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": "stderr",
     "output_type": "stream",
     "text": [
      "2016-04-25 03:15:49,473 [INFO] graphlab.cython.cy_server, 176: GraphLab Create v1.8.5 started. Logging: C:\\Users\\PHILIP~1\\AppData\\Local\\Temp\\graphlab_server_1461579348.log.0\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create is assigned to chohyu01@cs.washington.edu and will expire on September 21, 2016. For commercial licensing options, visit https://dato.com/buy/.\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",
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       "    <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 0x15243c88>"
      ]
     },
     "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": [
    "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": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x15243860>"
      ]
     },
     "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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tZjXMrDjHbyk7OVeZyRy/l8dvSSY9d8IQETlfTROa8nmvz3li9hMMWzTM63BC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1febda20>"
      ]
     },
     "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",
      "-4.537e+05 x  + 1.129e+06 x  + 4.821e+05 x  - 3.81e+06 x \n",
      "              12             11             10             9\n",
      " + 3.536e+06 x  + 5.753e+04 x  - 1.796e+06 x  + 2.178e+06 x\n",
      "              8             7            6             5             4\n",
      " - 3.662e+06 x + 4.442e+06 x - 3.13e+06 x + 1.317e+06 x - 3.356e+05 x\n",
      "             3        2\n",
      " + 5.06e+04 x - 4183 x + 160.8 x - 1.621\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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tDYeLPB+Zfolpdtx4+a2zzdg+g3fWv8OaAdYmDNDBcmU/N3aH5vfOz7i24xi5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\nStlMk4ZSSimb/T+ikUYtd6V/AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x200653c8>"
      ]
     },
     "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",
      "-4.537e+05 x  + 1.129e+06 x  + 4.821e+05 x  - 3.81e+06 x \n",
      "              12             11             10             9\n",
      " + 3.536e+06 x  + 5.753e+04 x  - 1.796e+06 x  + 2.178e+06 x\n",
      "              8             7            6             5             4\n",
      " - 3.662e+06 x + 4.442e+06 x - 3.13e+06 x + 1.317e+06 x - 3.356e+05 x\n",
      "             3        2\n",
