Overfitting_Demo_Ridge_Lasso.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Overfitting demo\n",
    "\n",
    "## Create a dataset based on a true sinusoidal relationship\n",
    "Let's look at a synthetic dataset consisting of 30 points drawn from the sinusoid $y = \\sin(4x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import graphlab\n",
    "import math\n",
    "import random\n",
    "import numpy\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create random values for x in interval [0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to amitha353@gmail.com and will expire on May 07, 2019.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: C:\\Users\\Amitha\\AppData\\Local\\Temp\\graphlab_server_1531821659.log.0\n"
     ]
    }
   ],
   "source": [
    "random.seed(98103)\n",
    "n = 30\n",
    "x = graphlab.SArray([random.random() for i in range(n)]).sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = x.apply(lambda x: math.sin(4*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add random Gaussian noise to y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.seed(1)\n",
    "e = graphlab.SArray([random.gauss(0,1.0/3.0) for i in range(n)])\n",
    "y = y + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Put data into an SFrame to manipulate later"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">X1</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">Y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0395789449501</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.587050191026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0415680996791</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.648655851372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0724319480801</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.307803309485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.150289044622</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.310748447417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.161334144502</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.237409625496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.191956312795</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.705017157224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.232833917145</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.461716676992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.259900980166</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.383260507851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.380145814869</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.06517691429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.432444723508</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.03184706949</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[30 rows x 2 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tX1\tfloat\n",
       "\tY\tfloat\n",
       "\n",
       "Rows: 30\n",
       "\n",
       "Data:\n",
       "+-----------------+----------------+\n",
       "|        X1       |       Y        |\n",
       "+-----------------+----------------+\n",
       "| 0.0395789449501 | 0.587050191026 |\n",
       "| 0.0415680996791 | 0.648655851372 |\n",
       "| 0.0724319480801 | 0.307803309485 |\n",
       "|  0.150289044622 | 0.310748447417 |\n",
       "|  0.161334144502 | 0.237409625496 |\n",
       "|  0.191956312795 | 0.705017157224 |\n",
       "|  0.232833917145 | 0.461716676992 |\n",
       "|  0.259900980166 | 0.383260507851 |\n",
       "|  0.380145814869 | 1.06517691429  |\n",
       "|  0.432444723508 | 1.03184706949  |\n",
       "+-----------------+----------------+\n",
       "[30 rows x 2 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = graphlab.SFrame({'X1':x,'Y':y})\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a function to plot the data, since we'll do it many times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d1091d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_data(data):    \n",
    "    plt.plot(data['X1'],data['Y'],'k.')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "\n",
    "plot_data(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define some useful polynomial regression functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function to create our features for a polynomial regression model of any degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def polynomial_features(data, deg):\n",
    "    data_copy=data.copy()\n",
    "    for i in range(1,deg):\n",
    "        data_copy['X'+str(i+1)]=data_copy['X'+str(i)]*data_copy['X1']\n",
    "    return data_copy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function to fit a polynomial linear regression model of degree \"deg\" to the data in \"data\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_regression(data, deg):\n",
    "    model = graphlab.linear_regression.create(polynomial_features(data,deg), \n",
    "                                              target='Y', l2_penalty=0.,l1_penalty=0.,\n",
    "                                              validation_set=None,verbose=False)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* l2_penalty and l1_penalty -> 0, standard mean square error "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function to plot data and predictions made, since we are going to use it many times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_poly_predictions(data, model):\n",
    "    plot_data(data)\n",
    "\n",
    "    # Get the degree of the polynomial\n",
    "    deg = len(model.coefficients['value'])-1\n",
    "    \n",
    "    # Create 200 points in the x axis and compute the predicted value for each point\n",
    "    x_pred = graphlab.SFrame({'X1':[i/200.0 for i in range(200)]})\n",
    "    y_pred = model.predict(polynomial_features(x_pred,deg))\n",
    "    \n",
    "    # plot predictions\n",
    "    plt.plot(x_pred['X1'], y_pred, 'g-', label='degree ' + str(deg) + ' fit')\n",
    "    plt.legend(loc='upper left')\n",
    "    plt.axis([0,1,-1.5,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a function that prints the polynomial coefficients in a pretty way :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def print_coefficients(model):    \n",
    "    # Get the degree of the polynomial\n",
    "    deg = len(model.coefficients['value'])-1\n",
    "\n",
    "    # Get learned parameters as a list\n",
    "    w = list(model.coefficients['value'])\n",
    "\n",
    "    # Numpy has a nifty function to print out polynomials in a pretty way\n",
    "    # (We'll use it, but it needs the parameters in the reverse order)\n",
    "    print 'Learned polynomial for degree ' + str(deg) + ':'\n",
    "    w.reverse()\n",
    "    print numpy.poly1d(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit a degree-2 polynomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit our degree-2 polynomial to the data generated above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = polynomial_regression(data, deg=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect learned parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 2:\n",
      "        2\n",
      "-5.129 x + 4.147 x + 0.07471\n"
     ]
    }
   ],
   "source": [
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Form and plot our predictions along a grid of x values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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j3wzaVG/jdUlFJpy7sEREQpLP5yM5ORmfz4eZ8dRVT/FG5ze4efzNzN4y2+vy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\nICIiEhAFiIiIBEQBIiIiAfn/frJ+U6mtnw4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d7d5358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Fit a degree-4 polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 4:\n",
