13.461538</td>\n",
       "      <td>2.599837</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.125000</td>\n",
       "      <td>0.062500</td>\n",
       "      <td>1740.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>4880.000000</td>\n",
       "      <td>9.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>19.230769</td>\n",
       "      <td>2.956512</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4040.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>7370.000000</td>\n",
       "      <td>14.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>27.777778</td>\n",
       "      <td>3.324236</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>21.000000</td>\n",
       "      <td>4.410000</td>\n",
       "      <td>9.261000</td>\n",
       "      <td>19.448100</td>\n",
       "      <td>5610.000000</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>8190.000000</td>\n",
       "      <td>18.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>528.845673</td>\n",
       "      <td>6.270697</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>47.000000</td>\n",
       "      <td>22.090000</td>\n",
       "      <td>103.823000</td>\n",
       "      <td>487.968100</td>\n",
       "      <td>100000.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>100000.000000</td>\n",
       "      <td>22.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              wage        lwage          sex          shs          hsg  \\\n",
       "count  5150.000000  5150.000000  5150.000000  5150.000000  5150.000000   \n",
       "mean     23.410410     2.970787     0.444466     0.023301     0.243883   \n",
       "std      21.003016     0.570385     0.496955     0.150872     0.429465   \n",
       "min       3.021978     1.105912     0.000000     0.000000     0.000000   \n",
       "25%      13.461538     2.599837     0.000000     0.000000     0.000000   \n",
       "50%      19.230769     2.956512     0.000000     0.000000     0.000000   \n",
       "75%      27.777778     3.324236     1.000000     0.000000     0.000000   \n",
       "max     528.845673     6.270697     1.000000     1.000000     1.000000   \n",
       "\n",
       "               scl          clg           ad           mw           so  \\\n",
       "count  5150.000000  5150.000000  5150.000000  5150.000000  5150.000000   \n",
       "mean      0.278058     0.317670     0.137087     0.259612     0.296505   \n",
       "std       0.448086     0.465616     0.343973     0.438464     0.456761   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "50%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "75%       1.000000     1.000000     0.000000     1.000000     1.000000   \n",
       "max       1.000000     1.000000     1.000000     1.000000     1.000000   \n",
       "\n",
       "                we           ne         exp1         exp2         exp3  \\\n",
       "count  5150.000000  5150.000000  5150.000000  5150.000000  5150.000000   \n",
       "mean      0.216117     0.227767    13.760583     3.018925     8.235867   \n",
       "std       0.411635     0.419432    10.609465     4.000904    14.488962   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     5.000000     0.250000     0.125000   \n",
       "50%       0.000000     0.000000    10.000000     1.000000     1.000000   \n",
       "75%       0.000000     0.000000    21.000000     4.410000     9.261000   \n",
       "max       1.000000     1.000000    47.000000    22.090000   103.823000   \n",
       "\n",
       "              exp4            occ         occ2            ind         ind2  \n",
       "count  5150.000000    5150.000000  5150.000000    5150.000000  5150.000000  \n",
       "mean     25.118038    5310.737476    11.670874    6629.154951    13.316893  \n",
       "std      53.530225   11874.356080     6.966684    5333.443992     5.701019  \n",
       "min       0.000000      10.000000     1.000000     370.000000     2.000000  \n",
       "25%       0.062500    1740.000000     5.000000    4880.000000     9.000000  \n",
       "50%       1.000000    4040.000000    13.000000    7370.000000    14.000000  \n",
       "75%      19.448100    5610.000000    17.000000    8190.000000    18.000000  \n",
       "max     487.968100  100000.000000    22.000000  100000.000000    22.000000  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "efe55f50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['sex', 'shs', 'hsg', 'scl', 'clg', 'ad', 'mw', 'so', 'we', 'ne', 'exp1',\n",
       "       'exp2', 'exp3', 'exp4', 'occ', 'occ2', 'ind', 'ind2'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.log(data['wage']).values\n",
    "Z = data.drop(['wage', 'lwage'], axis=1)\n",
    "Z.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f5982c23",
   "metadata": {},
   "outputs": [],
   "source": [
    "Zbase = patsy.dmatrix('0 + sex + exp1 + shs + hsg+ scl + clg + mw + so + we + C(occ2) + C(ind2)',\n",
    "                      Z, return_type='dataframe').values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "4f6dd381",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(Zbase, y, test_size=0.25, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "14c90868",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr_base = LinearRegression().fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "15a83271",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2853\n"
     ]
    }
   ],
   "source": [
    "print(f'{r2_score(y_test, lr_base.predict(X_test)):.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "28ca983a",
   "metadata": {},
   "outputs": [],
   "source": [
    "cv = KFold(n_splits=5, shuffle=True, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9b55f8f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29533051768666346"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(LinearRegression(), Zbase, y, scoring='r2', cv=cv))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "ee347051",
   "metadata": {},
   "outputs": [],
   "source": [
    "Zflex = patsy.dmatrix('0 + sex + (exp1+exp2+exp3+exp4)*(shs+hsg+scl+clg+C(occ2)+C(ind2)+mw+so+we)',\n",
    "                      Z, return_type='dataframe').values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "485f2a97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4310928603349694.5"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(LinearRegression(), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eac564a",
   "metadata": {},
   "source": [
    "OLS is very unstable!! Result depends on exactly how you implemented ols for ill-posed covariance matrices!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "330f26e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyOLS(BaseEstimator):\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        X = np.hstack([np.ones((X.shape[0], 1)), X])\n",
    "        self.ols_ = sm.OLS(y, X).fit()\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        X = np.hstack([np.ones((X.shape[0], 1)), X])\n",
    "        return self.ols_.predict(X)\n",
    "    \n",
    "    @property\n",
    "    def coef_(self):\n",
    "        return self.ols_.params[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "e4e3caf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25217224997945015"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(MyOLS(), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "1ace3445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2796914535001022"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(LassoCV(cv=cv), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "4a9bb885",
   "metadata": {},
   "outputs": [],
   "source": [
    "Zflex = StandardScaler().fit_transform(Zflex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1631c35f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29591518129317207"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(LassoCV(cv=cv), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "3bf36cb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.285263522612187"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(RidgeCV(cv=cv), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "2f350e3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29603340816822693"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(cross_val_score(ElasticNetCV(cv=cv), Zflex, y, scoring='r2', cv=cv, n_jobs=-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "5624cb83",
   "metadata": {},
   "outputs": [],
   "source": [
    "lcv = LassoCV(cv=cv).fit(Zflex, y)\n",
    "ridge = RidgeCV(cv=cv).fit(Zflex, y)\n",
    "enet = ElasticNetCV(cv=cv).fit(Zflex, y)\n",
    "lr = MyOLS().fit(Zflex, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "06b00255",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.abs(lcv.coef_)[np.argsort(np.abs(lcv.coef_))[::-1]], label='lcv')\n",
    "plt.plot(np.abs(ridge.coef_)[np.argsort(np.abs(ridge.coef_))[::-1]], label='ridge')\n",
    "plt.plot(np.abs(enet.coef_)[np.argsort(np.abs(enet.coef_))[::-1]], label='enet')\n",
    "# plt.plot(np.abs(lr.coef_)[np.argsort(np.abs(lr.coef_))[::-1]])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f26b8e2",
   "metadata": {},
   "source": [
    "In the end vanilla OLS on the low dimensional feature map is pretty good. It's not always the case that going to very high dimensional features and using penalization will improve your R-square. Never forget poor OLS on a small set of hand-picked features. After all OLS is also a machine learning algorithm :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1d9a15e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}