      " + 5.06e+04 x - 4183 x + 160.8 x - 1.621\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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eWctLP7zEnmf3ZDgb95BlQ2hQpgHDmg1zSjwigjEmW9OCW9U9tQwY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\nStlMk4ZSSimb/T+ikUYtd6V/AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x201cf978>"
      ]
     },
     "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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DBw5k8uTJDdp2ZN+RzFg5g4rKiniEtl9KGiIiAZgyZQoFBQXMnj2b3NzcBm17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\nREQkakoaIiISNSUNERGJ2v8HGGA1xVd6mr4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20257198>"
      ]
     },
     "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",
      "-4.537e+05 x  + 1.129e+06 x  + 4.821e+05 x  - 3.81e+06 x \n",
      "              12             11             10             9\n",
      " + 3.536e+06 x  + 5.753e+04 x  - 1.796e+06 x  + 2.178e+06 x\n",
      "              8             7            6             5             4\n",
      " - 3.662e+06 x + 4.442e+06 x - 3.13e+06 x + 1.317e+06 x - 3.356e+05 x\n",
      "             3        2\n",
      " + 5.06e+04 x - 4183 x + 160.8 x - 1.621\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  + 3074 x  - 3.332e+04 x  - 2.786e+04 x + 1.032e+04 x\n",
      "              7        6             5             4        3         2\n",
      " + 2.962e+04 x - 1440 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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Jack0Ht2YL6O/5IPnPyA+Pp59jfZRp2Mdfhj4g+MrRwYTVeWlpS8xcd1Evrnr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2048e908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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r/pSSloKqEhIU4nQoQBFLGgBd6nVh6Y6lTofhNU5f6yg5LZl759zLrNhZ/HjP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\nR7awbNcy9pzaw12t7uLXB36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      "text/plain": [
       "<matplotlib.figure.Figure at 0x201afe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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c/QbJJyYXyLLl6FJTU0lNTc3fQnI7RregXkA7YHKWz/cB9xxnnu+A6jl8n+dx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x207da358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cngVKA/9096fM7C4Adx9pZr8Afg5kAfsI9aT6IJf5FDhp5OTurMtYx+dbPj/h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\niEjE/j/M3QMBJNvJuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20a0beb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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u9XFTN/eJiEjc0qV6SkREagAlDRERiZuShoiIxE1JQ0RE4qakISIi\ncVPSEBGRuClpiIhI3JQ0REQkbkoaItUs8sKnBWbWwMwaR17yc0TQcYlUB90RLpIEZnY7sB/QEFjp\n7ncHHJJItVDSEEkCM6tH+MF5PwF9XP9oUkuoekokOZoBjYEmhK82RGoFXWmIJIGZTQEmAB2Alu5+\nfcAhiVSLtHg0ukg6MbPhwHZ3f9bMMoBZZhZy94KAQxPZZ7rSEBGRuKlNQ0RE4qakISIicVPSEBGR\nuClpiIhI3JQ0REQkbkoaIiISNyUNERGJm5KGiIjE7f8Dnfvm7CZqimYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20b6cb00>"
      ]
     },
     "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": 30,
   "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": 31,
   "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": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RyYknnhh7P8Vq165dLF++nKqqKmbPns3BBx/MxIkTmTBhAkOGDNFpKZGExHEEMreV73N3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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23e07320>"
      ]
     },
     "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": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12915496650148839"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_l2_penalty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Oc87xbe63ZOzM4MsdX5KxK4NV2as4nH+YHq16lCWH7+7bN2+vnkYnqGzg4b4j+1j4zULm\nrJ/Dgo0LGNRhEGMuHMMN599A88bNfYpaQklJQ+qMYlfMhn0byNiZUZIkdn7Jil0raNaoGX0T+9Iv\nsR99E/vSq00vOsR2UHLwoCoDD/Py85i7fi5vr3mbxZsXM/Tcodzb714CnQLa13WIkoZEpMLiQjL3\nZpYliIydGazctZKWMS3pm9i3LEmkJKbQumlrv8ONWKmpqSxYsID+/ftX6RK5+4/u5+3Vb/PSFy9R\n5Ir4Sf+fMLb3WOLO0rQikU5Jox6KtKmr84vyWbdnXUn10s4MMnZlsDp7Ne1j25ckiLYlSSIlMYUW\nTVr4HW6dUtN5pJxzLNmyhD99/ic+/OZDbu5xM78Y9AvOaXFOCKKVcFDSqIdq81xHxwqPsTp7dVn1\nUsbODNbtWUfn+M5l1Ut9E/vSp20fYhvH+h2uVMGuvF388bM/8tIXLzGs6zAmXjqR7q26+x2WVJGS\nRj1U3SqHYDucf5ivsr86qQ1iw74NnJdw3iltEE0bNfUlRgm+A8cO8MfP/8gLy1/g8o6X88hlj9Cn\nbR+/wxKPlDTqIT+mrj54/CArd60s68GUsTODb3O+5YLWF5RVL/Vr148LW1/IWVFnhSUm8dfh/MNM\n+XIKv1v6O67ofAVPDXmKTnGd/A5LKqGkUQWR1hbgl/1H97Ni54qTqpi2H9pOrza9Tqpi6tGqB40a\nNvI73LCpi9+fYHymvPw8/vtf/83k5ZMZ13scj17+KPFN4kMQrQSDkkYV1Oa2AL/sPrz7pB5MGTsz\n2HtkL33a9jmpiqlby261fiqNUKuL359gfqZdebt44tMnmJs1l6eHPM24PuM0oLIWqk7SqLf/+fX5\nugfOOXbm7TxpkFzGzgzy8vPKejCN7D6Sp698mnNbnKt/9grUxe9PMD9T22ZteeVHrzB+x3jum38f\nUzKm8NK1L6m9ow6ot2ca9eUyls45thzYclIDdcbODIpc0UnVS30T+9I5rrMGbnlUF78/ofpMxa6Y\n11e8zsRPJnJPyj08PvhxtXXVEqqe8qgu1kfD96OoV+wqaYP47r5xw8YnVS/1TexLUmySEoSE1a68\nXdw3/z7W7lnLq8NfZWCHgX6HVO8paXhUF+qjC4oKWLdn3UnJ4avsr2gV04qUxBT6