      "       4         3         2\n",
      "23.87 x - 53.82 x + 35.23 x - 6.828 x + 0.7755\n"
     ]
    },
    {
     "data": {
      "image/png": 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6VouIhIf/6vxfVClfhR4TevDJrZ/QsW5Hr0sKmOTkZJKTk0tkWV6PgcQDw51z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\nFwWIiIj4RQEiIiJ++f+NJk2XA+gw5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d7e1208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = polynomial_regression(data, deg=4)\n",
    "print_coefficients(model)\n",
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit a degree-16 polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 16:\n",
      "           16             15             14             13\n",
      "2.583e+06 x  - 1.092e+07 x  + 1.443e+07 x  + 1.873e+06 x \n",
      "              12             11             10             9\n",
      " - 2.095e+07 x  + 1.295e+07 x  + 9.366e+06 x  - 1.232e+07 x\n",
      "              8             7             6             5             4\n",
      " - 2.544e+06 x + 1.181e+07 x - 9.325e+06 x + 3.887e+06 x - 9.666e+05 x\n",
      "              3             2\n",
      " + 1.441e+05 x - 1.215e+04 x + 506.6 x - 7.325\n"
     ]
    }
   ],
   "source": [
    "model = polynomial_regression(data, deg=16)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Woah!!!!  Those coefficients are *crazy*!  On the order of 10^6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mP8XwW4cXqMfkDYF64STle5dPxg9pP4TzzvNM3jzZ6tBs72zaWYqFFbPdPnL2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\n6mSGPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d7d55f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Above: Fit looks pretty wild, too.  Here's a clear example of how overfitting is associated with very large magnitude estimated coefficients."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Ridge Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ridge regression aims to avoid overfitting by adding a cost to the RSS term of standard least squares that depends on the 2-norm of the coefficients $\\|w\\|$.  The result is penalizing fits with large coefficients.  The strength of this penalty, and thus the fit vs. model complexity balance, is controled by a parameter lambda (here called \"L2_penalty\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define our function to solve the ridge objective for a polynomial regression model of any degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_ridge_regression(data, deg, l2_penalty):\n",
    "    model = graphlab.linear_regression.create(polynomial_features(data,deg), \n",
    "                                              target='Y', l2_penalty=l2_penalty,\n",
    "                                              validation_set=None,verbose=False)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform a ridge fit of a degree-16 polynomial using a *very* small penalty strength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 16:\n",
      "           16             15             14             13\n",
      "2.583e+06 x  - 1.092e+07 x  + 1.443e+07 x  + 1.873e+06 x \n",
      "              12             11             10             9\n",
      " - 2.095e+07 x  + 1.295e+07 x  + 9.366e+06 x  - 1.232e+07 x\n",
      "              8             7             6             5             4\n",
      " - 2.544e+06 x + 1.181e+07 x - 9.325e+06 x + 3.887e+06 x - 9.666e+05 x\n",
      "              3             2\n",
      " + 1.441e+05 x - 1.215e+04 x + 506.6 x - 7.325\n"
     ]
    }
   ],
   "source": [
    "model = polynomial_ridge_regression(data, deg=16, l2_penalty=1e-25)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mP8XwW4cXqMfkDYF64STle5dPxg9pP4TzzvNM3jzZ6tBs72zaWYqFFbPdPnL2\nisZHXOmBxFSM4WzaWUuuazBl8xTOpZ1jYNOBPm/7gkC9cJLyvcsn48uULsOoTqMYMn8IjlT9YXI1\njlQHpYqUsjqMKwRnAkkueAIREe6odQfzf5/v5agulZKewtAFQ3mv43uEhoT6tO2LBeqFk5Q1Lt8q\nvmW1lrSt3ZY3l3hki7uAZcf5DwjWBOJCDwR8O4x1YcuIEUtG0LxKc1pVb+WTdvMSqBdO8ieF3UbE\n7ka0HcH49ePZfmK71aHYliPVQWSE/T57mkAK4I7ad7Dg9wUsX77cqx/iC/MNcR3ieHPBm7wS+4rX\n2nJFoF44yR8EwxzUtSWvZWjrofxt7t/06oV5OJN6Roew7MLVBFIutBynj52mTXfvfohzFvY1z8Ak\nGc4f0svqBrtgmYN6psUz7D61m1k7Znmlfn/vxekQlk2kZ6RzJvWMS1tKJyYmkr4jnYwaGV79EMfE\nxFD/pvrQBOofq6/zDSpo5qAiQiN4v9P7/G3u3zjv9OwPp0DoxekQlk2cSD5BuWLlXDodLiYmhurO\n6kgd8eqHODIyknavteO++vex6udVOmSkgmoOqn2d9jSKasR/lv/Ho/UGQi/OkeanCUREnhGRa3wR\njC8cO3eMqJJR+Re8SGRkJIsmLKJ4g+IsTFjotQ/x8XPHmZQ0if92+29OG/7e9VaFF0xzUP9p/x/e\nWfkO+0/vz79wAQVCL86f50CigNUi8rWIdBQ/XzLq6vzHBbWialGvfD2STnvv18vby9+mR3SPnM0I\nA6HrrZQral9Tm6ebPc3z8573WJ2B0Iuz23WJLsg3gRhjXgGuA8YDjwE7ReSfIlLHy7F5hbsJBKBT\n3U7M2TXHwxFlOXbuGOPXj2do3NCcxwKh662Uq15s/SIrDqwgYU+Cx+r0916c3w5hQfbVRuBI9p8T\nuAb4RkRGejE2rzh67igVi7uXQO687k5m75zt4YiyjPxlJD1jelK1VNWcxwKh662Uq4qHF+e/Hf7L\ngFkDPD6h7q/89iwsEXlORNYCI4FfgBuMMU8CTYBuXo7P4wrTA2lRtQX7z+zn4JmDHo3p6NmjTFg/\ngRdbv3jJ44HQ9VbKHV0bdKVRVCPeWPyG1aHYgj/PgZQF7jPGdDDGTDPGpAMYYzKBzl6NzgsKk0DC\nQsLoUKeDx4exRv4ykl6NeuW6z7+/d72VcteoTqMYt24c6w6vszoUy/ntabzGmNeMMXvzeM71a59a\nrDAJBDxZs0bjAAAVT0lEQVQ/jHXYcZiJGyZe0ftQKthdW/Ja3m73Nn1n9CU9I93qcCzlt0NYgaaw\nCaRj3Y4s2L2Ac2nnPBLP/y37Px678TEqR1b2SH1KBZLejXtTsURF3l7+ttWhWMpveyCB5ti5Y1Qo\nUcHt15cvXp4WVVp4pBey7/Q+Jm+erL0PpfIgInzS+RPeXfkuG45ssDocy/jzHEhAOZ16mmuKFm5d\n5IPRD/JV0leFjuXNJW8yoMkAS6+3rpTd1ShTg3c7vMtD3z5Ecnqy1eFYQoewbMAY45EFOV0bdGXe\n7/MKdRGcXSd3MX3rdP73lv8tVCxKBYNejXrRpFITnpn9jNWhAL7dISLne0uHsKyVnJ5MkbAihIUU\n7lLwZYuVpXX11szcMdPtOt5Y/AbPtnjWpU0dlQpmH9/1MSsOrGDcunGWxuHrHSLOO88THhpOeGi4\nV9txR+G+Sf2MJ8cRe93Qi3Hrx9Hzhp4uv3bL8S3M/W0uH9z5gUdiUSoYRBaJ5LsHvyNuYhzRFaJp\nWa2lT9pNz0hn9aHVrDm0huT0ZP449AeJhxLJcP61O3dsbKzX2j+TesaWvQ+wQQ8ke3+tbSKyQ0SG\n5FHmfRHZKSIbRORGd9vyZALp1rAbW45vIemYa9uLGGMY/PNghrQaYstJMaXsrH75+nx272fc9/V9\n7Pxjp1fbOnL2CEPmDaHau9UYNHsQW45v4VTKKY6EHEH6CvKYUKdZHa/vEGHX+Q+wOIGISAjwAdAB\niAYeEpHrLyvTCahjjLkOGACMdrc9TyaQiNAIBjQZwAe/utaLmLljJnv+3MOg5oM8EodSwabTdZ14\nI/4NOk7u6NFdey84m3aWofOH0vDDhpx3nmfxY4tZN2AdozuPZkS7EXze/XOOv3icZzo8w7G7j7Ho\n0CKPx3Axu85/gPU9kObATmPM3uwV7lOBey4rcw8wCcAYswooLSKu7ceezdOnwg1oMoCpSVM5lXKq\nQOWT05P5n7n/w/sd3yciNMJjcSgVbPo36c/TzZ7mts9u81gSMcbwVeJXNPiwAQcdB9n05Cbe6/Qe\n9cvXv6JsmdJleK/He8x9ZC79ZvRj4e6FHokhN440h21HK6xOIFWAi//1D2Q/drUyB3MpUyCeTiCV\nIivRvUF33lr6VoHKvzDvBWKrxtKuTjuPxaBUsPp7y7/zTPNnuGXCLaw5tKZQdW06uom2n7fln8v+\nyZfdvmRS10mXbGyal6aVm/L1/V/z4DcPsvvU7kLFkJczqWdsO4QVcJPow4cPz7kdHx9PfHx8zn1v\nLMZ56463iP4omn439+P68tfnWe6nXT8xc8dMNg7c6NH2lQpmz8U+R/XS1ek0uROvx7/OwKYDXbra\n6GHHYYYtGsbMHTMZ1mYYA5sOdPkszfia8Tx/y/P0m9mP+Y/Mx9OXTPL0EFZCQgIJCQmeqcwYY9kf\nEAv8dNH9F4Ehl5UZDTx40f1tQFQe9ZmreX/l+2bQj4OuWsYd7yx/x9z+2e0mPSM91+cTjyaaqLej\nzKLdizzetlLKmC3HtpgWY1uYNhPbmGV7l+Vbft+f+8wLP79gyo4oa57/+XlzKuVUodpPz0g3zcc2\nN6NXjy5UPbkZs2aM6fdDP4/Xe0H296Zb3+FW90BWA3VFpAZwGOgBPHRZmRnA08BXIhIL/GmMOepO\nY97aDmBQ80HM2TWHJ2Y+wbi7x13yC2jHHzvoOLkj/2n/H+Jrxnu8baUUNKjQgF8e/4WJGybS67te\nVChegfsa3EfTyk2pVqoamSaTw2cPs/7wen7c+SMbjmzg0caPsvaJtdQsU7PQ7YeFhDG2y1jaf96e\nhxs9TMmIkoV/U9kcqfadA5GsBGRhACIdgffImo8Zb4z5l4gMICsrfpJd5gOgI3AO6GOMyXV/ZxEx\nV3s/L8x7gXLFyjGkda5nCxfKubRztP+iPeWKleOFVi8QGRHJnF1z+PfyfzOy3Ugev+lxj7eplLpS\nekY6i/cuZsb2GWw+tpkDZw4QFhJGheIVaBTViHa129G+TnuKhRfzeNs9vunBTdfe5NHvmNcWvYaI\nMDx+uMfqvJiIYIxxa9zN8gTiSfklkIGzBtI4qjFPNnvSK+2fSzvH+PXjGbN2DCESwg0Vb+Aft/2D\nOmX98uq/SikXbT2+lVs/vZVdz+7yWK/h73P/TpXIKgy+ZbBH6rtcYRKI1UNYPuXtHS1LRJTg2RbP\n8myLZ73WhlLKNxwOB4mJicTExBT4gm4NKjTgjtp3MHbtWI994Z9IPkGjqEYeqcvTrD6N16fsuiWy\nUspeCrPf1TPNn2H02tFkmkyPxHIi+QQVirt/CQpv0gSilFKXSUxMJCkpCafTmbPfVUG1rNqSEuEl\nWPD7Ao/Ecjz5eKGuYeRNQZdAShctbXUYSimbi4mJITo6mvDwcBo2bOjSflciwlPNnuKjNR/lPFaY\n7d+PnzuuPRA70B6IUqogIiMjWbp0KUuWLGHp0qUFngO5oOcNPUnYk8CRs0cKvf279kBsQhOIUqqg\nIiMjiY2NdTl5AJSMKEmXel34OunrQg2HJacnk5GZQYnwEi7H4AtBk0CMMbbeV18pFVh63tCTLxO/\nLNRw2InkE1QoUcHj26N4StAkkNSMVEIkhCJhRawORSllI966PO0dte7gt5O/cdx53O3hMDvPf0AQ\nJRAdvlJKXc6bl6cNDw3n/ob38+XmL90eDrPz/AdoAlFKBbHCzE8URI+YHny95Wu3X689EJvQBKKU\nulxh5icK4pZqt3DYcdjta4UcT9YEYgunz5/WBKKUukRhT9fNT2hIKHfXv5sftv/g1uuPnztO+eLl\nPRqTJwVNAtEeiFIqN4U5Xbcg7ql/D99v+96t1144C8uuNIEopZQXta3dlvVH1nMi+YTLr9UhLJvQ\nBKKUskKx8GK0rd2WWTtmufxaPQvLJjSBKKWs0qVeF/cSiJ6FZQ+aQJRSVulUtxPzfp9HWkaaS6/T\nHohNnE0769HrFCulVEFFlYyiQfkG/LT1pwKvej/550kcqQ5C00N9EKF7giaBJKcnUzy8uNVhKKWC\nVLsa7eg7om+BVr07HA7iOsSR4cjg1ja3enybFU8JmgSS4kzRBKKUssx15jpOlDtRoFXviYmJbN+/\nHZLxygp5TwmaBJKcnkyxsGJWh6GUClL3xt5LeJFwwq4Ny3fVe0xMDNVjqiPnxCsr5D0lzOoAfEWH\nsJRSVipVqhS9Y3tT7MZi/LPzP6+6cDEyMpKnhz3Nsh3LmDRqktcWORZW0PRAUpwpFAvXHohSyjpd\no7uyOXVzgRLCgXMHaN2gtW2TB1iYQETkGhH5WUS2i8hcEcn1YuUiskdENorIehH51d32tAeilLLa\n7bVuZ93hdZxKOZVv2Z0nd1K3bF0fROU+K3sgLwLzjTH1gYXA0DzKZQLxxpibjDHN3W0sJV0n0ZVS\n1ioWXoxba97K3N/m5lt218ldmkCu4h7gs+zbnwH35lFO8ECcOomulLKDztd1zndVujPTyZ4/91Cn\nbB0fReUeKxNIRWPMUQBjzBGgYh7lDDBPRFaLSH93G9MhLKWUHdxV7y7m7JqDM9OZZ5n9p/dTsURF\nioYV9WFkrvPqWVgiMg+IuvghshLCK7kUN3lU08oYc1hEKpCVSLYaY5bl1ebw4cNzbsfHxxMfHw/o\nOhCllD1ULVWV6qWrs/LASlpXb51rmV0nd3Fdueu80n5CQgIJCQkeqUuMyet727tEZCtZcxtHReRa\nYJExpkE+r3kNcBhj3snjeZPb+zHGEPaPMFJfSSUsJGjOXFZK2dSwhcNIz0znX23/levzH63+iI1H\nNjKmyxivxyIiGGPEnddaOYQ1A3gs+/ajwBWX7BKR4iJSMvt2CaA9kOhqQ2kZaYRKqCYPpZQtdK53\n9XkQf5hAB2sTyAignYhsB+4A/gUgIpVE5MKRjQKWich6YCUw0xjzs6sN6RoQpZSdNKvSjBPJJ/K8\nVvrOkzu9NoTlSZb9JDfGnATa5vL4YaBz9u3dwI2FbUsn0JVSdhIiIdx13V1M3zqdwbcMvuJ57YHY\niK4BUUrZzaM3PsqEDRO4fN726NmjHDl7hHrl6lkUWcEFRQLRNSBKKbuJqx5HekY6Kw+svOTxH7b/\nQMe6HYkIjbAosoILmgSiPRCllJ2ICP1u7se4deMuefz7bd/T9fquFkXlmqBIILoGRCllR70b92b6\ntukcPXsUyLr09rJ9y+hYt6PFkRVMUCSQ5PRkPQtLKWU715a8liebPsnjMx7HGMOcnXNoXb01pYqU\nsjq0AgmaBKI9EKWUHb0e/zrHzx3nril38eSPT9L3pr5Wh1RgQZFAUtJTdBJdKWVL4aHhTO0+leZV\nmrNx4Ea6NexmdUgFFhRLs7UHopSys9rX1GZ4/HCrw3BZcPRAdBJdKaU8LigSiK4DUUopzwuaBKI9\nEKWU8qygSCC6lYlSSnleUCQQXQeilFKeFxwJxKlDWEop+3E4HKxYsQKHw2F1KG4JigSi60CUUnbj\ncDiIi4ujTZs2xMXF+WUSCYoEopPoSim7SUxMJCkpCafTyZYtW0hKSrI6JJcFRQLRdSBKKbuJiYkh\nOjqa8PBwGjZsSHR0tNUhuSxoVqLrJLpSyk4iIyNZunQpSUlJREdHExkZaXVILguaBKI9EKWU3URG\nRhIbG2t1GG4LjiEsXQeilFIeFxQJRLcyUUopzwuaBKI9EKWU8qygSCApzhSdRFdKKQ+zLIGISHcR\nSRSRDBG5+SrlOorINhHZISJDXG0n02SS6kylaFjRwgWslFLqElb2QDYDXYHFeRUQkRDgA6ADEA08\nJCLXu9LIeed5ioYVJUSCorOllFI+Y9lpvMaY7QAiIlcp1hzYaYzZm112KnAPsK2g7egaEKWU8g67\n/yyvAuy/6P6B7McKTCfQlVLKO7zaAxGReUDUxQ8BBnjZGDPTG20OHz4853Z8fDyVYippAlFKqWwJ\nCQkkJCR4pC4xxnikIrcDEFkEDDbGrMvluVhguDGmY/b9FwFjjBmRR13m8vez/vB6+vzQhw0DN3g+\neKWU8nMigjHmalMJebLLEFZewa8G6opIDRGJAHoAM1ypWE/hVUop77DyNN57RWQ/EAvMEpE52Y9X\nEpFZAMaYDGAQ8DOQBEw1xmx1pZ0LZ2EppZTyLCvPwvoe+D6Xxw8DnS+6/xNQ3912Up2pFAkt4u7L\nlVJK5cEuQ1hek5qRSpEwTSBKKeVpgZ9AtAeilFJeEfAJJC0jjYjQCKvDUEqpgBPwCSQ1Q3sgSinl\nDYGfQJw6B6KUUt4Q+AlEeyBKKeUVgZ9AtAeilFJeEfgJRHsgSinlFYGfQLQHopRSXhH4CUR7IEop\n5RUBn0B0HYhSSnlHwCcQHcJSSinvCPwEokNYSinlFcGRQLQHopRSHhf4CUQ3U1RKKa8I/ASiPRCl\nlPKKwE8g2gNRSimvCPwEoj0QpZTyioBPIGkZadoDUUopLwj4BJLqTNWFhEop5QWBn0B0CEsppbwi\n8BOITqIrpZRXWJZARKS7iCSKSIaI3HyVcntEZKOIrBeRX11tR3sgSinlHVb2QDYDXYHF+ZTLBOKN\nMTcZY5q72kiw9kASEhKsDsEW9Dj8RY/FX/RYeIZlCcQYs90YsxOQfIoKhYgzWHsg+gHJosfhL3os\n/qLHwjP8YQ7EAPNEZLWI9Hf1xcHaA1FKKW8L82blIjIPiLr4IbISwsvGmJkFrKaVMeawiFQgK5Fs\nNcYsK8gLMzIzyDSZhIV49W0qpVRQEmOMtQGILAIGG2PWFaDsa4DDGPNOHs9b+2aUUsoPGWPym0rI\nlV1+mucavIgUB0KMMWdFpATQHng9r0rcPQhKKaVcZ+VpvPeKyH4gFpglInOyH68kIrOyi0UBy0Rk\nPbASmGmM+dmaiJVSSl3M8iEspZRS/skfzsK6hIh0FJFtIrJDRIbkUeZ9EdkpIhtE5EZfx+gr+R0L\nEemZvQhzo4gsE5EbrIjTFwry/yK7XDMRSReR+3wZny8V8DMSn704NzF7HjIgFeAzUkpEZmR/V2wW\nkccsCNMnRGS8iBwVkU1XKePad6cxxm/+yEp4u4AaQDiwAbj+sjKdgB+zb7cAVlodt4XHIhYonX27\nYzAfi4vKLQBmAfdZHbeF/y9KA0lAlez75a2O28JjMRT4vwvHAfgDCLM6di8dj9bAjcCmPJ53+bvT\n33ogzYGdxpi9xph0YCpwz2Vl7gEmARhjVgGlRSSKwJPvsTDGrDTGnM6+uxKo4uMYfaUg/y8AngG+\nAY75MjgfK8ix6Al8a4w5CGCMOeHjGH2lIMfCAJHZtyOBP4wxTh/G6DMma/nDqasUcfm7098SSBVg\n/0X3D3Dll+LlZQ7mUiYQFORYXKwfMMerEVkn32MhIpWBe40xH5P/7gf+rCD/L+oBZUVkUfYC3Ud8\nFp1vFeRYfAA0FJFDwEbgOR/FZkcuf3fa5TRe5UUichvQh6wubLD6L3DxGHggJ5H8hAE3A7cDJYAV\nIrLCGLPL2rAs0QFYb4y5XUTqkLVYuZEx5qzVgfkDf0sgB4HqF92vmv3Y5WWq5VMmEBTkWCAijYBP\ngI7GmKt1X/1ZQY5FU2CqiAhZY92dRCTdGDPDRzH6SkGOxQHghDHmPHBeRJYAjcmaLwgkBTkWfYD/\nAzDG/CYiu4HrgTU+idBeXP7u9LchrNVAXRGpISIRQA/g8i+AGUBvABGJBf40xhz1bZg+ke+xEJHq\nwLfAI8aY3yyI0VfyPRbGmNrZf7XImgd5KgCTBxTsM/ID0FpEQrMX67YAtvo4Tl8oyLHYC7QFyB7v\nrwf87tMofUvIu/ft8nenX/VAjDEZIjII+Jms5DfeGLNVRAZkPW0+McbMFpE7RWQXcI6sXxgBpyDH\nAhgGlAU+yv7lnW7c2BLf7gp4LC55ic+D9JECfka2ichcYBOQAXxijNliYdheUcD/F28Cn150ausL\nxpiTFoXsVSIyBYgHyonIPuA1IIJCfHfqQkKllFJu8bchLKWUUjahCUQppZRbNIEopZRyiyYQpZRS\nbtEEopRSyi2aQJRSSrlFE4hSSim3aAJRSinlFk0gSnmJiDTNvphXhIiUyL54U0Or41LKU3QlulJe\nJCJvAMWy//YbY0ZYHJJSHqMJRCkvEpFwsjb1SwFuMfqBUwFEh7CU8q7yQEmyrnZX1OJYlPIo7YEo\n5UUi8gPwJVALqGyMecbikJTyGL/azl0pf5J9qdg0Y8xUEQkBfhGReGNMgsWhKeUR2gNRSinlFp0D\nUUop5RZNIEoppdyiCUQppZRbNIEopZRyiyYQpZRSbtEEopRSyi2aQJRSSrlFE4hSSim3/D8F9LAz\n6mSGPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1da5dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform a ridge fit of a degree-16 polynomial using a very large penalty strength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 16:\n",
      "        16          15          14          13          12         11\n",
      "-0.301 x  - 0.2802 x  - 0.2604 x  - 0.2413 x  - 0.2229 x  - 0.205 x \n",
      "           10          9          8          7          6           5\n",
      " - 0.1874 x  - 0.1699 x - 0.1524 x - 0.1344 x - 0.1156 x - 0.09534 x\n",
      "            4           3           2\n",
      " - 0.07304 x - 0.04842 x - 0.02284 x - 0.002257 x + 0.6416\n"
     ]
    }
   ],
   "source": [
    "model = polynomial_ridge_regression(data, deg=16, l2_penalty=100)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1debd080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's look at fits for a sequence of increasing lambda values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lambda = 1.00e-25\n",
      "Learned polynomial for degree 16:\n",
      "           16             15             14             13\n",
      "2.583e+06 x  - 1.092e+07 x  + 1.443e+07 x  + 1.873e+06 x \n",
      "              12             11             10             9\n",
      " - 2.095e+07 x  + 1.295e+07 x  + 9.366e+06 x  - 1.232e+07 x\n",
      "              8             7             6             5             4\n",
      " - 2.544e+06 x + 1.181e+07 x - 9.325e+06 x + 3.887e+06 x - 9.666e+05 x\n",
      "              3             2\n",
      " + 1.441e+05 x - 1.215e+04 x + 506.6 x - 7.325\n",
      "\n",
      "\n",
      "lambda = 1.00e-10\n",
      "Learned polynomial for degree 16:\n",
      "           16             15             14             13\n",
      "4.975e+04 x  - 7.821e+04 x  - 2.265e+04 x  + 3.949e+04 x \n",
      "              12        11             10             9             8\n",
      " + 4.366e+04 x  + 3080 x  - 3.333e+04 x  - 2.785e+04 x + 1.032e+04 x\n",
      "              7        6             5             4        3         2\n",
      " + 2.962e+04 x - 1441 x - 2.597e+04 x + 1.839e+04 x - 5596 x + 866.1 x - 65.19 x + 2.159\n",
      "\n",
      "\n",
      "lambda = 1.00e-06\n",
      "Learned polynomial for degree 16:\n",
      "       16         15         14        13         12         11\n",
      "329.1 x  - 356.4 x  - 264.2 x  + 33.8 x  + 224.7 x  + 210.8 x \n",
      "          10         9       8         7         6         5         4\n",
      " + 49.62 x  - 122.4 x - 178 x - 79.13 x + 84.89 x + 144.9 x + 5.123 x\n",
      "          3         2\n",
      " - 156.9 x + 88.21 x - 14.82 x + 1.059\n",
      "\n",
      "\n",
      "lambda = 1.00e-03\n",
      "Learned polynomial for degree 16:\n",
      "       16         15         14         13         12          11\n",
