{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import\n",
    "import graphlab as gl\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import random\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gl.canvas.set_target('ipynb')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "creating 30 observation between 0,1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to atul9806@yahoo.in and will expire on February 02, 2018.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: C:\\Users\\Atul\\AppData\\Local\\Temp\\graphlab_server_1503201974.log.0\n"
     ]
    }
   ],
   "source": [
    "random.seed(98103)\n",
    "n=30\n",
    "x = gl.SArray([random.random() for i in range(30)]).sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Computing y = sin(4x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = x.apply(lambda v: math.sin(4*v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add random Gaussian noise to y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "random.seed(1)\n",
    "e= gl.SArray([random.gauss(0, 1.0/3.0) for i in range(n)])\n",
    "y = y+e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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",
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       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.161334144502</td>\n",
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       "    <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",
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       "    <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": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = gl.SFrame({'X1': x, 'Y':y})\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_data(data):\n",
    "    plt.plot(data['X1'], data['Y'], 'k.')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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kyEU2KCAAgFSYgQBAhTEDAQDkjgJSUvR4Y+QhQS4S5CIbFBAAQCrMQAAgJ1EUaWVlRVNT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\nIACAVP4fa5lcs6VGucAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x42fa9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_features(data, deg):\n",
    "    data1 = data.copy()\n",
    "    for i in range(1, deg):\n",
    "        data1['X'+str(i+1)] = data1['X'+str(i)]*data1['X1']\n",
    "    return data1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_regression(data, deg):\n",
    "    \n",
    "    model = gl.linear_regression.create(polynomial_features(data,deg),  target='Y', \n",
    "                                        validation_set=None, l2_penalty=0, l1_penalty=0,\n",
    "                                        verbose=False)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_poly_predictions(data, model):\n",