ti0ZIJfSNoXE\n5ol+hytS5r1173H/gvsZ13scT17xZL3qQFHbRFzSMLOhwP8ADYE/O+eeLbc+AMwB/l361HvOud9U\nsJ0qJY3aMrbBqyMFR1iVvaqsF9OKXSvKBsmltC1JDN8NklNPFYkEuw/v5u45d7MrbxfTb5zO+S3P\n9zukeimikoaZNQTWA1cB24HPgTHOua9PKBMA/q9zbngl26pS0qjN9dG5x3JZuWtlWRvEil0r+Dbn\nW7q36l529vDdILmY6Bi/wxWpNuccL3/xMo99+hjP/fA57k652++Q6p1ISxqXAE8454aWLv8KwDn3\n2xPKBID/cM79qJJtRdzgvqLiIjbu38iq7FV8lf1V2f3+o/vp3aZ32dlDSmJKvRsDIfXLuj3ruGnm\nTVycdDF/TP2jfgyFUaQljZuAa5xz40uXbwcuds7df0KZwcD7wDZKzkYecs6tq2BbtTpp5BzNYVX2\nqpMSxNo9a2nbrC292vSid5veZfed4zuri6vUO3n5edz793tZlb2KWTfP4ryE8/wOqV6ItHEaXo7y\nGUAH59wRMxsGzAYq/DZNmjSp7HEgECAQCAQhxKopLC5kw74NpySI3GO59GzTk16te9G/XX/uTrmb\nnq176sI2UuuFq6dhs0bNeGvEW0z5cgqXvnYp02+cztXnXB2S96rP0tPTSU9Pr9E2/DzTGABMOqF6\n6mGguHxjeLnXfAv0c87tL/d8WM80vhv7cOLlRdfsXsPXe78msVkivdv2plfrXiX3bXrRKa6Tzh4k\nIvnR03DJ5iXcPOtmHr70Ye6/6H51DQ+hSDvT+ALoamadgB3AaGDMiQXMrA2w2znnzOwiSpLc/vIb\nChXnHNsObjvl2tPr9qwjtnEsF7Qque70oA6DmNBvAj3b9KRZo2bhCq9G6upYFQkuP0a+X9bxMpbe\nvZTh7wxn7e61vJj6ItENo8Py3lI5v7vcDuP7LrevOueeMbMJAM65V8zsZ8BPgELgCCU9qZZVsJ0a\nnWk459hxaEeFySEmOqbkmtMnXH+6R6seEd+1tS6MVZHQ87On4aHjh7j1/VvJy89j1qhZJMQkhPX9\n64OIaggPJq9J43jhcTbu38j6fetZv3c9mfsyS+73ZtI4qnGFyaGuflEjbayK1E9FxUU8/PHDzFk/\nh4W3L6RjXEe/Q6pTlDQoOWvYc2QPmXu/Twjr95Xcbzu4jY5xHemW0I3zW55Pt4RudGtZ8rhlTEuf\nP0V41eaxKlL31LQ6dPLyyfxu6e/4x23/4ILWF4QoyvqnXieNcX8bV5YcDOP8luefkhi6xHfReAcR\nHwSjOnTG6hk8+OGD/G303zRvVZBEWkN4UF2afCk/7vtjuiV0o2VMS/W4CAI1lkuwBKNB/daet9Ki\nSQtueOcG3rjhDVK7pgYzRPGozpxp1IXPUduosVyCJZjVocu3Lef6d67n+auf57ZetwUpwvqpXp9p\nSPDVxQsNiT/i4uKC9qPj4qSL+WTcJ/zwrR9SWFzIuD7jgrJd8UZnGnJaaiyX2ixzbyZXTbuK3wz5\nDXf2udPvcCJSvW4Ij/TPofYDKU/ficqt37ueK6ddyX9e8Z+aJbcaVD0VAuH6x83KyiprP0hLS1P7\ngeg74UG3lt34ZNwnXDntSpxz3NP3Hr9DqvOUNCoRrn9ctR9IefpOeHNewnl8MvYThkwbAnBS4tDZ\nWgg45854A34OxFdWzs9byccIjWHDhjnA9e/f3+Xk5ITsfXJyctyoUaNC+h4SWfSdqJqsvVmu3fPt\n3Dur3yl7bvDgwY6SGbXdqFGjfIyudio9dlbpeFtpm4aZPUXJZIIZwGvAh66yF4VZKNs01BgsEjlW\nZa/ih2/9kNevf53UrqmaLqcSIWsIN7MGwNXAnUB/YCYlEwx+U404g64uNISXp9NqkepZtm0Zw98e\nzns3v0fPs3vqR98ZVCdpeLrIg3OuGNgFZANFQDwwy8x+V+UoxZPv2lIWLFhAWlqa3+GIRIwBSQOY\nMXIGI2eO5N9H/83MmTOVMIKo0qRhZg+Y2ZfAc8A/gQudcz8B+gE3hji+ekuNoCLVd1WXq3j5upe5\ndsa1ZO7N9DucWqWwuLBGr/dyptECuNE5d7VzbqZzrgDKzj5+VKN3l9OaMWMGo0aNUj2sSDXd2P1G\nnrnyGa6Zfg07Du3wO5xa49b3bmV25uxqv16D+0SkTntmyTO8u/ZdFt+1mNjGsX6H4yvnHEm/T2LJ\nXUvoEt8ldG0aIiKR6leX/opLki5h5MyR5Bfl+x2Or7Ye3EpRcRGd4zpXextKGiJSp5kZf0j9A02i\nmjB+3njqc63E0q1LGdhhYI0uHaGkISJ1XlSDKN4e+TaZezN5/NPH/Q7HN98ljZpQ0hCReqFpo6bM\nGzOPt9e8zZQv62ePxKVbl3JJ0iU12obmnhKReqN109YsuG0Bl71+GV