      "6.364 x  - 1.596 x  - 4.807 x  - 4.778 x  - 2.776 x  + 0.1238 x \n",
      "          10         9         8         7          6         5\n",
      " + 2.977 x  + 4.926 x + 5.203 x + 3.248 x - 0.9291 x - 6.011 x\n",
      "          4         3         2\n",
      " - 8.395 x - 2.655 x + 9.861 x - 2.225 x + 0.5636\n",
      "\n",
      "\n",
      "lambda = 1.00e+02\n",
      "Learned polynomial for degree 16:\n",
      "        16          15          14          13          12         11\n",
      "-0.301 x  - 0.2802 x  - 0.2604 x  - 0.2413 x  - 0.2229 x  - 0.205 x \n",
      "           10          9          8          7          6           5\n",
      " - 0.1874 x  - 0.1699 x - 0.1524 x - 0.1344 x - 0.1156 x - 0.09534 x\n",
      "            4           3           2\n",
      " - 0.07304 x - 0.04842 x - 0.02284 x - 0.002257 x + 0.6416\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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9nA6nUIpiv1NB+Ou42l/YnpEdRjLkqyE2yNBPrAYSQlwuFx8t+IgvJ37J9ddf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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x34d2e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PH164ferUqdStW5cWLVowYMAAbrjhBm655RaPztODDz7IE088QaNGjXjuuec8qsOYYBFI\nLRAJpsFJEdHs3Gzq/KUOZx8+S2hIaMHrNWIQtm/fvtxxxx3cfPPNTofidzXl/9iYJTuWMPnLySTf\nkuyV+tx/Ox71EwddCyQ8NJyGtRrWiBtLLV26lIMHD5KXl8fMmTNZv349I0aMcDosY4wPBcql3CEI\nB9HB3Y11aj/No5o7HYpPbd68mWuvvZbMzEzatGnDf//7X2JiYpwOyxjjQzaN18eaRzV3jYMEd/5g\n4sSJTJw40ekwjDF+lJUbOGMgQdeFBa6pvNVlJpYxxlRGILVAgjKBtKzfkr0n9zodhjHGeF0gLSR0\nPIGIyOsiclBEvi9l+y9E5LiIrHH/PFJenXH149hzco/3gzXGGIcFUgskEMZAZgBTgVlllFmqqr+s\naIVx0XHM2TCn8Hl8fLytZg5yRS8BY0wwC6QxEMcTiKouE5Hy/vor9ekfVz+OPSd+aoHs3LnTg8iM\nMSbwBFILxPEurArqJyLrROQTEelcXuG4aFcXli0sM8YEG1sHUjnfAq1UNVNERgIfAe1LKzxp0iQA\n8pblMa/HPH45vMI9X8YYE/CycrOoE17H4/2Tk5NJTk72SiwBcSkTdxfWPFXtWoGyO4Aeqnq0hG1a\n8H4ueOUC3rzyTS4870Kvx2uMMU75w6I/cF698/hD/z94pb5guJSJUMo4h4jEFHncG1fSOyd5FFd8\nHMQYY4JBIF2N1/EuLBGZDSQBjUVkN/AYEIHrNovTgatF5A4gBzgDXFeRem0qrzEmGGXlBc46EMcT\niKpeX872l4CXKltvq+hW1gIxpgIyMjJITU2lS5cuREVFOR2OKUcgXc49ULqwvK5gJpYxpnQZGRkM\nGjSIwYMHM2jQIDIyMpwOyZQjkLqwgjeBWBeWMeVKTU0lLS2N3NxcNmzYQFpamtMhmXIE0jTe4E0g\n0XHsPrHb6TCMCWhdunQhMTGR8PBwOnfuTGJiotMhmXIE0kJCx8dAfKVl/ZakZ6STr/mESNDmSWOq\nJCoqipSUFNLS0khMTLQxkGogkC5lErSfrLXCatGgVgMOnDrgdCjGBLSoqCj69u1ryaOaCKQWSNAm\nEICEBgnsOLbD6TCMMcZrrAXiJ20atmHHcUsgxpjgEUjrQII+gWw/tt3pMIwxxmtsGq+fWAIxxgQb\nW0joJ5ZAjDHBJjsv21og/mAJxBgTbGwQ3U9io2I5nHmYs7lnnQ7FGGO8wqbx+kloSCitolux8/hO\np0MxxhivsBaIHyU0tLUgxpjgkK/55ObnEh4S7nQoQA1IIG0a2DiIMSY4ZOdlExEagYhHNxD0uuBP\nIDaQbowJElm5gbOIEGpKAjluCcQYU/0F0qXcoQYkkLaN2rL1yFanwzBBKCMjg+XLl9tNmIzfBNIM\nLKgBCaR94/b8cOwH8vLznA7FBBG7k59xQiDNwIIakEDqhNchpm6MTeU1XmV38jNOsBaIAzo06cDm\nI5udDsMEEbuTn3GCtUAc0LFxRzYd3uR0GMZHnBiLKLiT39KlS0lJSbGbMRm/sBaIAzo06cDmw9YC\nCUZOjkXYnfyMv2XmZFInvI7TYRRyPIGIyOsiclBEvi+jzBQR2Soi60Tkwsoeo2OTjmw6Yi2QYOSt\nsQibUWWqgzM5Z6gdXtvpMAqFOR0AMAOYCswqaaOIjATaqmo7EekDTAP6VuYAHZtYF1awKhiL2LBh\nA507dya2bSwr9q5g5/GdHMk8wqnsU4RICPUi6tGyfktaRbcivkE8DWo1KKyjoBWTlpZGYmKidUmZ\ngBVoLRDHE4iqLhOR+DKKXI47uajqShGJFpEYVT1Y0WM0r9ecMzlnOHbmGA1rN6xqyCaAhNcO59FZ\njzL7m9mszVhLp1c70alpJ1o3aE3TOk2pG14XgG1HtzFvyzz2nNzDzuM7aVm/JYNaDWJw/GAaHWt0\nTiumb99KfUcxxi/O5J6xBFJJscCeIs/3uV+rcAIRkcKZWH1b2gdDMFi7fy0vrHyBDzd9yAXNLmBM\n+zE82u5REpsmEhoSWua+efl5fH/we1J2p/Dhpg/5fPvn1J5Qm8yVmXQI6WAzqkzAyszJpHaYdWH5\nzKRJkwofJyUlkZSUBECHxh3YdHiTJZBqTFWZu3kuf1/+d3Ye38mdve5k293baFq3aaXqCQ0J5aLm\nF3FR84u4p889nM4+zbvfvcsbF7xB2sk0Hv3qUe7pcw8JDRN89E6M8Yw3urCSk5NJTk72Sjyiql6p\nqEpBuLqw5qlq1xK2TQOWqOq77uebgF+U1IUlIlra+3k65WmOnjnK34b9zbvBG79YsXcFf1j0BzKy\nM3hk0CNc2elKwkK8//1n94ndvLjqRV5f+zpDEobw58F/pmvMOb+WxjjiqaVPkZmTyVOXPOW1OkUE\nVfXo8r6Oz8JyE/dPSeYCNwGISF/geGXGPwp0jenKdwe/8zxC44j0jHSue/86rp5zNRO6T2DNb9dw\nTeI1PkkeAK2iW/Hs0GfZee9O+rXsx7A3hzHu/XHlTsJwahaXv45rs9QCQ6ANojueQERkNvA10F5E\ndovIrSJym4j8FkBVFwA7RGQb8C/gd54cp9t53SyBVCOqysx1M7lw2oW0b9SeLXdv4ZYLbyl3fMNb\noiKj+H2/37Ptnm1ceN6FDJ4xmAlzJ3Dg1IFzyjq1FsVfx7XrfgWOM7mBNY3X8QSiqteragtVjVTV\nVqo6Q1X/parTi5S5S1XPV9VuqrrGk+PERsWSm5/LwVOVbrwYP0vPSGf026N5fsXzfHbDZzwx5AnH\nvnXVi6jHgwMfZOvdW2lYqyFdXu7C0ylPczb3bGEZp66L5a/j2nW/Aoe1QBwiItaNVQ0s+mERPab3\noGfznqyauIqLml/kdEgARNeK5m/D/saKCStYnb6aTi914r2091DVEq+L5Y8uH39dj8uu+xU4Ai2B\nBMQgureUNYgOcN/C+2hZvyV/6P8HP0ZlKiI3P5dJyZOYsW4Gb131Fkmtk5wOqUxLdizh/332/4iK\njOKfw/9J+6j2hQsRAb8tTMzIyCg8ji8XP/rrOKZs17x3Ddd2vpZrEq/xWp3BMIjuF91ibBwkEB07\nc4zh/xnOyn0rWfPbNQGfPAAuTriYb3/7LTd3u5nRb4/mrs/vIq5zHFFRUX7t8vHX9bjsul+BIdBa\nIDUqgXSN6cp3ByyBBJKdx3cy4I0BdIvpxsJfLySmXozTIVVYaEgoE7pPYPNdm4mNiqXrtK5MTp5M\nQocE6/IxPhFo18KqUQkksVkiW49uJTsv2+lQDLB632r6v96fO3rewXPDn/PbDCtvqx9Zn79c8hfW\n/HYNm45sotfMXtzxrztY8uUSu66W8SprgTioVlgtzm90PusPrnc6lBpv7ua5jJo9ildGvcLdfe52\nOhyviG8Qz9tj32bO1XOYmTqT29bexqI9i8jXfKdDM0Ei0BJI0F3KpDx9Yvuwct9KerTo4XQoNdbU\nlVN5etnTfHL9J/SK7eV0OF7XL64fX43/ik+3fcqfl/yZJ1Oe5JFBj3BFxysCppWVr/nsO7mP7ce2\ns/3Ydvaf2s+p7FPkaz6RoZE0q9uM+AbxdI3pSlz9OEQ8GmM1XnYm90xAXQurRs3CAnj121dJ2Z3C\nrCtLvHq88aG8/Dz+uPiPLNy2kE+u/6RGXGtKVfl488c8+9WzHDh1gHv73Mv4i8YTFenfbq1T2adY\nuXcly3Yv46s9X7Fy30rqhtelTcM2tG3Ulhb1WlAvoh4hEsLZ3LMcOn2I7ce3s+7AOiJDIxl5/khu\n6HoDA1sNtGTioNjnYlk1YRWx9WO9VmdVZmHVuATy/cHvuea9a9h8l92h0J8yczK54YMbOHrmKB9e\n92GNvKz+8j3LeX7F8yzevpgx7cdwQ9cbGJIwxCeXZUnPSOer3V8VJoyNhzdy0XkXMSBuAANaDaB/\nXH+a1GlSbj2qysbDG5m/ZT4zv5tJvubz0MCHuP6C6312ORlTukbPNGLbPdtoVLuR1+q0BOJWkQSS\nl59Hg2casOu+XV79TzClO3T6EL98+5e0a9yO18a8RmRY4NzT2QkHTh3g3dR3eWv9W+w5uYdhbYcx\npPUQhiQMIS46rtL1nck5w9oDa1m9bzWr01fz9Z6vOZF1wpUs4gYwsNVAerToQa2wWoBrTUdqaipd\nunSp1AC/qvL5js+Z/OVkTpw9wcujXmZgq4GVjtd4rtaTtTj+4PHC/0tvsATiVpEEAnDxzIt5YMAD\njDh/hB+iqtk2H97MZbMv4/ou1/P4xY9b90cxPxz9gcXbF/PFji9YsnMJ4SHhdGjSgfaN2tOmYRui\nIqOoF1GPOuF1OJNzhpNZJzmRdYL0jHS2Hd3G1qNbSc9Ip3PTzvRq0YteLXrRP64/HZp0IETOnSPj\njbsvqirvbXiP33/2e65NvJanL3m6xn8p8Ie8/DzCnwgn79E8r/4dWQJxq2gCefB/D1I7rDaPJT3m\nh6hqrpRdKVz93tU8fcnTjL9ovNPhBLyCge3NRzaz5cgWdhzbQUZ2BqdzTpOZk0mtsFpER0YTHRlN\nTL0Y2jVqR7vG7WjdoDURoREVOsby5csZPHgwubm5hIeHs3TpUo/vvngk8wgT501k14ldfDzuY1rW\nb+lRPaZiTmefptnfm3H6T6e9Wm9VEkiN7MTsE9uH6Wuml1+wGvG0W8JX3l7/NvcuvJe3rnqLoW2H\nOh1OtRAiIcRFxxEXHcelbS71yTGK30O+KoscG9dpzH+v/S9/+/pv9HmtD3PHzbXZjT4UaFN4oYat\nAykwoNUAvt7zNbn5uU6H4hWBdLltVeXplKd54H8P8PlNn1vyCDBRUVGkpKSwdOlSryxyFBHuH3A/\nL132EiPfGknKrhQvRWqKC7Tb2UINTSDN6jYjPjqeb9K/cToUrwiUy23n5OVw2/zbmLNhDismrOCC\nmAscicOUzRfXtbqi4xXMHjubsXPGWhLxkTO5Z6wFEiguSbiEL3Z84XQYXhEIl9s+cfYEY94ew96T\ne1l6y1JaRLXwewzGWZe2ubQwiQTLl7NAkpmTGVDXwYIanECGJAxh0dZFQXGbTm93S1TW9mPb6fd6\nP9o2bMvcX831+yI5pwTrbV6r8r4ubXMp08dMZ8zbY9hxbIcPoqu5zuRYCyRgXNT4IlJ2pDDo4kGO\njxt4g1OX2166ayn9X+/Pnb3u5KVRL9WYxWWBNO7kTd54X1d0vII/DfwTo98ezYmzJ3wQZc1kg+gB\nZM/WPeQfyCevRZ7dptNDM9bO4Oo5VzPrylnc2ftOp8Pxq0AZd/I2b72vu/vcTVJ8Ejd/dDPBtFTA\nSTaIHkC6dOlCs1PNCGkXYvdsqKTc/Fz+uOiPPJXyFEtvXcqwtsOcDsnvAmHcyRe8+b6eH/E86Rnp\n/HPFP70YYc0ViIPoNaO/oQRRUVHMeHAG4+ePZ8GtCwJi7UR1cODUAX71318RFhLGygkraVynsdMh\nOaJg3CnYbvPqzfcVERrBu1e/S5/X+tA/rj99WvbxYqQ1jw2iB5CMjAweuvkhDh49yJDrhgRNH7Yv\nLd21lJ7TezK41WAW/nphjU0eBYL1Nq/efF8JDROYPmY6171/HUfPHPVCdDXXmZwz1AkLrBZIjU0g\nqampbEjbAJtga+jWoOnD9oXc/Fwe//JxrnnvGl775WtMvnhywNzXwgS+KzpewZUdr2T8x+NtPKQK\nrAVSAhEZISKbRGSLiDxQwvZfiMhxEVnj/nnEG8ct6OsN3RpKZLfIoOnD9ratR7Yy8I2BLNu9jDW/\nXWMXoDQeeWboM2w/tp231r/ldCjVls3CKkZEQoAXgeFAIvArEelYQtGlqtrd/fOkN45d0Neb/O9k\narWoxbH8Y96oNmjk5efx0qqX6P9Gf359wa9ZeMNCr97ExtQsEaERzLh8Br//7Pfsz9jvdDjVUiAO\nojvdAukNbFXVXaqaA7wDXF5COZ9cAzwqKoqB/QdyXeJ1zFw30xeHqJa+Tf+Wvq/35d20d1l6y1Lu\n7nN3iZcGN6YyerTowW09buP2T263riwP2DTec8UCe4o83+t+rbh+IrJORD4Rkc7eDuI33X/DG+ve\nIF/zvV11tfLj6R+5a8FdjJo9ijt73cmXt3xJp6adnA7LBABvrbp/ZPAjbD+2ndnrZ3spspojEFei\nV4dpvN/yAspOAAAY3ElEQVQCrVQ1U0RGAh8B7UsrPGnSpMLHSUlJJCUllXuAHs17UD+yPkt2LOGS\nNpdUOeDqJiMrg+eWP8eUVVO4vsv1pP0urcbPsDI/8cZNqApEhkXy78v/zWWzL+PSNpcSUy/Gy9EG\nr8xc7wyiJycnk5ycXPWAcPiGUiLSF5ikqiPczx8EVFWfKWOfHUAPVT1nTmBFbyhVkikrp7Bi7wpm\nj60534yOZB5hytdTeHH1iwxtO5S/DP0LbRq2cTosE2C8eROqAvcvvp8Dpw4w68pZXooy+F357pXc\n2PVGrup0lVfrrcoNpZzuwloNnC8i8SISAYwD5hYtICIxRR73xpX0vD6h/MauN/LZD5+x6/gub1cd\ncDYd3sTvPvkd5085n6mzp3Ji6gk2/WUTTcOaOh2aCUC+WHX/6C8eJXlnMl/u/NILEdYMgdiF5WgC\nUdU84C5gEZAGvKOqG0XkNhH5rbvY1SKSKiJrgX8C1/kiloa1GzKx+0T+9vXffFG9446eOcrLq1+m\nz2t9uHjmxTSu3Zg3+75JxpsZ5O2364GZ0vnias/1Iurx/PDn+d2C35GTl+OFKINfIA6i18h7opfm\n4KmDdHqpE2m/S6N5VHMvRuaM7ce2M2/zPOZumcvqfasZ1X4UN3W9iaFthxIWElbYt11we1MnLgVv\napait16uV68el82+jCGth/DHAX90OrSA1+vVXrx82cv0iu3l1Xqr0oVlCaSY+xbeR05eDi+NeslL\nUfnHqexTfJv+Lav2rWLlvpWs2reK7LxsRrUbxZgOYxjaZih1I+qes19GRkbQXc/JBKaSBuMP5hyk\n72t9WXvbWuKi45wOMaAlvpzIu1e/S5dmXbxaryUQN28kkKNnjtL5pc7Mv34+PVv09FJk3pWbn0vq\noVRW7VtVmDC2H9tO15iu9IntQ+/Y3vSO7U3bhm0RqfoSmqLfGi3JGE+VNhg/KXkSqYdSef/a950O\nMaAlvJDA5zd97vWJLlVJINVhGq9fNardiGeHPstt829j1YRVjl/zSVXZdWIXK/e6WhWr0lexdv9a\nWkW3ondsb/rE9uGOnndwQcwFRIRGeP343pzCaWq2gsH4gi7TgsH4BwY8wAWvXMDCbQvtUjllOJ19\nmrrh5/YiOMlaICVQVYb/Zzjdm3fnr5f+1QuRVdzZ3LN8m/4tX+35iq/2fMXyPcsJCwmjT8s+9G7h\naln0bNGT6FrRfonHF1M4Tc1VWpfpp1s/5e5P7yb1d6nUCqvlYISBq9aTtTj+4HGvnx/rwnLzVgIB\nOJx5mF6v9uKZS5/h2sRrvVJnSbLzslmxdwWLfljEkp1LWHdgHZ2adGJA3AAGtBpAv5b9aFm/pVe6\nojxhA+3GX8bOGUu3mG48+otHnQ4l4GTlZhH1dBRZj2R5/bPAEoibNxMIwNr9axn+n+FMGz3Nq4t3\nfjj6Awu3LeSzHz7jy11f0r5xe4a1GcaQhCF0ju7Mzi07A2q8wQbanVVTxqB2n9hN9391Z/XE1SQ0\nTHA6nIByOPMwHV/syOH7D3u9bksgbt5OIOBKIqNmj+LO7nfyi8hf0O2CbpX+I87KzWLprqUs2LqA\nBdsWcDLrJCPOH8HwtsO5JOESmtZ1LeCz8QZTXE37nXhq6VOsTl/NR+M+cjqUgLL92HYunXUp2+/d\n7vW6LYG4+SKBAHy/53v6P9Of01mnSdiVwNr31xJdv/QxiHzNZ9PhTaTsSuHTbZ+yZOcSEpsmclm7\ny7is3WVceN6FJV7d1sYbTHE17XfibO5ZurzchakjpzKy3Uiv1VvdW3HrDqzjlo9uYd3t67xet83C\n8rHTe09z9l9nIRF29N9Bx1c6MqLjCLo07UKTOk1QlJNZJ9l5fGfh9NomdZrQL64f1yZey2u/fI0m\ndZqUe5zSZqmYmqum/U7UCqvFlJFTuGfhPaQmpBIZFlnlOoOhFXcy6yT1I+s7HcY5rAVSAUUHkjt1\n7sT0D6ez9shaNh/ezOEzhwmREKIiooiPjqdT0070ie1T2C3lybFsvMEUVRN/Jy5/53J6t+jNw4Mf\nrnJdwdCKm79lPtO+mcb86+d7vW6fdmGJyN3Af1Q14G/Z56sEAs79EVf3prcxnthxbAc9X+3Jmt+u\nIb5BfJXqCoaZhLPXz2b+lvk+uVq4r6/GGwOsFpE57vuXOzOf1GFRUVH07dvX78lj0KBBDB48mEGD\nBlX5Zj7GVBcJDRO4p/c9/H7R76tcly8uBulvgdqFVW4CUdVHgHbA68AtwFYR+YuItPVxbDVeamoq\naWlp5Obm2tVyTY1z/4D7WXdgHQu2LqhyXU58AfSmaptAwHWHJ+CA+ycXaAi8LyLP+jC2Gs8X92Ew\nprqoHV6baaOmcccnd3Aq+5TT4Tiq2iYQEblXRL4FngW+Ai5Q1TuAHsBYH8dXowVD09uYqhjadigX\nt76YR754xOlQHFVtEwjQCLhKVYer6nuqmgOgqvnAaJ9GZ6p909uYqvrHsH/wbtq7rNy70ulQHFNt\nE4iqPqaqJd7nVVU3ej8kY4z5SeM6jXlu2HNMmDeB7Lxsp8NxRLVNIMYY47RxXcbRKroVTy19yulQ\nHGEJxBhjPCQivDrmVf717b9I2ZXidDh+ZwnEGGOqoEVUC17/5evc8OENHD1z1Olw/MoSiDHGVNGo\n9qO4suOVTJw3EScvw5SRkcHy5cv9trjXEogxxnjBM5c+w/Zj2/nXt/9y5PhOXCEiUBOIXY3XGFOt\nRIZF8s7Ydxg0YxBdY7rSP66/z495MuskX+78kvSMdH7Y/gOpP6aSl5dXeIUIX16cMS8/jzO5ZwLu\nfugQAC0Q9/W1NonIFhF5oJQyU0Rkq4isE5EL/R2jMSawdGjSgZlXzGTsnLHsOLbDZ8f5es/XXPXu\nVcQ+F8uUVVP4dv+37A/ZT+j1oXAntBrUyudXiMjIziAqIsqx21qXxdEEIiIhwIvAcCAR+JWIdCxW\nZiTQVlXbAbcB0/weqDEm4IxsN5KHBz3MsP8MIz0j3at17zq+i7FzxnL9f69nSMIQ9v/ffhbfuJjp\nY6bz5tVvcvjRwzx96dOcvewsr3z/ilePXVygdl+B8y2Q3sBWVd3lXuH+DnB5sTKXA7MAVHUlEC0i\nMf4N0xgTiO7qfRfjLxzPJbMu8UoSOZNzhse/fJzu07vTLaYbG+/cyF2976JeRL2flYuKiuLByx9k\n5cSVTP92OlNXTq3ysUsTyAnE6TGQWGBPked7cSWVssrsc7920LehGWOqg4cGPQRAv9f7Mf9X87kg\n5oJK16GqzN08l/s+u48ezXtU+D4ksfVj+fymz+n3ej+6ndeNwfGDK33s8lgC8aNJkyYVPk5KSiIp\nKcmxWIwx/vHQoIeIbxDPxTMv5ulLnmZC9wkVHjPYcmQL9y28jx3HdzB99HSGth1aqWPHN4hn2uhp\njP94PN/d/h11I7w72O3tBJKcnExycrJX6nL0lrYi0heYpKoj3M8fxHX1+GeKlJkGLFHVd93PNwG/\nUNVzWiC+vCOhMSbwpR5K5cYPb6RBrQY8cfETDGw1sMRyqsraA2v554p/smDrAh4Y8AD39r2XiNAI\nj49944c30qxOM/4x/B8e11GSOWlzeH/D+8y5Zo5X6y1QlTsSOt0CWQ2cLyLxwH5gHPCrYmXmAncC\n77oTzvGSkocxxnRp1oVVE1bx5vdvctOHNxEZFsmodqPo0LgD9SPrcyLrBN8f/J4vdnzB2dyzTOg+\ngSkjp9CgVoMqH/sfw/5Bp5c6cV/f+4iLjvPCu3E5mXWSqIjAvBq3oy0QcE3jBV7ANaD/uqr+VURu\nw9USme4u8yIwAjgN3Kqqa0qpy1ogxhgA8jWfb9K/YfEPi/nh2A9kZGdQP6I+ic0SGRA3gN6xvb0+\nNfaBxQ9wMuskr4z23sys55Y/x54Te3h+xPNeq7OoqrRAHE8g3mQJxBjjpMOZh+nwYocKD8JXxKTk\nSagqky+e7JX6iqtKAnF6Gq8xxgQkT6531aROE8ZfOJ6pq7w3rTeQZ2FZAjHGmGKqcr2r23vezszv\nZnI296xXYjmceZgmdZp4pS5vswRijDHFpKamkpaWRm5ubuH1riqqbaO29Gjeg/fS3vNKLIdOH6JZ\n3WZeqcvbLIEYY0wxXbp0ITExkfDwcDp37lzp613d0fMOpn3701WXqnL5d0sgxhhTjURFRZGSksLS\npUtJSUkhKqpy02hHtR/FjmM72HR4U5Uv//5j5o80rdu0Uvv4iyUQY4wpQVRUFH379q108gAICwnj\nusTreCf1nSp1h6kqh04fomkdSyDGGFNjjOsyjrdT3yYxMdHj7rCTWSeJDI2kdnhtH0bqOadXohtj\njKMyMjJITU2lS5cuHrU2StM7tje5+blsO72NlJQU0tLSSExMrNQxfsz8MWDHP8BaIMaYGsyXt6cV\nEcYljuPt9W973B126PShgB3/AEsgxpgarCrjExVxTeI1fLjpQzy9QkYgz8ACSyDGmBqsqtN1y9Mt\nphtZeVlsPrLZo/1/PP0jzeoEbgKxMRBjTI1VMF3Xk/GJihARRrcbzbzN8+jYpGP5OxRjXVjGGBPA\nqjJdtyJGtx/N/K3zPdrXurCMMaYGG5IwhLX713L0zNFK73so0xKIMcbUWLXDa5PUOomF2xZWet8f\nT/8YsIsIwRKIMcb43Jj2Y5i3ZV6l97MuLGOMqeFGtR/FZ9s+Iycvp1L7WQIxxpgarkVUC9o0bMPi\nzYsrfFXeEydPcDjzMJF5kX6I0DOWQIwxxg+Gxg/llr/cUqFV7xkZGQy4dAB5mXkMSRri1RXy3mQJ\nxBhj/KA97fmx0Y8VWvWemprKpt2b4DQ+WSHvLZZAjDHGD8b2G0tYnTDCmoWVu+q9S5cuxHeJR06L\nT1bIe4t4eo2WQCQiGkzvxxgTXG56/yaa5DVh8mWTy124OOWrKSzeuJjZ18322SJHcK2WV1XxZF9r\ngRhjjJ9c3vlyNuRsqFBC2H16NwM7DvRp8qgqxxKIiDQUkUUisllEPhOR6FLK7RSR70RkrYis8nec\nxhjjLZe2uZSv9nxFZk5muWW3Ht1Ku8bt/BCV55xsgTwI/E9VOwBfAA+VUi4fSFLVi1S1t9+iM8YY\nL4uuFU3PFj1ZsmNJuWW3HNlC+8bt/RCV55xMIJcDM92PZwJXlFJOsK42Y0yQGHn+SD7Z+kmZZfLy\n89hxbAdtG7b1U1SecfKDuZmqHgRQ1QNAacstFVgsIqtFZKLfojPGGB8Y3X4087fML/MmU7tO7CKm\nXkzA3gu9gE/vByIii4GYoi/hSgiPlFC8tLM5QFX3i0hTXIlko6ouK+2YkyZNKnyclJREUlJSZcM2\nxhif6dSkE7XCarFm/xp6tOhRYpmtR7bSrpFvxj+Sk5NJTk72Sl2OTeMVkY24xjYOish5wBJV7VTO\nPo8BGar6XCnbbRqvMSbg3b/4fiJDI3liyBMlbp+6ciobD2/k5VEv+zyW6jqNdy5wi/vxzcDHxQuI\nSB0Rqed+XBcYBqT6K0BjjPGFKzpewUebPyp1+9ajvmuBeJOTCeQZYKiIbAYuAf4KICLNRaTg9l0x\nwDIRWQusAOap6iJHojXGGC/pE9uHH0//yLaj20rcXh1mYIGtRDfGGEfcPv92WkW34k+D/nTOtoQX\nEvjshs/8kkSqaxeWMcbUWOMvGs/ra18nX/N/9vq2o9s4m3uW8xud71BkFWcJxBhjHNCrRS/qRdTj\nix1f/Oz1Dzd+yOUdLidEAv/jOfAjNMaYICQiTOw+kVfXvPqz1z/Y9AFXdbrKoagqxxKIMcY45Iau\nN7Doh0VsPbIVgPSMdDYf3kxS6yRnA6sgSyDGGOOQBrUa8OTFTzLuv+PIys3ize/eZFT7UUSERjgd\nWoXYLCxjjHGQqjJ2zlhW7VtF7fDavDP2nVJXqPtCVWZhWQIxxhiHnTh7gpTdKYw8fyShIaF+PbYl\nEDdLIMYYUzm2DsQYY4zfWQIxxhjjEUsgxhhjPGIJxBhjjEcsgRhjjPGIJRBjjHFIRkYGy5cvJyMj\nw+lQPGIJxBhjHJCRkcGgQYMYPHgwgwYNqpZJxBKIMcY4IDU1lbS0NHJzc9mwYQNpaWlOh1RplkCM\nMcYBXbp0ITExkfDwcDp37kxiYqLTIVWarUQ3xhiHZGRkkJaWRmJiIlFRUY7EYJcycbMEYowxlWOX\nMjHGGON3lkCMMcZ4xBKIMcYYj1gCMcYY4xHHEoiIXC0iqSKSJyLdyyg3QkQ2icgWEXnAnzEaY4wp\nnZMtkPXAlcCXpRUQkRDgRWA4kAj8SkQ6+ic8Y4wxZQlz6sCquhlARMqaPtYb2Kqqu9xl3wEuBzb5\nPkJjjDFlCfQxkFhgT5Hne92vGWOMcZhPWyAishiIKfoSoMDDqjrPF8ecNGlS4eOkpCSSkpJ8cRhj\njKmWkpOTSU5O9kpdjq9EF5ElwP+p6poStvUFJqnqCPfzBwFV1WdKqctWohtjTCUEw0r00oJfDZwv\nIvEiEgGMA+b6LyxjjDGlcXIa7xUisgfoC8wXkU/drzcXkfkAqpoH3AUsAtKAd1R1o1MxG2OM+Ynj\nXVjeZF1YxhhTOcHQhWWMMaaasQRijDHGI5ZAjDHGeMQSiDHGGI9YAjHGGOMRSyDGGGM8YgnEGGOM\nRyyBGGOM8YglEGOMMR6xBGKMMcYjlkCMMcZ4xBKIMcYYj1gCMcYY4xFLIMYYYzxiCcQYY4xHLIEY\nY4zxiCUQY4wxHrEEYowxxiOWQIwxxnjEEogxxhiPWAIxxhjjEUsgxhhjPOJYAhGRq0UkVUTyRKR7\nGeV2ish3IrJWRFb5M0ZjjDGlc7IFsh64EviynHL5QJKqXqSqvX0fVnBITk52OoSAYOfhJ3YufmLn\nwjscSyCqullVtwJSTlHButoqzf5AXOw8/MTOxU/sXHhHdfhgVmCxiKwWkYlOB2OMMcYlzJeVi8hi\nIKboS7gSwsOqOq+C1QxQ1f0i0hRXItmoqsu8HasxxpjKEVV1NgCRJcD/qeqaCpR9DMhQ1edK2e7s\nmzHGmGpIVcsbSiiRT1sglVBi8CJSBwhR1VMiUhcYBkwurRJPT4IxxpjKc3Ia7xUisgfoC8wXkU/d\nrzcXkfnuYjHAMhFZC6wA5qnqImciNsYYU5TjXVjGGGOqp+owC+tnRGSEiGwSkS0i8kApZaaIyFYR\nWSciF/o7Rn8p71yIyPXuRZjficgyEbnAiTj9oSK/F+5yvUQkR0Su8md8/lTBv5Ek9+LcVPc4ZFCq\nwN9IfRGZ6/6sWC8itzgQpl+IyOsiclBEvi+jTOU+O1W12vzgSnjbgHggHFgHdCxWZiTwiftxH2CF\n03E7eC76AtHuxyNq8rkoUu5zYD5wldNxO/h7EQ2kAbHu502cjtvBc/EQ8HTBeQCOAGFOx+6j8zEQ\nuBD4vpTtlf7srG4tkN7AVlXdpao5wDvA5cXKXA7MAlDVlUC0iMQQfMo9F6q6QlVPuJ+uAGL9HKO/\nVOT3AuBu4H3gkD+D87OKnIvrgf+q6j4AVT3s5xj9pSLnQoEo9+Mo4Iiq5voxRr9R1/KHY2UUqfRn\nZ3VLILHAniLP93Luh2LxMvtKKBMMKnIuipoAfOrTiJxT7rkQkRbAFar6CuVf/aA6q8jvRXugkYgs\ncS/QvdFv0flXRc7Fi0BnEUkHvgPu9VNsgajSn52BMo3X+JCIXAzciqsJW1P9EyjaBx7MSaQ8YUB3\nYAhQF1guIstVdZuzYTliOLBWVYeISFtci5W7quoppwOrDqpbAtkHtCryvKX7teJl4sopEwwqci4Q\nka7AdGCEqpbVfK3OKnIuegLviIjg6useKSI5qjrXTzH6S0XOxV7gsKqeBc6KyFKgG67xgmBSkXNx\nK/A0gKr+ICI7gI7AN36JMLBU+rOzunVhrQbOF5F4EYkAxgHFPwDmAjcBiEhf4LiqHvRvmH5R7rkQ\nkVbAf4EbVfUHB2L0l3LPhaq2cf8k4BoH+V0QJg+o2N/Ix8BAEQl1L9btA2z0c5z+UJFzsQu4FMDd\n398e2O7XKP1LKL31XenPzmrVAlHVPBG5C1iEK/m9rqobReQ212adrqoLROQyEdkGnMb1DSPoVORc\nAH8GGgEvu79552gQXhK/gufiZ7v4PUg/qeDfyCYR+Qz4HsgDpqvqBgfD9okK/l48Cfy7yNTW+1X1\nqEMh+5SIzAaSgMYisht4DIigCp+dtpDQGGOMR6pbF5YxxpgAYQnEGGOMRyyBGGOM8YglEGOMMR6x\nBGKMMcYjlkCMMcZ4xBKIMcYYj1gCMcYY4xFLIMb4iIj0dN/MK0JE6rpv3tTZ6biM8RZbiW6MD4nI\n40Bt988eVX3G4ZCM8RpLIMb4kIiE47qo3xmgv9ofnAki1oVljG81AerhuttdLYdjMcarrAVijA+J\nyMfA20AC0EJV73Y4JGO8plpdzt2Y6sR9q9hsVX1HREKAr0QkSVWTHQ7NGK+wFogxxhiP2BiIMcYY\nj1gCMcYY4xFLIMYYYzxiCcQYY4xHLIEYY4zxiCUQY4wxHrEEYowxxiOWQIwxxnjk/wPHCbW6ZHc1\n5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x34cd5e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Eoi8eQDTwZY7XjwGPFvKZHUB4PsuKPwwzl5e+e0nbT2mvrlRXiesqLfaf2K+3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\nGK9YAjHGGOOV/wcFvv2A11wugwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3524f898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SCkG/Y5HIqApLRESiTglEREQiEngCMbOXzGybmS0qZPnFZrbLzD4LP34T7RhFROR45aER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\nRAlEREQi8v8Bt59n0x5NvjQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x351b96d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SGkTPYosWLeKCCy5g69at9O/fn6effpqePXuGHZaItBLqwpKcoN+xSHLUhSUiIhmnBCIi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\nKUogIiKSFCUQERFJyv8HrqYLcmNEiuMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x354779e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l2_penalty in [1e-25, 1e-10, 1e-6, 1e-3, 1e2]:\n",
    "    model = polynomial_ridge_regression(data, deg=16, l2_penalty=l2_penalty)\n",
    "    print 'lambda = %.2e' % l2_penalty\n",
    "    print_coefficients(model)\n",
    "    print '\\n'\n",
    "    plt.figure()\n",
    "    plot_poly_predictions(data,model)\n",
    "    plt.title('Ridge, lambda = %.2e' % l2_penalty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">X1</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">Y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0395789449501</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.587050191026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0415680996791</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.648655851372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0724319480801</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.307803309485</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.150289044622</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.310748447417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.161334144502</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.237409625496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.191956312795</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.705017157224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.232833917145</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.461716676992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.259900980166</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.383260507851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.380145814869</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.06517691429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.432444723508</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.03184706949</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[30 rows x 2 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tX1\tfloat\n",
       "\tY\tfloat\n",
       "\n",
       "Rows: 30\n",
       "\n",
       "Data:\n",
       "+-----------------+----------------+\n",
       "|        X1       |       Y        |\n",
       "+-----------------+----------------+\n",
       "| 0.0395789449501 | 0.587050191026 |\n",
       "| 0.0415680996791 | 0.648655851372 |\n",
       "| 0.0724319480801 | 0.307803309485 |\n",
       "|  0.150289044622 | 0.310748447417 |\n",
       "|  0.161334144502 | 0.237409625496 |\n",
       "|  0.191956312795 | 0.705017157224 |\n",
       "|  0.232833917145 | 0.461716676992 |\n",
       "|  0.259900980166 | 0.383260507851 |\n",
       "|  0.380145814869 | 1.06517691429  |\n",
       "|  0.432444723508 | 1.03184706949  |\n",
       "+-----------------+----------------+\n",
       "[30 rows x 2 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform a ridge fit of a degree-16 polynomial using a \"good\" penalty strength"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will learn about cross validation later in this course as a way to select a good value of the tuning parameter (penalty strength) lambda.  Here, we consider \"leave one out\" (LOO) cross validation, which one can show approximates average mean square error (MSE).  As a result, choosing lambda to minimize the LOO error is equivalent to choosing lambda to minimize an approximation to average MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# LOO cross validation -- return the average MSE\n",
    "def loo(data, deg, l2_penalty_values):\n",
    "    # Create polynomial features\n",
    "    data = polynomial_features(data, deg)\n",
    "    \n",
    "    # Create as many folds for cross validatation as number of data points\n",
    "    num_folds = len(data)\n",
    "    folds = graphlab.cross_validation.KFold(data,num_folds)\n",
    "    \n",
    "    # for each value of l2_penalty, fit a model for each fold and compute average MSE\n",
    "    l2_penalty_mse = []\n",
    "    min_mse = None\n",
    "    best_l2_penalty = None\n",
    "    for l2_penalty in l2_penalty_values:\n",
    "        next_mse = 0.0\n",
    "        for train_set, validation_set in folds:\n",
    "            # train model\n",
    "            model = graphlab.linear_regression.create(train_set,target='Y', \n",
    "                                                      l2_penalty=l2_penalty,\n",
    "                                                      validation_set=None,verbose=False)\n",
    "            \n",
    "            # predict on validation set \n",
    "            y_test_predicted = model.predict(validation_set)\n",
    "            # compute squared error\n",
    "            next_mse += ((y_test_predicted-validation_set['Y'])**2).sum()\n",
    "        \n",
    "        # save squared error in list of MSE for each l2_penalty\n",
    "        next_mse = next_mse/num_folds\n",
    "        l2_penalty_mse.append(next_mse)\n",
    "        if min_mse is None or next_mse < min_mse:\n",
    "            min_mse = next_mse\n",
    "            best_l2_penalty = l2_penalty\n",
    "            \n",
    "    return l2_penalty_mse,best_l2_penalty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run LOO cross validation for \"num\" values of lambda, on a log scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "l2_penalty_values = numpy.logspace(-4, 10, num=10)\n",
    "l2_penalty_mse,best_l2_penalty = loo(data, 16, l2_penalty_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot results of estimating LOO for each value of lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jm0JEerpzgOfJzmy6XcGqcsvN7H4z+4OZPWRmOwWvnWtmz5vZUjO71bIGB593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\niIhIZAoRERGJTCEiIiKR/X8uIQZClA4KEAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x35491c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l2_penalty_values,l2_penalty_mse,'k-')\n",
    "plt.xlabel('$\\ell_2$ penalty')\n",
    "plt.ylabel('LOO cross validation error')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the value of lambda, $\\lambda_{\\mathrm{CV}}$, that minimizes the LOO cross validation error, and plot resulting fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12915496650148839"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_l2_penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learned polynomial for degree 16:\n",