    "    plot_data(data)\n",
    "    \n",
    "    #get polynomial degree\n",
    "    deg = len(model.coefficients['value'])-1\n",
    "    \n",
    "    #creating 200 points on x axis and predicting the Y value\n",
    "    x_pred = gl.SFrame({'X1':[i/200.0 for i in range(200)]})\n",
    "    y_pred = model.predict(polynomial_features(x_pred, deg))\n",
    "    \n",
    "    #plotting\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": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def print_coefficients(model):\n",
    "    deg = len(model.coefficients['value'])-1\n",
    "    coeff = list(model.coefficients['value'])\n",
    "    \n",
    "    #Numpy has a very nice function to print out the polynomial in a pretty way\n",
    "    #but we need the coeff in reverse order for that\n",
    "    print 'Learning polynomial for degree '+str(deg)+':'\n",
    "    coeff.reverse()\n",
    "    print np.poly1d(coeff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a deg 2 polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = polynomial_regression(data, deg=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning polynomial for degree 2:\n",
      "        2\n",
      "-5.129 x + 4.147 x + 0.07471\n"
     ]
    }
   ],
   "source": [
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zzjiPpIT4/7vF5/PxzbJvSDoriZz9OSzZvoTF2xaz5Icl1D+9fmExqd+RTg070aFBB6ok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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4327b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a deg 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning 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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PytUBw50XjeRQ9V5EIlX9k+sz/7r5xMfGc+nrl7Ln4J5jxuibhMFTriksX9Ho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\nzEcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x158e7400>"
      ]
     },
     "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": [
    "### Fitting deg 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning 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"
     ]
    },
    {
     "data": {
      "image/png": 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q6LtRP0AfYDewF3g273djgAfzHj8CxAHbgPVAp2LaKvJKg2HfDtOfbvvUmYsS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\nugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x158e7588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = polynomial_regression(data, deg=16)\n",
    "print_coefficients(model)\n",
    "plot_poly_predictions(data, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Above fit looks pretty wild, here's a clear example of how overfitting is associated with very large magnitute estimated coefficient. **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_ridge_regression(data, deg, l2_penalty=0):\n",