3iu3BVl6v8DilsDucf5uu9\nX9OvXb8abUdnGiJSr3RN6Mq7N73Lre/dWuUxHGlpaQQCAVJTU8nNzQ1RhKHx+Y7P6dWmF2dFnVWj\n7ShpiEi9M7jTYJ696lmum3Ed+47s8/y6SJ6pYdGmRVza4dIab8fXpGFmQ80s08w2mNkvT1Nmcun6\nr8wsJdwxikjddFfKXdzU4yZunHmj5664kTxTw6ebPmVI5yE13o5vScPMGgIvAkOBHsAYM+terkwq\ncK5zriuQBrwU9kBFpM56+sqnadGkBff+/V5PXXEjdaaGowVH+WLHF1yaHNlnGhcBG51zm0qnJnkH\nuL5cmeHAmwDOueVAnJm1CW+YIlJXNbAGTB8xnZW7VvK7pZXPvxoXFxeREyAu3bqU3m1707xx8xpv\ny8+k0R7YesLyttLnKiuTFOK4RKQeadqoKXPHzGXy8sk1mpOpNvvk20+4otMVQdmWn11uvQ7LLD90\nscLXTZo0qexxIBAgEAhUKygRqX+SYpOYfctshv1lGMlnJ9M3sa/fIQXVp5s+5TdDfkN6ejrp6ek1\n2pZvExaa2QBgknNuaOnyw0Cxc+7ZE8q8DKQ7594pXc4EBjvnssttSxMWikiNvbfuPR788EGW/3g5\nic0T/Q4nKA4cO0DS75PY/dBumkQ3OWldpE1Y+AXQ1cw6mVkjSi4pO7dcmbnAWChLMrnlE4aISLCM\n7DGSCf0mcP0713O04Kjf4QTFwm8WcmnypackjOryLWk45wqB+4APgXXAu865r81sgplNKC0zH/i3\nmW0EXgF+6le8IlI/TLxsIl0TunLXnLvqxOSGH2z4gGu7Xhu07el6GiIi5RwrPEbgjQCpXVN5fHDk\nTnBY7IpJfD6RZfcso3P8qdOhR1r1lIhIrXRW1FnMvmU2r654lZlrZ/odTrV9seMLEpokVJgwqksT\nFoqInCAtLY2srCxiYmKY/sJ0Rs4eSee4zvyg/Q/8Dq3KPsgKbtUUKGmIiJzku/mlAJo1a8aU/5zC\niHdHsOzHy0iKjaxhYrPXz+bFYS8GdZtKGiIiJyg/v1RcXBzr967n+neuZ/Gdi2naqKnPEXqTuTeT\nvUf2Mih5UFC3qzYNEZETVDS/1C8G/YILW1/IuNnjKHbFnrfl51Tq7655l1E9RtHAgnuYV+8pEREP\njhce58ppV3JFpyv49ZBfe3pNIBAoq+oaNWoUM2eGr1H9gj9dwNQfTT3j5V3Ve0pEJEQaRzXmb6P/\nxvTV05mxeoan1/g1lfqa3Ws4dPwQA5IGBH3bShoiIh61atqKeWPm8X/+8X9Ytm1ZpeX9mkp92lfT\nuOXCW4JeNQWqnhKReurErrUzZsyo0kH9g6wPGD9vPMt+vIzks5NDGGXV5Rfl0+H3HVhy1xLOSzjv\njGVVPSUi4lFNLt167XnX8tDAh/jR2z/i0PFDIYqweuaun0v3lt0rTRjVpaQhIvVSTdsbHhzwIAPa\nD+Cmv97k+XKx4TA1Yyrj+44P2fZVPSUi9VJubi5paWllYzGqo7C4kJEzRxLbOJY3b3gzJG0IVZG1\nL4tBrw1i64NbOSvqrErLV6d6SklDRKQGjhQc4appV3FZ8mU8+8NnK39BCKXNSyOxWSJPXvGkp/LV\nSRoaES4iUgMx0THMGzOPQa8Nom2ztjx4yYO+xLHz0E5mrZtF1v1ZIX0fJQ0RkRpKiElg4R0Lufz1\ny4mJjmFC/wlhj+GF5S9wW8/baBnTMqTvo6QhIhIEyWcn8/HYjwm8GaBJdBPG9h4btvfefnA7UzOm\nsmLCipC/l5KGiEiQnNPiHBbevpAh04bQuGFjRl84Oizv+9injzG+7/iwjBlR0hARCaLurbrzj9v+\nwdC/DOVo4VHu7HNnSN9v5a6VfLDhA7LuC21bxneUNEREgqx32958Ou5Trpl+DbnHcln32jrPo8+r\nMlK9oKiAu+fczVNDnuLss84OxUc5hbrcioiEyJYDW7j6ras5+uVRtryxBah8ttuqzIz7ZPqTLNu+\njPm3zsesSj1nAXW5FRGpVZLPTmbJXUvourkr3AQpW1MqHX3udaR6+qZ0/vTFn8hIy6hWwqguTSMi\nIhJCrZq24utffk2n9p04ettRsguzz1jey8y4WfuyGD1rNG+PfJv2se1DEfZpqXpKRCRM/pzxZx7+\n+GFeGPoCYy4cU60zhKx9WVz91tU8evmj/Ljvj2sUT8RMI2JmLYB3gY7AJuBm59wp10I0s03AQaAI\nKHDOXXSa7SlpiEhE+HLHl9w55046xXXi99f8nnNbnOv5tYs3L2b0rNE8NeQp7k65u8axRNLU6L8C\nPnLOnQd8XLpcEQcEnHMpp0sYIiKRpF+7fnyZ9iUDkwYy4M8DmDBvAmt3rz3ja7Lzsvn5gp9zy6xb\neG34a0FJGNXl15lGJjDYOZdtZm2BdOfc+RWU+xbo75zbV8n2dKYhIhFn35F9vLD8Bf6c8WfaNW/H\nNedcQ882PUlslsixwmN8k/MNizYvYuE3Cxlz4Rh+M+Q3tGjSImjvH0nVUznOufjSxwbs/265XLl/\nAwcoqZ49URkFAAAIc0lEQVR6xTk39TTbU9IQkYhVUFTA0q1L+d9//y/r961nV94uzoo6i6TYJAZ1\nGMQN599AQkxC0N+3VnW5NbOPgLYVrHrkxAXnnDOz0x3xBznndppZK+AjM8t0zi2pqOCkSZPKHgcC\nAQKBQLXiFhEJt+iG0QzuNJjBnQaH9H3S09NJT0+v0Tb8rJ4KOOd2mVki8GlF1VPlXvMEkOece76C\ndTrTEBGpokhqCJ8LjCt9PA6YXb6AmcWYWfPSx02Bq4HVYYtQRERO4WeX25lAMid0uTWzdsBU59y1\nZtYFeL/0JVHAX5xzz5xmezrTEBGpoohpCA82JQ0RkaqLpOopERGJQEoaIiLimZKGiIh4pqQhIiKe\nKWmIiIhnShoiIuKZkoaIiHimpCEiIp4paYiIiGdKGiIi4pmShoiIeKakISIinilpiIiIZ0oaIiLi\nmZKGiIgP0tLSCAQCpKamkpub63c4nilpiIj4ICsri0WLFrFgwQLS0tL8DsczJQ0RER/ExMQA0L9/\nf6ZMmeJzNN7pyn0iIj7Izc0lLS2NKVOmEBcX50sMutyriIh4psu9iohISClpiIiIZ0oaIiLimZKG\niIh45kvSMLNRZrbWzIrMrO8Zyg01s0wz22BmvwxnjCIiciq/zjRWAyOAxacrYGYNgReBoUAPYIyZ\ndQ9PeCIiUpEoP97UOZcJJd29zuAiYKNzblNp2XeA64GvQx2fiIhUrDa3abQHtp6wvK30ORER8UnI\nzjTM7COgbQWrJjrn5nnYRJVG602aNKnscSAQIBAIVOXlIiJ1Xnp6Ounp6TXahq8jws3sU+A/nHMZ\nFawbAExyzg0tXX4YKHbOPVtBWY0IFxGpokgdEX66gL8AuppZJzNrBIwG5oYvLBERKc+vLrcjzGwr\nMAD4wMwWlD7fzsw+AHDOFQL3AR8C64B3nXNqBBcR8ZEmLBQRqacitXpKREQihJKGiIh4pqQhIiKe\nKWmIiIhnShoiIuKZkoaIiHimpCEiIp4paYiIiGdKGiIi4pmShoiIeKakISIinilpiIiIZ0oaIiLi\nmZKGiIh4pqQhIiKeKWmIiIhnShoiIuKZkoaIiHimpCEiIp4paYiIiGdKGiIi4pmShoiIeOZL0jCz\nUWa21syKzKzvGcptMrNVZrbCzD4LZ4wiInIqv840VgMjgMWVlHNAwDmX4py7KPRhRb709HS/Q6g1\ntC++p33xPe2LmvElaTjnMp1zWR6LW0iDqWP0D/E97YvvaV98T/uiZmp7m4YD/tfMvjCz8X4HIyJS\n30WFasNm9hHQtoJVE51z8zxuZpBzbqeZtQI+MrNM59yS4EUpIiJVYc45/97c7FPgP5xzGR7KPgHk\nOeeer2Cdfx9CRCSCOeeq1AQQsjONKqgwYDOLARo65w6ZWVPgauDJispW9UOLiEj1+NXldoSZbQUG\nAB+Y2YLS59uZ2QelxdoCS8xsJbAc+LtzbqEf8YqISAlfq6dERCSy1PbeU2XMbKiZZZrZBjP75WnK\nTC5d/5WZpYQ7xnCpbF+Y2W2l+2CVmf3TzHr5EWc4ePlelJb7gZkVmtmN4YwvnDz+jwRKB8uuMbP0\nMIcYNh7+R1qa2T/MbGXpvrjThzBDzsxeM7NsM1t9hjJVO24652r9DWgIbAQ6AdHASqB7uTKpwPzS\nxxcDy/yO28d9cQlwdunjofV5X5xQ7hPg78BIv+P28XsRB6wFkkqXW/odt4/7YhLwzHf7AdgHRPkd\newj2xWVACrD6NOurfNyMlDONi4CNzrlNzrkC4B3g+nJlhgNvAjjnlgNxZtYmvGGGRaX7wjn3L+fc\ngdLF5UBSmGMMFy/fC4D7gVnAnnAGF2Ze9sWtwHvOuW0Azrm9YY4xXLzsi51AbOnjWGCfc64wjDGG\nhSsZopBzhiJVPm5GStJoD2w9YXlb6XOVlamLB0sv++JE9wDzQxqRfyrdF2bWnpIDxkulT9XVRjwv\n34uuQAsz+7R0wOwdYYsuvLzsi6nABWa2A/gKeCBMsdU2VT5u1oYut154/Ucv3/W2Lh4gPH8mM7sC\nuBsYFLpwfOVlX/wP8CvnnDMzo+5OS+NlX0QDfYErgRjgX2a2zDm3IaSRhZ+XfTERWOmcC5jZOZQM\nHu7tnDsU4thqoyodNyMlaWwHOpyw3IGSjHimMkmlz9U1XvYFpY3fU4GhzrkznZ5GMi/7oh/wTkm+\noCUwzMwKnHNzwxNi2HjZF1uBvc65o8BRM1sM9AbqWtLwsi8GAk8BOOe+MbNvgW7AF2GJsPao8nEz\nUqqnvgC6mlknM2sEjAbK/9PPBcYCmNkAINc5lx3eMMOi0n1hZsnA+8DtzrmNPsQYLpXuC+dcF+dc\nZ+dcZ0raNX5SBxMGePsfmQNcamYNSwfPXgysC3Oc4eBlX2QCVwGU1uF3A/4d1ihrhyofNyPiTMM5\nV2hm9wEfUtIz4lXn3NdmNqF0/SvOuflmlmpmG4HDwF0+hhwyXvYF8DgQD7xU+gu7wNXBqeU97ot6\nweP/SKaZ/QNYBRQDU51zdS5pePxePA28bmZfUfLj+RfOuf2+BR0iZvY2MBhoWTqg+glKqimrfdzU\n4D4REfEsUqqnRESkFlDSEBERz5Q0RETEMyUNERHxTElDREQ8U9IQERHPlDRERMQzJQ0REfFMSUMk\nyEov+PSVmTU2s6alF/np4XdcIsGgEeEiIWBmvwbOApoAW51zz/ockkhQKGmIhICZRVMycd5R4BKn\nfzSpI1Q9JRIaLYGmQDNKzjZE6gSdaYiEgJnNBWYAXYBE59z9PockEhQRMTW6SCQxs7HAcefcO2bW\nAFhqZgHnXLrPoYnUmM40RETEM7VpiIiIZ0oaIiLimZKGiIh4pqQhIiKeKWmIiIhnShoiIuKZkoaI\niHimpCEiIp79f27eIX/Ce2IDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3d072e8>"
      ]
     },
     "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": 36,
   "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": 37,
   "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",
      "-1.18 x  - 0.001318 x  + 0.08745 x  + 0.7389 x  + 3.828 x + 0.4761 x\n",
      "           7            6          5         4             3         2\n",
      " + 0.1282 x + 0.001952 x - 0.6151 x - 10.11 x - 0.0003954 x + 6.686 x - 1.28 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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Gjx+f6/SjRo3illtu4eGHH2bfvn107dr1hHX4/vvvAdi7dy/79++nY8eOhdvIxpiwKNHV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\nePb/AVld6cj/7KWNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f3ec668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hJcyrVGcaFbE9Ohx5SSJ9QzrpG9NZuXMl3Zt1J6VVCn1b96Vn855Uja8adJhS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\n35T/pW39tiW+Tx3hIiKVULU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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c02a048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PPQAMHjyYCy64IG/8uHHjGDlyZN5nw4cP55FHHuHjjz8GIDs7m7vvvhvwjvx79uyZb/pV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\nA2TcvElyGL3ZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f7badd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tm/jla79k5eaVTLpoEj3b9KzkKMOT1KunzKwHcA0wEHgT6A380zn320QDrWzV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\nCUxJQ0REAvv/m5ZHmbVAwoEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1f7bad30>"
      ]
     },
     "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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    "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."
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