03-04-Regularized Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized Method for Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some examples:\n",
    "\n",
    "* [Ridge Regression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html)\n",
    "* [Least Absolute Shrinkage and Selection Operator (LASSO)](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html)\n",
    "* [Elastic Net](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.ElasticNet.html)\n",
    "\n",
    "## Ridge Regression\n",
    "Source: [scikit-learn](http://scikit-learn.org/stable/modules/linear_model.html#ridge-regression)\n",
    "\n",
    "Ridge regression addresses some of the problems of **Ordinary Least Squares** by imposing a penalty on the size of coefficients. The ridge coefficients minimize a penalized residual sum of squares,\n",
    "\n",
    "$$\\min_{w}\\big|\\big|Xw-y\\big|\\big|^2_2+\\alpha\\big|\\big|w\\big|\\big|^2_2$$\n",
    "\n",
    "$\\alpha>=0$ is a complexity parameter that controls the amount of shrinkage: the larger the value of $\\alpha$, the greater the amount of shrinkage and thus the coefficients become more robust to collinearity.\n",
    "\n",
    "Ridge regression is an L2 penalized model. Add the squared sum of the weights to the least-squares cost function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shows the effect of collinearity in the coefficients of an estimator.\n",
    "\n",
    "Ridge Regression is the estimator used in this example. Each color represents a different feature of the coefficient vector, and this is displayed as a function of the regularization parameter.\n",
    "\n",
    "This example also shows the usefulness of applying Ridge regression to highly ill-conditioned matrices. For such matrices, a slight change in the target variable can cause huge variances in the calculated weights. In such cases, it is useful to set a certain regularization (alpha) to reduce this variation (noise)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.16.5\n",
      "0.25.1\n",
      "3.7.4 (default, Aug 13 2019, 15:17:50) \n",
      "[Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "0.21.3\n"
     ]
    }
   ],
   "source": [
    "print(np.__version__)\n",
    "print(pd.__version__)\n",
    "import sys\n",
    "print(sys.version)\n",
    "import sklearn\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "\n",
    "# X is the 10x10 Hilbert matrix\n",
    "X = 1. / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])\n",
    "y = np.ones(10)\n",
    "\n",
    "# ###########################################################################\n",
    "# Compute paths\n",
    "\n",
    "n_alphas = 200\n",
    "alphas = np.logspace(-10, -2, n_alphas)\n",