      "       16         15          14          13          12           11\n",
      "1.345 x  + 1.141 x  + 0.9069 x  + 0.6447 x  + 0.3569 x  + 0.04947 x \n",
      "           10          9          8         7         6         5\n",
      " - 0.2683 x  - 0.5821 x - 0.8701 x - 1.099 x - 1.216 x - 1.145 x\n",
      "           4           3          2\n",
      " - 0.7837 x - 0.07406 x + 0.7614 x + 0.7703 x + 0.3918\n"
     ]
    }
   ],
   "source": [
    "model = polynomial_ridge_regression(data, deg=16, l2_penalty=best_l2_penalty)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CpObJK8hj/cH1xUGxct9Kvt7/Na1jWzOwzUCSWicxIGEAfeP7Et8ovlbuUVRFVU9yPHTi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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ddeb6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data,model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Lasso Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lasso regression jointly shrinks coefficients to avoid overfitting, and implicitly performs feature selection by setting some coefficients exactly to 0 for sufficiently large penalty strength lambda (here called \"L1_penalty\").  In particular, lasso takes the RSS term of standard least squares and adds a 1-norm cost of the coefficients $\\|w\\|$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define our function to solve the lasso objective for a polynomial regression model of any degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_lasso_regression(data, deg, l1_penalty):\n",
    "    model = graphlab.linear_regression.create(polynomial_features(data,deg), \n",
    "                                              target='Y', l2_penalty=0.,\n",
    "                                              l1_penalty=l1_penalty,\n",
    "                                              validation_set=None, \n",
    "                                              solver='fista', verbose=False,\n",
    "                                              max_iterations=3000, convergence_threshold=1e-10)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explore the lasso solution as a function of a few different penalty strengths"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We refer to lambda in the lasso case below as \"l1_penalty\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l1_penalty = 1.000000e-04\n",
      "number of nonzeros = 17\n",
      "Learned polynomial for degree 16:\n",
      "       16        15         14         13         12         11\n",
      "29.02 x  + 1.35 x  - 12.72 x  - 16.93 x  - 13.82 x  - 6.698 x \n",
      "          10         9         8         7         6         5\n",
      " + 1.407 x  + 8.939 x + 12.88 x + 11.44 x + 3.759 x - 8.062 x\n",
      "          4         3         2\n",
      " - 16.28 x - 7.682 x + 17.86 x - 4.384 x + 0.685\n",
      "\n",
      "\n",
      "l1_penalty = 1.000000e-02\n",
      "number of nonzeros = 14\n",
      "Learned polynomial for degree 16:\n",
      "        16           15           11          10        9          8\n",
      "-1.182 x  - 0.00533 x  + 0.09194 x  + 0.7401 x  + 3.83 x + 0.4778 x\n",
      "           7             6          5         4             3         2\n",
      " + 0.1229 x - 0.0007619 x - 0.6133 x - 10.11 x - 0.0005617 x + 6.686 x - 1.281 x + 0.5056\n",
      "\n",
      "\n",
      "l1_penalty = 1.000000e-01\n",
      "number of nonzeros = 5\n",
      "Learned polynomial for degree 16:\n",
      "      16         6         5\n",
      "2.21 x  - 1.002 x - 2.962 x + 1.216 x + 0.3473\n",
      "\n",
      "\n",
      "l1_penalty = 1.000000e+01\n",
      "number of nonzeros = 2\n",
      "Learned polynomial for degree 16:\n",
      "        9\n",
      "-1.526 x + 0.5755\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Th/lg1Qe8vfRtykWU44mOT9CvZT8bKryEm71lNkOmD6FLTBf+0+0/VCtXzeuQ\nTC4sgbhyuw5k3/F9PDT9IbYc3sKYnmOQXRKW104UBcv3LuetJW8xee1kbrr4Jh654hGurn91ies+\nbXJ2/Mxxnvv+OT5b+xmv3/g6tze/3euQTA7COoGISHfgNZwuxeNU9ZUs07sCU4Ff3LemqOqLOSwr\nxwQCTm3kk8RPeHL2k1x70bUsH7mcTSs3hcW1E15LSUvh08RPeWvJW+xJ3sND7R5i0OWDqFWxlteh\nmSLsp50/MWjaIJrXbM4bN75hg2AWQWGbQESkFLARuA7YAywB+qnqep8yXYEnVfXmfCwv1wSS6djp\nYwyPH86EVRO4J+YenrvhOWpUtWEzsrPu13WMXzme/678L23qtOGRKx6hx8U9bFwqk28paSm8OO9F\n3l3+Lq93f52+Lft6HZIB3vj5DXo37c1FVS7yO4F4fSFhe2CTqm5X1VTgY6B3NuUC2jZSqUwlXu32\nKvH3xbMhbQPtJ7Rn0ppJZGhGIFcTto6kHGHM0jF0fK8j1024DoCfBv3ErLtncXPTmy15mAIpG1GW\nF699kRn9ZzB87nD6f97fLkAsAv71079IzUgt1DK8TiD1gJ0+r3e572V1pYisFJEZIhKwO960vKAl\nM++aybibx/Haote4fMzlfJr4KekZ6YFaRdhIz0hn9pbZ9P+8P7GvxfLd1u/4W9e/seOJHYy8fiSN\nqzX2OkTjoUBcdd+ubjuWP7icCypcQKu3W/HN5m8CGKEpiDPpZ9h7fC/1K9Uv1HK8bsK6Deimqg+6\nr+8G2qvqYz5lKgIZqnpSRG4ERqlqkxyWp8OGDTv7Oi4ujri4uHzFoqpM3zidv8//O4dTDvP01U9z\n16V3FeseRRmawcKdC/k08VMmr5tM7Yq1GXjZQO5seSfVy1f3OjxTRASjx+L3v3zP/dPup+fFPRl5\n/UgqRFUIULQmL/Hx8Uz5egoTVk3gjx3/yIgRI8L2HEhHYLiqdndfP4NzUcsrucyzFWirqufVgQMx\nGq+qEr8tnpd/fJmV+1Zy/2X3M6TdEGKrxBZquUVFekY6i3Yt4vN1n/PZ2s+oFFmJq6tczZDOQ2gb\n09br8EwRFKzRno+kHOGxrx9j4a6FfNjnQzpc2CEA0Zr8+HbLt7y04CXm3DsnrAdTXAI0FpEYEYkC\n+gHTfAuISC2f5+1xkl7QGlBFhGsaXMM3d3/D/IHzOZ1+mnZj29H9w+5MXDWR5NPhN3DekZQjfJLw\nCQO+GEDfyQq+AAAWm0lEQVTtf9fmkZmPEB0Vzee3fE7ke5GMHzieQb0HFbtBAU1g5HYTqsKoUrYK\nE/pM4KXrXqLXR714ecHLdh4yRH45/AsNqzYs9HKKSjfeUfzWjfdlERmCUxMZKyJ/AB4GUoFTwBOq\nujiHZRW6BpKdk6knmbp+KpMSJjF/+3y6Ne7GzU1upnvj7kWyqedU6ikW7lpI/LZ44rfFs3LfSrrE\ndKHHxT3o0aQHF1W+CAjf+4iY0Av2Vfc7ju7gril3UTaiLBNumWDdfYPs6W+fpnLZyvy585/Dtxtv\noIXihlIHTh7gy/VfMn3jdH7Y9gOtarXi2thr6RzTmSsvvDLkbbmqyrYj21i2dxnL9izjx50/snzv\nclrVakVcbBxxsXFcXf/qbOMKt/uImPCXnJxMQkICLVu2PG9fS8tI48V5LzJm2RjG3TyOmy6+yaMo\ni787PruDPs36cOeld1oCyRTqOxKmpKUwd9tc5m6fy7zt81i5byVNqjehde3WtK7VmksvuJTG1Rpz\nYaULC931NTU9lR1Hd7D50Ga2HN7C5kObWZ20muV7l1M+sjxt67bl8tqXc1X9q7iq/lVUjKqYr+UW\n1/GcTNGT35Pxc7fN5Z4v7uH25rfz0nUvFeuOLF5pN7Ydb970Jh0u7GAJJJPXt7Q9lXqK1UmrWZW0\nilX7VpHwawK/HP6F/Sf2U79SfWpXrE3NCjWpUa4GlctWpmxEWcqULkNU6SjSMtJIzUglNT2Vo6eP\ncvDUQQ6ePMiBkwc4eOog+47vo07FOjSu1pjG1RrTqGojWl7QkjZ12gT9avDcfjUak18FaTI9ePIg\ng6YNYuexnXxy+yfWjTzAqr1SjQ1DN1CzQk1LIJm8TiA5OZ12mu1Ht5N0PIlfT/7KgZMHOJpylNPp\np0lJS+FM+hkiSkUQWSqSyNKRVCpTierlqlOjfA2ql69O9XLVqRtd15NfYjbopAmUgjaZqipvLnmT\n5+c+z9heY7ml2S0hjLb4OpJyhAtfvZDkZ5MREUsgmYpqAglndqLdBJI/TaaLdy3mjsl30LdFX/5x\n3T+IKBUR5CiLtxV7V3Dvl/ey+uHVgN0T3QRRsLpwmpIpOjqajh07FqgW2+HCDix7cBmrk1Zz3YTr\n2Ju8N4gRFn9bj2ylQdUGAVmWJZAiJhBDRgRSdHQ08+fPZ968edZ85ZGitk94oUb5GszoP4NrY6+l\n3bvtmLttrtchha0th7bQoIolkJAKxZc4s424S5cudO7cucgcMPz51WgCo6juE14oXao0w+KG8f7N\n79N3cl/++eM/sSbrgtt4cCNNqzcNyLIsgeRDqL7ECQkJJCYmkpaWxtq1a0lMTAzKekz4sH3ifN0a\nd2PJ4CV8uvZT7ppyF6dST+U5j9XifrPh4Aaa1rAEEjKh+hLb+QaTle0T2atfuT7z7ptHKSlF5/Gd\n2XVsV45lrRZ3rvUH1lsNJJRC9SW28w0mK9snclYushwT+0zkjhZ30OG9DizcuTDbclaL+83hU4c5\nlXaKutF1A7K8PLvxisijwIeqejggawyiYHbj9eqKbbuIz5i8zdg4g4FTB/LK715h4OUDz5lmQ/b8\nZtGuRQydOZSlDy49+16wu/HWApaIyKci0l1EAnp3wHDhxYlkq3obkz89mvRg7n1zeWnBSzwx6wnS\nMtLOTrNa3G/WH1gfsPMfkI8Eoqp/AS4GxgH3AZtE5B8i0ihgUZhsWdXbmPy7pOYlLH5gMWsPrKXn\npJ7n3HrBehI6NhzYQLPqzQK2vHydA3Hbhfa5jzSgKjBZREYGLBJzHjuBakzBVC1XlRn9ZxBbJZbO\n4zuz+9hur0MqUgLZAwvykUBE5HERWQaMBH4ELlXVh4G2wG0Bi8Scx6rexhRcRKkI3u7xNv0v7c+V\n465kddJqr0MqMtYfWE+zGoGrgeTnJPoI4H1V3Z7NtEtUdV3AoikkGwvLGOPrk4RPePTrR/nw1g+5\nodENXofjqbSMNCr+oyKHnz5MuchyZ98P6kl0VR2WXfJwpxWZ5GGMMVn1bdmXKX2nMOCLAYxfMd7r\ncDy19fBWalesfU7yKCwb1tIYU6x1uqgT8wbOo9uH3fj15K/86eo/eR2SJ1YnraZVrVYBXaZdSGiM\nKfaaVG/CgoEL+GDVBzw1+6kSOYaWJRBjjPFTvUr1mD9wPgt2LuD+afefc61ISbAqaRWta7UO6DIt\ngRhjSoxq5arx3T3fse/4Pm779LZ8DcSYnXAcnNFqIMYYU0gVoiowtd9UKkRW4KZJN3H8zPECzR+O\nI0QcO32MpBNJAb+3vCUQY0yJE1U6iol9JtKoaiO6f9idY6eP5XvecBwhYk3SGlrUbEHpUqUDulzP\nE4