    "\n",
    "coefs = []\n",
    "for a in alphas:\n",
    "    ridge = linear_model.Ridge(alpha=a, fit_intercept=False)\n",
    "    ridge.fit(X, y)\n",
    "    coefs.append(ridge.coef_)\n",
    "\n",
    "# ###########################################################################\n",
    "# Display results\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "ax = plt.gca()\n",
    "\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization')\n",
    "plt.axis('tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LASSO Regression\n",
    "\n",
    "A linear model that estimates sparse coefficients.\n",
    "\n",
    "Mathematically, it consists of a linear model trained with $\\ell_1$ prior as regularizer. The objective function to minimize is:\n",
    "\n",
    "$$\\min_{w}\\frac{1}{2n_{samples}} \\big|\\big|Xw - y\\big|\\big|_2^2 + \\alpha \\big|\\big|w\\big|\\big|_1$$\n",
    "\n",
    "The lasso estimate thus solves the minimization of the least-squares penalty with $\\alpha \\big|\\big|w\\big|\\big|_1$ added, where $\\alpha$ is a constant and $\\big|\\big|w\\big|\\big|_1$ is the $\\ell_1-norm$ of the parameter vector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elastic Net\n",
    "\n",
    "A linear regression model trained with L1 and L2 prior as regularizer. \n",
    "\n",
    "This combination allows for learning a sparse model where few of the weights are non-zero like Lasso, while still maintaining the regularization properties of Ridge. \n",
    "\n",
    "Elastic-net is useful when there are multiple features which are correlated with one another. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.\n",
    "\n",
    "A practical advantage of trading-off between Lasso and Ridge is it allows Elastic-Net to inherit some of Ridge’s stability under rotation.\n",
    "\n",
    "The objective function to minimize is in this case\n",
    "\n",
    "$$\\min_{w}{\\frac{1}{2n_{samples}} \\big|\\big|X w - y\\big|\\big|_2 ^ 2 + \\alpha \\rho \\big|\\big|w\\big|\\big|_1 +\n",
    "\\frac{\\alpha(1-\\rho)}{2} \\big|\\big|w\\big|\\big|_2 ^ 2}$$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Outliers Impact "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "%matplotlib inline\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient Estimate:  [0.47134857]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "n_samples = 100\n",
    "rng = np.random.randn(n_samples) * 10\n",
    "y_gen = 0.5 * rng + 2 * np.random.randn(n_samples)\n",
    "\n",
    "lr = LinearRegression()\n",
    "lr.fit(rng.reshape(-1, 1), y_gen)\n",
    "model_pred = lr.predict(rng.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(rng, y_gen);\n",
    "plt.plot(rng, model_pred);\n",