g7vtZ6EdkoIk/nUOZ1EdkkIitF5LJQx2iMKX5KlyrN2F5jaVWrFddPvJ7Dp/I3Xmw4jhARjPMf\n4HECEZFSwBtAN6AFcKeINMtS5kagkapeDAwB3gl5oMaYYqmUlOLNm97kqguv4roJ13Hw5ME85wnH\nESKCcf4DvK+BtAc2qep2VU0FPgZ6ZynTG5gAoKqLgcoiUiu0YRpjiisR4dVur3JDoxu45oNr2H9i\nf57zhNvgjKuSVtG6djGrgQD1gJ0+r3e57+VWZnc2ZYwxxm8iwkvXvcQtzW7h2g+u5dcTv3odUsCk\npqeyOmk1l9UOfOt/sbsSffjw4Wefx8XFERcX51ksxpjwISKMiBtBekY610+8njn3zqFauWpeh1Vo\nq5NW07BqQyqVqQRAfHw88fHxAVl2noMpBpOIdASGq2p39/UzOKPHv+JT5h3gB1X9xH29HuiqqknZ\nLM8GUzTGFIqq8tS3TxG/LZ7vBnxHlbJVvA6pUN78+U1W7FvBeze/l+30YN+RMJiWAI1FJEZEooB+\nwLQsZaYBA+BswjmSXfIwxphAEBH+ef0/uar+Vdz4vxvPuTFVOFq8ezEd6nUIyrI9TSCqmg4MBWYD\nicDHqrpORIaIyINumZnAVhHZDIwBHvEsYGNMiSAijOo+ita1WnPTpJs4ceaE1yH5bfHuxXS4MDgJ\nxNMmrECzJixjTCBlaAYPTHuAHUd3MKP/DMpElPE6pAI5fOowMa/FcPjpwzleRBjOTVjGGFMkJScn\ns3jRYl6Ne5Wq5arSf0r/sBuA8efdP9O2btuAX4GeyRKIMcZk4TveVVzXON7+3dskn07moekPhdVQ\n8At3LQza+Q+wBGKMMefJOt7V5g2bmdJ3Cgn7E3j6u2xHXCqS5mydwzWx1wRt+ZZAjDEmi+zGu6oY\nVZGZd81k5qaZvLLglbwX4sOL4d9PnDnB8r3L6XRRp6Cto9hdSGiMMYWVOd5VYmIiLVq0ODtkSbVy\n1Zh9z2w6vd+JauWqMbjt4DyXldkclrmsUI2ftWDHAtrUaUOFqApBW4fVQIwxJhs5jXdVN7ous++Z\nzfC5w/ks8bM8l+PV8O9zts7h2gbXBnUdlkCMMaaAGldrzMz+Mxn69VBmb5mda1mvhn//fuv3XNfg\nuqCuw64DMcaUaMnJySQkJNCyZcsCNy0t2LGAWz+5len9p9O+Xvtc15G1OSyYMq//OPCnA0SVjsq1\nrF0HYowxfijs7Wk7XdSJ93u/T++Pe7P+wPocy4V6+PeZm2bSNbZrnsmjsCyBGGNKrECcn+jZpCev\n/O4Vun3YjZ1Hd+Y9Qwh8sf4Lbm12a9DXYwnEGFNiBer8xIDWA3is/WN0+7Bbvu5qGEynUk/x7S/f\n0qtpr6Cvy7rxGmNKrJy66/rjyaue5NeTv9JjUg++G/AdFaMqBjDS/Pv2l29pU6cNNcrXCPq67CS6\nMcYEiKrywLQH2J28m2l3Tgv6OYjs3PflfbSt05ZHOzyar/J2Et0YY4oAEWFMrzGUjSjLfV/eR4Zm\nhHT9J1NP8tXGr+hzSZ+QrM8SiDHGBFBEqQg+uu0jdifv5vGvHw/p4IuT106mQ70OXFjpwpCszxKI\nMcYEWLnIckzrN435O+bzwrwXQrbed5e/y+A2eQ+vEiiWQIwxJggql63MrLtn8b81/+OfP/4z6Otb\n9+s6Nh/aTM8mPYO+rkyWQIwxJkhqV6zNnAFzGLNsDKMWjSrQqLwFHcH3rSVvMfCygUSWjixs2Plm\nvbCMMSbIdhzdQZf3u5A2L42k6Ul5jspb0BF8dx/bTat3WrH2kbXUqlirQLFZLyxjjCnCLqp8Ef9u\n9W92x+4mrV3eV70X9Ar5lxa8xP2X3V/g5FFYlkCMMSYEbmh/A5csugTaQdXbqtK8efMcyxbkCvnt\nR7Yzac0knrr6qWCEnStrwjLGmBBJTk5mwYoFPLf2OTpc2IE3bnqD0qVK51g2ryvkVZXu/+tO15iu\n/Lnzn/2KqTBNWJZAjDEmxI6dPsYtH99CdJloJvaZSKUylfxazvsr3ufNJW+yaNAiv0+eh+U5EBGp\nKiKzRWSDiHwjIpVzKLdNRFaJyAoR+TnUcRpjTKBVKlOJWXfPonaF2lw57koS9xd8FOCle5by9HdP\nM773+JD2vPLl5TmQZ4DvVLUpMAd4NodyGUCcql6uqjnfscUYY8JIVOkoxvQaw5NXPkncB3GMXjya\n9Iz0fM278eBGen3Ui/d6vUerWq2CHGnOPGvCEpH1QFdVTRKR2kC8qjbLptxWoJ2q5jlGsjVhGWPC\n0caDGxn81WCOnznOK797hesaXIdI9q1Kn6/9nIdnPMzI60dy32X3FXrdYXkOREQOqWq1nF77vP8L\ncARIB8aq6ru5LNMSiDEmLKkqHyd8zIvzXySyVCS/b/57usZ2pW50XY6fOc7KfSt5b/l77Enew0e3\nfcQV9a4IyHqLbAIRkW8B347JAijwF+C/WRLIQVWtns0y6qjqXhGpCXwLDFXVBTmsT4cNG3b2dVxc\nHHFxcQH5LMYYEwoZmsGcrXOYvnE6C3ctJOl4EhWiKtCsRjPubHknvZv2LtQ5j/j4eOLj48++HjFi\nRNFMILmuWGQdzrmNzCasH1T1kjzmGQYkq+qrOUy3GogxxhRAWPbCAqYB97nP7wWmZi0gIuVFpKL7\nvAJwA5AQqgCNMcbkzMsaSDXgU6A+sB24Q1WPiEgd4F1V7SkiDYAvcJq9IoD/qerLuSzTaiDGGFMA\nRfYcSKhZAjHGmIIJ1yYsY4wxYcwSiDHGGL9YAjHGGOMXSyDGGGP8YgnEGGOMXyyBGGOM8YslEGOM\nMX6xBGKMMcYvlkCMMcb4xRKIMcYYv1gCMcYY4xdLIMYYY/xiCcQYY4xfLIEYY4xHkpOTWbhwIcnJ\nyV6H4hdLIMYY44Hk5GQ6d+5Mly5d6Ny5c1gmEUsgxhjjgYSEBBITE0lLS2Pt2rUkJiZ6HVKBWQIx\nxhgPtGzZkhYtWhAZGUnz5s1p0aKF1yEVmN2R0BhjPJKcnExiYiItWrQgOjrakxjslrYuSyDGGFMw\ndktbY4wxIWcJxBhjjF8sgRhjjPGLJRBjjDF+8SyBiMjtIpIgIuki0iaXct1FZL2IbBSRp0MZozHG\nmJx5WQNZA/QB5uZUQERKAW8A3YAWwJ0i0iw04RljjMlNhFcrVtUNACKSW/ex9sAmVd3ulv0Y6A2s\nD36ExhhjclPUz4HUA3b6vN7lvmeMMcZjQa2BiMi3QC3ftwAFnlPVr4KxzuHDh599HhcXR1xcXDBW\nY4wxYSk+Pp74+PiALMvzK9FF5AfgSVVdns20jsBwVe3uvn4GUFV9JYdl2ZXoxhhTAMXhSvScgl8C\nNBaRGBGJAvoB00IXljHGmJx42Y33FhHZCXQEpovI1+77dURkOoCqpgNDgdlAIvCxqq7zKmZjjDG/\n8bwJK5CsCcsYYwqmODRhGWOMCTOWQIwxxvjFEogxxhi/WAIxxhjjF0sgxhhj/GIJxBhjjF8sgRhj\njPGLJRBjjDF+sQRijDHGL5ZAjDHG+MUSiDHGGL9YAjHGGOMXSyDGGGP8YgnEGGOMXyyBGGOM8Ysl\nEGOMMX6xBGKMMcYvlkCMMcb4xRKIMcYYv1gCMcYY4xdLIMYYY/xiCcQYY4xfPEsgInK7iCSISLqI\ntMml3DYRWSUiK0Tk51DGaIwxJmde1kDWAH2AuXmUywDiVPVyVW0f/LCKh/j4eK9DKBJsO/zGtsVv\nbFsEhmcJRFU3qOomQPIoKlhTW4HZF8Rh2+E3ti1+Y9siMMLhwKzAtyKyREQGex2MMcYYR0QwFy4i\n3wK1fN/CSQjPqepX+VzM1aq6V0Rq4iSSdaq6INCxGmOMKRhRVW8DEPkBeFJVl+ej7DAgWVVfzWG6\ntx/GGGPCkKrmdSohW0GtgRRAtsGLSHmglKoeF5EKwA3AiJwW4u9GMMYYU3BeduO9RUR2Ah2B6SLy\ntft+HRGZ7harBSwQkRXAIuArVZ3tTcTGGGN8ed6EZYwxJjyFQy+sc4hIdxFZLyIbReTpHMq8LiKb\nRGSliFwW6hhDJa9tISL93YswV4nIAhG51Is4QyE/+4Vb7goRSRWRW0MZXyjl8zsS516cm+CehyyW\n8vEdqSQi09xjxRoRuc+DMENCRMaJSJKIrM6lTMGOnaoaNg+chLcZiAEigZVAsyxlbgRmuM87AIu8\njtvDbdERqOw+716St4VPue+B6cCtXsft4X5RGUgE6rmva3gdt4fb4lngpcztABwEIryOPUjboxNw\nGbA6h+kFPnaGWw2kPbBJVberairwMdA7S5newAQAVV0MVBaRWhQ/eW4LVV2kqkfdl4uAeiGOMVTy\ns18APApMBvaHMrgQy8+26A98rqq7AVT1QIhjDJX8bAsFot3n0cBBVU0LYYwho87lD4dzKVLgY2e4\nJZB6wE6f17s4/6CYtczubMoUB/nZFr4eAL4OakTeyXNbiEhd4BZVfZu8Rz8IZ/nZL5oA1UTkB/cC\n3XtCFl1o5WdbvAE0F5E9wCrg8RDFVhQV+NhZVLrxmiASkWuAgThV2JLqNcC3Dbw4J5G8RABtgGuB\nCsBCEVmoqpu9DcsT3YAVqnqtiDTCuVi5laoe9zqwcBBuCWQ3cJHP6wvd97KWqZ9HmeIgP9sCEWkF\njAW6q2pu1ddwlp9t0Q74WEQEp637RhFJVdVpIYoxVPKzLXYBB1Q1BUgRkXlAa5zzBcVJfrbFQOAl\nAFXdIiJbgWbA0pBEWLQU+NgZbk1YS4DGIhIjIlFAPyDrAWAaMABARDoCR1Q1KbRhhkSe20JELgI+\nB+5R1S0exBgqeW4LVW3oPhrgnAd5pBgmD8jfd2Qq0ElESrsX63YA1oU4zlDIz7bYDvwOwG3vbwL8\nEtIoQ0vIufZd4GNnWNVAVDVdRIYCs3GS3zhVXSciQ5zJOlZVZ4rITSKyGTiB8wuj2MnPtgD+ClQD\n3nJ/eadqMRwSP5/b4pxZQh5kiOTzO7JeRL4BVgPpwFhVXeth2EGRz/3iReC/Pl1b/6SqhzwKOahE\nZBIQB1QXkR3AMCCKQhw77UJCY4wxfgm3JixjjDFFhCUQY4wxfrEEYowxxi+WQIwxxvjFEogxxhi/\nWAIxxhjjF0sgxhhj/GIJxBhjjF8sgRgTJCLSzr2ZV5SIVHBv3tTc67iMCRS7Et2YIBKR54Fy7mOn\nqr7icUjGBIwlEGOCSEQicQb1OwVcpfaFM8WINWEZE1w1gIo4d7sr63EsxgSU1UCMCSIRmQp8BDQA\n6qrqox6HZEzAhNVw7saEE/dWsWdU9WMRKQX8KCJxqhrvcWjGBITVQIwxxvjFzoEYY4zxiyUQY4wx\nfrEEYowxxi+WQIwxxvjFEogxxhi/WAIxxhjjF0sgxhhj/GIJxBhjjF/+P65LxR/dJyoWAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dc0f828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TGpv3bObck84lNSGV1E6p9GnbJ2bvzZCqb8m3S7jinSu4oPMF/HXwX3VFG7BY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\nEBERCcv/B2bu7n9aDjGKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dd3ad30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OfpGSVmxdwVX/vgoz4/FzHqdHqx5Rh1SnHEoCibrxsROwJub9WmBwKeWGmNk8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\nteg7fEaXsiIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1dec4eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6tcVkJ5B7gNHAAmAq8Hp9HeqUDqOwYukiPpHESMQXwBWfr2DMS2PIzsxm6gVT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\nERGRuCiBiIhIXP4/o79MnTn6kzoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x34f454a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for l1_penalty in [0.0001, 0.01, 0.1, 10]:\n",
    "    model = polynomial_lasso_regression(data, deg=16, l1_penalty=l1_penalty)\n",
    "    print 'l1_penalty = %e' % l1_penalty\n",
    "    print 'number of nonzeros = %d' % (model.coefficients['value']).nnz()\n",
    "    print_coefficients(model)\n",
    "    print '\\n'\n",
    "    plt.figure()\n",
    "    plot_poly_predictions(data,model)\n",
    "    plt.title('LASSO, lambda = %.2e, # nonzeros = %d' % (l1_penalty, (model.coefficients['value']).nnz()))"
   ]
  },
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   "source": [
    "Above: We see that as lambda increases, we get sparser and sparser solutions.  However, even for our non-sparse case for lambda=0.0001, the fit of our high-order polynomial is not too wild.  This is because, like in ridge, coefficients included in the lasso solution are shrunk relative to those of the least squares (unregularized) solution.  This leads to better behavior even without sparsity.  Of course, as lambda goes to 0, the amount of this shrinkage decreases and the lasso solution approaches the (wild) least squares solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### fista -> fancy version the gradient descent - optimizing the lass function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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