    "print(\"Coefficient Estimate: \", lr.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = rng.argmax()\n",
    "y_gen[idx] = 200\n",
    "idx = rng.argmin()\n",
    "y_gen[idx] = -200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient Estimate:  [1.50556072]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(rng, y_gen);\n",
    "\n",
    "o_lr = LinearRegression(normalize=True)\n",
    "o_lr.fit(rng.reshape(-1, 1), y_gen)\n",
    "o_model_pred = o_lr.predict(rng.reshape(-1,1))\n",
    "\n",
    "plt.scatter(rng, y_gen);\n",
    "plt.plot(rng, o_model_pred);\n",
    "print(\"Coefficient Estimate: \", o_lr.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient Estimate:  [1.00370714]\n"
     ]
    },
    {
     "data": {
      "image/png": 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s9j4OHJrJ1L7ZqcFeYXIlIWnLqRsfVrbYNFs3G9eNZNOGZO9D3ceDVmuqcb6upfwezvdDt/ffa6fi5o3r8+aXPk3Y6iB0ASe9fkeEFgam5517Vv7im/f0/cG1lHr+0/97Z+554DtHnXcpIWIp4WAQtmzemKt+8e8v6wP2WAu7+3nf3abslhqSOnVbD77YNNtC89dj8q7JvPOWH/d8zWpNNV563rYl19lrhOxlF2zLX3zznqN2Lxrd6q5J6CqlrEvy7iRPTzKd5JW11m+3qBtYuhN1N9zxatebPvH1Y+7muvL6249aNDw5tS/vv+XOI8f3M2rRK1y89s9vy6s/dOuRINe5G2xyat+qjEwlWXT7/0JT+w70PWpz/e7JXPXfvn5kpKqX+bDVb3haGM6OFZI2b1zf82f3dWnb/Pt67Z/f1vW6dLslxMSmPdm2tfcoUbd2n6iWM0LG0VqNdF2aZFOt9VmllIuSXJPkJY3qBpZgJeuABhmKOs915uaNeejgoTx44PCRn09O7cvO627LVf/t67lv34Ge9V2/ezJv+sTXj+xSWzgic/3uya472ObrmD+mM2D1Mh/Ukod/MP3i07f2/NCd/wBfGORW6vGPPDU/3Du97HVN/Qauef2M2ly/ezI7P3xbDhw+9rnnF3b3O8K0cCH4wpCw5dSNmZnJUb8vvcJQr0Xl8+dc6pqoS8/bln/4ls8uqa4T0XJGyPg7IzNL/KNajlLKW5N8udb6Z3PPJ2utPXvt1ltvnRkdXd3vjTpZ7d+/P5s2bVrtZqxJn/3O3vzpV3+Sex44mLNO25BfO/8R+fknHZ87Uh+rHxdry69dd2d++MDD7zf0mNM25E//6eMWPec7bv5RphdsnT9jdF3+zc8+qud7XdiWZ/69zfnLv7m/5zqYxawfSV5z8VlH6vrsd/bmbTfdk4OHex/X6/0ms2tVPvVrT8o//7PvZs/04a7HtPbvnvWovOOL9y56zKd/7UlHHs9f317vcdDmr1kvi13vTqPrR/Lvfu7RR/Xl/O/J2Oi6PPDQ4XT+qi08vl/dfm/7OVe/f8+df4vLrYvV1c/n4oMPPjh+wQUXPONY52o10nVGkvs6nh8qpWyotXb9yxsdHc327dvbtIyjTExMuPbHwfW7J/POW773dwuFHziYd97y42zbuvh/NS535GixfjxWW+554DtdX3fPAwcX/d145cc/+7DAlSR7pg/3fK/d2vLJuveY76+XQzPJe78ylcsv+dkjbVoYuOaP++Dt92fb1m2LBoCZJC/60+7Xo7XOqauPTHQfMZnX2U/btyeXX5KeoyyDtnXL5kV/T3r9fs0bmTvHwt/1+fcxb1Cjqtu3J9u2Lv1cC9vTS+ff4nLrYnX187k4Pj7e17laha49STpj/LpegYvV9dnv7M0rP/7Znv8gnKhrfVbDUq7FUu8APX/+btN8X/nejx+2eHu+jvmyy552enr9G3GstvRaP7NuZCRPfN0ne77XxdalzK9bWtj2B6Yffo+plepcJ7RYm+bXSrXUuej4rql9WdfnmqmFU1c7d5SebX9El113yeLXYn7t1sL/X6p+7sW02PqspXxNziCnuVpOmZmeO7m1Cl03JfmFJH8+t6br9kb1sgTX7548auh74VqeYb7z9VL0E6aWei2WegfopHc4WriYe+d1tyUzObJGZnJqX95x8/5s2zq5rLb0Wj/Tue6o23s91mLnQzMzD1t4fry0vkFn5+jMYgum9x04lL/45j1HgkW3+091s3Db/aXnbctXvvfjh63/2rh+JG/8hb/f9Ry9+mckyTX/7OkP+4+rfnfpzet3t9rOHaXrmq6N60fcPJM1r1Xo+liSF5ZSbs7s3/jLG9XLEly9qz5seqhzBGQ5ozUnqoW7px5x6sYjH1b9hKmlXoul3gE66R2OFo4/dPv6kelDM8tuy8LFx91GY7q916Vspx8m244RJruNzix2HTr7tfNaLzb6060ff+/Sp+UZj39k36Ot3fpnJMn/dtHjHvaahe1aOAK2ktsBzL+m29/fsP07AkvVJHTVWg8neVWLuli+Y42ALGe0ppvVnqLstnvqJw8eyM7rbstpp2zoK0wt9Vr0+sDrvCt1cvQU4ZZTN/bcVdePpbRl4bRQ5xTIE3uMGi08f7cP09U0fzPOXrsXFws68+avy2I3hVw4OnOs2wp022HXbSS5s/5eljJVtdTt/sdzGswUGycrN0fliGONgCxntGahpaxTOl7/KF+9q3bdrt55h+uFFgaMpV6LhSMHnXdw7jVFuHHdSDauHzlqJKvXnZ+76act/VzvXu91Jsd/Gq/X+13KmqPFPuB7fbVMt1tQ9DtKNF9nt9f081Ur8/1y1mkb8jv/5GcG+ncg7MDqEro4YueOkt++7rajphg7PySW+n1d3fS7Tul4rhVbzo0IFwaY5VyLxe7V022K8MDhmWzZvDGnjW446g7onTfOTGaDQmdgS2a3offTlk/d/rf5tx/46qrdfLNXqJqfsus1+vOyC7Y97Dp02rK5+2LyTksJn8v92pTlvGb+57M7pgQkWEuELo649LxtmbxrMh+8/f6jbiT46g/dmqt31ezcUfLmlz5tRVOD/a5TOp5rxZbz/Wm9ppCWcy2WEvru23cgt77xHx9V1m0dT2dbZjK7pqtVkHrhU8/Oe/9l99vTHOtrc7qFyM7wuth1fsbjH3nUtOG8jetGctUvdl9MvtBSp+eW+vtoZAnoJHRxlJ9/0lguv+Rne04DvvmlT+t7S3c3Swk8x+urMXrtnurl9E0beo5+LOcDdSnXYOuWzbnjnvvz/Gs+3/Xnx+u2B1/+D8/PY8ZWfpPcfq7RsRaD9zpH51ootzEBhoHQRVfHa6dirwXl3eLP8fpqjF67p3otWp9awWL2bnbuKHnth2/LoT5C3+TUvp6Bayke/6hT8/mdz1vxeY6HlY4GGU0ChoXQRVeD2qm4ULfpomNNMR0P3T6oV/K9aPdPH8zPvHHXwNrXj89c8eyce84ZXX/mmwUATjxCF10NYqdiL90Cz1LuN3S89LrP1OTUviY323z06aP5ypUvOO71ALA6hC66GsROxaVoMUV0+PBM3vKZb+b//st236V33auelWc84ZHN6gPgxCV00dVKdue19P0fP5hL33VT7n3goSb1jW3akFt/9x9n/bqRJvUBsHYIXfS0WguU33/L93Ll9V9rVt8H//WF+bknP7pZfQCcnIQujrs9+w/kjR//ej62e7JJfb903ra85WVPy+iG9U3qA4B+CF0syy3fuTf/+r9+JXv3H2xS33/59Wfmeec+pkldAHA8CF0kmV1k/v2fPJib73wg7xgfz6e/dvdxre9XnvnYXPlPnprTR/0KAnBy8Im3hj0wfTB//cP7U+/ek2/evTd17n/Ha9H5e371gvyvP3POcTk3AAw7oWuIzMzM5G/v2z8bnn4wG6Bmw9Se9PmNNovatmVztp0+kq2P3pK9+w/mF//B1jx/+9lGowBgAHyarrL9Bw7ljnvuPzIKNT8idfee/Ss+98b1I/nps8dSzhnLueeMpZxzRs49ZyyPGRvNyEj3Wx64kzkAHB9C13Fwz97pjtGoPUfC1PTBwys+91ljo7MBai5MlXPG8lOPOT2nnqIrAeBE5pO6DwcOHc53f/TAkVGob969N/UHe/L9H6/sewjn/fTZpx8ZhZoPU9u2bM46N+AEgDXjpA1dUw8+lHr33nzrB3uPWmS+d3rlt0DYcurGo0aizj1nLE85eyxnbNo4gJYDAMPopAxd/88t38sblnjH8yc++rQjQercuTD1uEeemg3r1x2nVgIAa8lJGbp+7smPyhMedWoeedops6NRZ88uMi/njOWRp52y2s0DANagkzJ0Pfms0/O5nc9b7WYAACcRc2MAAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA1sGNSJSikjSf5nkr+eK/pirfX1pZRfSPK7SQ4meV+t9b2DqhMAYFgMLHQleXKSr9Zaf2G+oJSyMcnbkjwzyQNJbiqlfKLWevcA6wUAOOENMnRdkGRbKeUvkuxL8uoko0m+XWv9SZKUUr6Q5NlJPjzAegEATnjLCl2llFdkNlR1ujzJm2utHy6lXJzk/XPH3NdxzN4kZx7r/NPT05mYmFhO01ih/fv3u/ZrgH4cfvpwbdCPw2+Qfbis0FVrvTbJtZ1lpZRTM7tuK7XWL5RStmU2ZI11HDaWZOpY5x8dHc327duX0zRWaGJiwrVfA/Tj8NOHa4N+HH799OH4+Hhf5xrk9OIbk9yb5A9KKU9PcmeSbyR5SinlkUnuT/KPkvzhAOsEABgKgwxdb0ny/lLKJZkd8fr1WuuBUsprkuzK7O0p3ldrnRxgnQAAQ2FgoWtusfwlXco/keQTg6oHAGAYuTkqAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQANCFwBAA0IXAEADQhcAQAMbVvLiUsovJfnlWutlc88vSvL2JAeT3FBrfVMpZV2Sdyd5epLpJK+stX57Zc0GABguyx7pKqW8PcmbF5zjPUkuS3JxkgtLKecnuTTJplrrs5K8Lsk1y28uAMBwWsn04s1JfmP+SSnljCSjtdY7aq0zSXYleX5mA9hnkqTWekuSZ6ygTgCAoXTM6cVSyiuSvHpB8ctrrR8qpTy3o+yMJHs6nu9N8qS58vs6yg+VUjbUWg/2qnN6ejoTExPHahrHwf79+137NUA/Dj99uDbox+E3yD48ZuiqtV6b5No+zrUnyVjH87EkU0lOXVC+brHAlSSjo6PZvn17H1UyaBMTE679GqAfh58+XBv04/Drpw/Hx8f7OtfAdi/WWvckeaiU8uRSykiSHUluTHJTkhcnRxba3z6oOgEAhsWKdi928aokH0iyPrO7F79USvmrJC8spdycZCTJywdcJwDACW9FoavW+rkkn+t4fkuSixYcczizYQwA4KTl5qgAAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANCF0AAA0IXQAADQhdAAANbFjJi0spv5Tkl2utl809f2mSq5N8f+6QNya5Mcm7kzw9yXSSV9Zav72SegEAhs2yQ1cp5e1JdiS5taP4/CS/VWv9SMdxL02yqdb6rFLKRUmuSfKS5dYLADCMVjK9eHOS31hQdkGSf1VKubGUck0pZUOSi5N8JklqrbckecYK6gQAGErHHOkqpbwiyasXFL+81vqhUspzF5T/9yTXJ/mbJO9J8qokZyS5r+OYQ6WUDbXWg73qnJ6ezsTERB/NZ9D279/v2q8B+nH46cO1QT8Ov0H24TFDV6312iTX9nm+99Vap5KklPLxJC/LbOAa6zhm3WKBK0lGR0ezffv2PqtkkCYmJlz7NUA/Dj99uDbox+HXTx+Oj4/3da6B7V4spYwk+f9KKX9vruj5ScaT3JTkxXPHXJTk9kHVCQAwLFa0e7FTrXWmlPLKJB8tpexL8o0k701yKMkLSyk3JxlJ8vJB1QkAMCxWFLpqrZ9L8rmO5zckuaHLoa9aST0AAMPOzVEBABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELp30uA0AAAGI0lEQVQAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGhC6AAAaELoAABoQugAAGtiwnBeVUs5M8v4kZyQ5Jclraq1fLKVclOTtSQ4muaHW+qZSyrok707y9CTTSV5Za/32QFq/DNfvnszVu2rumtqXrVs2Z+eOkkvP27ZazQEAThLLHel6TZL/UWt9TpJfT/KuufL3JLksycVJLiylnJ/k0iSbaq3PSvK6JNesqMUrcP3uybz+o7dncmpfZpJMTu3L6z96e67fPblaTQIAThLLDV1vS/JHc483JNlfSjkjyWit9Y5a60ySXUmen9kA9pkkqbXekuQZK2vy8l29q2bfgUNHle07cChX76qr1CIA4GRxzOnFUsorkrx6QfHLa61/VUo5J7PTjFdkdqpxT8cxe5M8aa78vo7yQ6WUDbXWg73qnJ6ezsTERJ9voX93Te3rWX486htG+/fvdy3WAP04/PTh2qAfh98g+/CYoavWem2SaxeWl1KeluTPkvz7Wuvn50a6xjoOGUsyleTUBeXrFgtcSTI6Oprt27f30fyl2brlbzPZJXht3bL5uNQ3jCYmJlyLNUA/Dj99uDbox+HXTx+Oj4/3da5lTS+WUp6a5MNJLqu1fjpJaq17kjxUSnlyKWUkyY4kNya5KcmL5153UZLbl1PnIOzcUbJ54/qjyjZvXJ+dO8oqtQgAOFksa/dikjcn2ZTk7aWUJLmv1vqSJK9K8oEk6zO7e/FLpZS/SvLCUsrNSUaSvHzlzV6e+V2Kdi8CAK0tK3TNBaxu5bckuWhB2eHMhrETwqXnbROyAIDm3BwVAKABoQsAoAGhCwCgAaELAKABoQsAoAGhCwCgAaELAKABoQsAoAGhCwCgAaELAKABoQsAoAGhCwCgAaELAKABoQsAoAGhCwCggZGZmZnVbsPDjI+P35Pke6vdDgCAPjz+ggsuOOtYB52QoQsAYK0xvQgA0IDQBQDQgNAFANCA0AUA0IDQBQDQgNAFANDAhtVuAKuvlHJmkvcnOSPJKUleU2v9YinloiRvT3IwyQ211jetYjPpUynll5L8cq31srnn+nGIlFLWJXl3kqcnmU7yylrrt1e3VfSrlHJhkt+vtT63lPJTSf4kyUySryW5vNZ6eDXbx+JKKRuTvC/JE5KMJvm9JN/IgPrRSBdJ8pok/6PW+pwkv57kXXPl70lyWZKLk1xYSjl/dZpHv0opb0/y5hz9t60fh8ulSTbVWp+V5HVJrlnl9tCnUspvJfnjJJvmit6a5Mpa67OTjCR5yWq1jb79apJ75/rsRUnemQH2o9BFkrwtyR/NPd6QZH8p5Ywko7XWO2qtM0l2JXn+ajWQvt2c5Dfmn+jHoXRxks8kSa31liTPWN3msAR3JHlpx/MLknx+7vGnk7ygeYtYqg8neUPH84MZYD+aXjzJlFJekeTVC4pfXmv9q1LKOZmdZrwis1ONezqO2ZvkSW1aybEs0o8fKqU8t6NMPw6fM5Lc1/H8UCllQ6314Go1iP7UWj9SSnlCR9HI3H/sJLN/e2e2bxVLUWu9P0lKKWNJrktyZZI/HFQ/Cl0nmVrrtUmuXVheSnlakj9L8u9rrZ+fGyEZ6zhkLMlUm1ZyLL36sYs90Y/DZmGfrRO4hlbnuh9/e0OilPLYJB9L8u5a6wdLKX/Q8eMV9aPpRVJKeWpmh1Qvq7V+OklqrXuSPFRKeXIpZSTJjiQ3rmIzWQb9OJRuSvLi5MgmiNtXtzmswO6OkecXxd/eCa+UcnaSG5L8dq31fXPFA+tHI10kswuvNyV5eyklSe6rtb4kyauSfCDJ+szuevvS6jWRFdCPw+VjSV5YSrk5s4t2X77K7WH5XpvkvaWUU5JMZHa6ihPb7yR5RJI3lFLm13b9ZpJ3DKIfR2ZmZo59FAAAK2J6EQCgAaELAKABoQsAoAGhCwCgAaELAKABoQsAoAGhCwCggf8fSEsj498Pl+4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ridge_mod = Ridge(alpha=0.5, normalize=True)\n",
    "ridge_mod.fit(rng.reshape(-1, 1), y_gen)\n",
    "ridge_model_pred = ridge_mod.predict(rng.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(rng, y_gen);\n",
    "plt.plot(rng, ridge_model_pred);\n",
    "print(\"Coefficient Estimate: \", ridge_mod.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient Estimate:  [1.06289489]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso_mod = Lasso(alpha=0.4, normalize=True)\n",
    "lasso_mod.fit(rng.reshape(-1, 1), y_gen)\n",
    "lasso_model_pred = lasso_mod.predict(rng.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(rng, y_gen);\n",
    "plt.plot(rng, lasso_model_pred);\n",
    "print(\"Coefficient Estimate: \", lasso_mod.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elastic Net Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import ElasticNet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient Estimate:  [0.74724704]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "en_mod = ElasticNet(alpha=0.02, normalize=True)\n",
    "en_mod.fit(rng.reshape(-1, 1), y_gen)\n",
    "en_model_pred = en_mod.predict(rng.reshape(-1,1))\n",
    "\n",
    "plt.figure(figsize=(10,8));\n",
    "plt.scatter(rng, y_gen);\n",
    "plt.plot(rng, en_model_pred);\n",
    "print(\"Coefficient Estimate: \", en_mod.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary\n",
    "\n",
    "[Question in StackExchange](https://stats.stackexchange.com/questions/866/when-should-i-use-lasso-vs-ridge)\n",
    "\n",
    "**When should I use Lasso, Ridge or Elastic Net?**\n",
    "\n",
    "* **Ridge regression** can't zero out coefficients; You either end up including all the coefficients in the model, or none of them. \n",
    "\n",
    "* **LASSO** does both parameter shrinkage and variable selection automatically. \n",
    "\n",
    "* If some of your covariates are highly correlated, you may want to look at the **Elastic Net** instead of the LASSO.\n",
    "\n",
    "# Other References\n",
    "\n",
    "1. [The Lasso Page](http://statweb.stanford.edu/~tibs/lasso.html)\n",
    "\n",
    "2. [A simple explanation of the Lasso and Least Angle Regression](http://statweb.stanford.edu/~tibs/lasso/simple.html)\n",
    "\n",
    "3. [The Elements of Statistical Learning](https://web.stanford.edu/~hastie/Papers/ESLII.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}