    "    \n",
    "    model = gl.linear_regression.create(polynomial_features(data,deg),  target='Y', \n",
    "                                        validation_set=None, l2_penalty=l2_penalty, l1_penalty=0,\n",
    "                                        verbose=False)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Performace a ridge fit of a deg 16 polynomial using a very small penalty**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning 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, 16, l2_penalty=1e-25)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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q6LtRP0AfYDewF3g273djgAfzHj8CxAHbgPVAp2LaKvJKg2HfDtOfbvvUmYsS\n9N7Te3XNyTX1uYxzTu3vTYfPHNY3z75ZX/fhdXrD4Q1F7rdy5coS21q/fr0ODAzUgA4KCtIbNhTd\nnq9yJg9lhTu5KHjForsGfzNYvx7zutvtuMNXPxcfbf5IP7DgAUPbxIevwkJrvVRr3UJr3Uxr/Ube\n7z7SWk/PezxVax2ltb5Oa91Va/2rK8fZm7SX5tWLHDq5RNOwpnSs15Ev47505VAes2z/MtpPb0/3\nBt359YFf6Xy1a90I+fx1PSdhPKNWe7bb7fQP7c9b698iJT3FoOjKjpT0FEudgZSJpUy01oRNDmPP\nuD1O3yntp30/MX75eLaN2WaJG+NM+XUKr699nTl3zqFXeC/D2vXX9ZyE9RS89XKV4VUYNXgU/+7z\nb7PD8ikTlk/AVsHGP7v/07A2ZSmTEpw+fxqAGpVqOP2am5rcRHpWOjGHYjwVllO01oxfNp5pm6ex\nbtQ6Q4sHOPc/S3cv4RQCLl0qPnVRKtO3TudE2gmzw/IpyenJVKtYzewwLioTBWTP6T00C2tWqjOJ\nABXAox0fZcpvUzwYWfG01jz989MsP7CcdaPWlWol24KX7LnD12+cZFQe/IHZubhk+aCrI7kn6h5e\nX2vOhSpm58JVVuvCKhMFZO9p58c/ChrRegS/HPiFw2cOl7yzwbTW/N+y/2NlwkqW3buMsOAwr8cA\nvnnjJGFNNpuNmJgY1qxZQ0xMDJN6T2L2H7M5dOaQ2aH5jOT0ZKoFyxmIV+WfgZSWrYKNe1vdyweb\nP/BAVEXTWjNhxQSWH1jO8hHLXSoe+ZOH3OXrA+1G5cEfWCEXBbtMa1euzUPtHuKl1S95PQ4r5MIV\nVruMt0wUkNJcgXW5Rzo8wsdbP+Z85nmDoyqc3W7nsbmPsXDXQpbf61rxMNLl/2uUgXbv8+cxqKe7\nPs2C3QvYc3qP2aH4hJT0FBkD8bY9p/e4fPeuZtWb0aFeBz7Z9InH/4jtdjtRQ6J4f/P78AWUzy7v\ncltG9vEadQmnGXy1rzufkWNQVsxFteBqPNn5SSaumujV41oxF86QLiwv01qzL2mfS11Y+ca2HstT\n3z1F957dPTqQPHvNbA5FHoIvYN+WfTLeIMrEGNRjnR5jVcIqfj/+u8eO4Q9ncVprGUT3tsS0RELK\nh1C1YlWX2wg7E8aFlAtkN8/22B/xzr92MmnHJBpva0xQkvvjDb7ax2s0X8+DkWNQVs1FSPkQ/tnt\nnzy/0uUIyUpAAAAZh0lEQVR7xRWrsLM4q+aiOGczz1K+XHnKl3O9Z8Jofl9A9iftp0m1Jm61ce21\n19LocCPoAS0jWho+kJxoT+Tvc/7Ov2/6N7Hfxcp4g7iorIxBPdjuQf448YdHbqXgL2dxyeetNQcE\nnCggSqlHlVLWiroUjtmPUa9KYbcYcZ7NZiP2m1haNGvBUzOfMvSP2H7BTr8v+zGqzSjua3PfFeMN\nrp56+2ofr9H8IQ9GjUFZORcVAiswsedE/rnin4bfdKqwszgr56IoyenWugILnDsDqQ1sUkp9nXf/\ncvPX9SiFxLRE6lSu43Y7VapUYeodU3lx3YtcyLpgQGSQkZ3BwK8H0q5OO57vceXpu69P4hOiNEa0\nHkFiWiLL/zRuqXLwn7O4lPQUSw2ggxMFRGv9PNAMmAlEA3uVUq8ppdzrF/KS42nHDSkgADc2vpGW\nNVoyddNUt9vK0TlEz4+mcvnKTOs7rdBZ8u6cevtiH68nSB4crJ6LwIBAXr7hZf75i/FnIZefxVk9\nF4Wx2hwQcHIMJG+FwuN5P1lANWCeUmqyB2MzRGJaIldVvsqw9ibfNJnX177u1ux0rTVP/vQkR1KP\nMGfgHAIDCr8ti69P4hOitAZFDCIrJ4v5u+abHYrlWG0dLHBuDOQfSqktwGRgHXCt1nos0A6408Px\nue142nHq2Iw5AwGIqBnB450eZ9TCUS7/L+ml1S+x4sAKFg5dSHBQcJH7uXPq7Yt9vJ4geXDwhVwE\nqABe7f0qz698nuycbI8dxxdycTmrTSIE585AwoCBWutbtNbfaK0zAbTWOUA/j0ZngES7sWcgAOO7\njSf1Qirv/vpuqV6nteaFX17g6x1fs/ze5U6djvryJD4hXHFr01upVrEac7bPMTsUS7FiF5bf3w+k\n5r9rEjc2jtqVaxt6rD+T/6TbJ92Y1nca/a/pX+L+GdkZjF08lq3Ht/LT8J+oFVLL0HiE8CdrDq4h\nen40u8btstS8BzM99uNjNK7WmMc7P25ou3I/kCJkZmeSkp5SqvuAOKtxtcYsGrqIBxc9yPc7vy92\n3/1J++n9eW9OnT9FzMgYKR5ClKBHwx40r96cmVtnmh2KZfhqF5bPOnH2BDUr1aRcQDmPtN+ubjuW\nDFvCkz8/yaNLHuWY/dglz588e5JJqybR6eNODGw5kO/u/o7K5St7JJbL+WIfrydIHhx8LRev9n6V\nV2Je4VzmOcPb9rVcgO/OA/FZifZEQwfQC9O+bnu2PLgFjSZyWiTXf3I9g74eRIcZHWg2pRnH7MfY\n+MBGnuzypMcKmRD+qF3ddvRo2IPXYl4zOxRLSD5vrYUUwc/HQBbtXsRHWz5i8T2LvXL8M+lniD0e\ny4mzJ7i6ytW0rt2akPIhXjm2EP7omP0YrT5oxbpR62hRo4XZ4Vxkt9uJi4sjKirKaxe4RE2LYs6d\nc2hVu5Wh7bozBlL4BAQ/YfQckJJUrViVnuE9vXY8IfxdXVtdnu/xPGN/GMuKEStKdVtqI+ToHDYd\n3cSWxC3YL9hpGtaUdjXa0f/m/sTHxxMZGem12e1J55NkDMSbEu3GLGPii3yxj9cTJA8OvpqLcR3H\nkZaRxvQt0w1rs6RcZGRnMPW3qYS/E87IBSP5/fjvnDp3ipnbZtJqRiv+qPkHWcp7izPm6BxOnTtl\nuQtwTD8DUUr1Ad4ht5jN1Fq/Wcg+7wG3AmeBaK11rDNtH087zrW1rzUyXCGElwUGBPJZ/8/o+VlP\n+jTtQ8PQhh493sYjG4meH014aDjfDf6O9nXbX/L87mO76ZTQiTPNztB8c3OvrBCRfD6ZSkGVqBBY\nwePHKg1Tz0CUUgHA+8AtQCQwVCl1zWX73Ao00Vo3A8YAHzrbvre7sKzEF9f68QTJg4Mv5yKiZgTP\ndH2G4d8PJysny+32CstFjs7h5dUv039uf16+4WWWDl96RfEAaFG3BYf+c4h7O99LQHQAmYGZbsdT\nkhNnTxg+l80IZndhdQT2aq0P5s1wnwvccdk+dwCzALTWvwJVlVJOZdKolXiFEOZ7uuvThASF8MIv\nLxje9pn0Mwz4agBL9y9l65it3BV5V7H7V6lShc/v/Zye4T0ZtcD1ZY2cdfLsSWqHSAG5XD2g4KqE\nR/J+V9w+RwvZp1DH046X2TMQX+3vNprkwcHXcxGgApg9YDb/2/4/vt3xrVttFczFzr920unjTtSz\n1WPlfSupa6vrVBtKKd66+S0OnjnIx1s/diuekpxIs+YZiOljIEaLjo4mPDwcgMRNieyM2EmjmxsB\njg9N/umrbPv/dmxsrKXiMXM7NjbWUvG4ur1wyEJu+d8tJMYlElUryq32Vh1YxdRTU3njxjdoktqE\n9THrS93eFwO/oMenPQg9HkrNkJoeef8nzp4gc18mq1atcru9/McJCQm4y9R5IEqpzsAkrXWfvO1n\nyV09/s0C+3wIrNRaf5W3vQvoqbU+UUh7F+eBZGRnEPJaCBnPZ3j90j8hhGf9uPdHohdEs3DIQjpd\n3anUr8/MzmT88vF8v+t75t01j3Z127kVz7PLn+XUuVN8fLtnzkSeW/EcFQIr8K+e/zK8bV9eC2sT\n0FQp1VApVR4YAiy8bJ+FwAi4WHBSCisel8u/f7AUDyH8z63NbuWT2z+h35f9WLpvaaleeyD5AL1n\n9Wb36d1seXCL28UD4Nluz7JozyLiTsa53VZhZAykEFrrbGAc8DMQD8zVWu9USo1RSj2Yt88S4IBS\nah/wEfCwM20np1tv2r83FTxdLcskDw7+lou+zfvy3d3f8cDCBxi/bDznM88Xu/+5zHNMXjeZDjM6\nEJkWyaKhiwgLDjMkltCKoUzoNoHnf7ny1tRGkKuwiqC1Xqq1bqG1bqa1fiPvdx9pracX2Gec1rqp\n1rq11nqrM+0mnU8y7MMhhLCm7g27s23MNvYn76fplKa8veFtDiQfuPh8js4h/mQ8k1ZNoul7Tdl4\nZCMbH9jIkGuHEKCM/fp7sN2DrD+8nt2ndhvaLuQVEAuegfjtWlg/7PmBqZumsmTYEpOjEkJ4w5Zj\nW5jy2xSW7ltKRnYGVSpU4eTZk9QKqcWAawYQ3Saa1le1dro9V9a7mrhyIifOnuDDfk5PV3NK+Dvh\nrBixgiZhTQxtF2QtrEKV9S4sIcqadnXb8Vn/z8jROSSfTyb1Qio1Q2q6dAsFu91O9+7dS73e1SMd\nH6HF+y14+YaXqRlS05W3cQWtde4YiHRheU/+IHpZ5W/93a6SPDiUlVwEqACqV6pOo2qNiiweJeUi\nLi6O+Ph4srJKt95VrZBa3NnyTkPnhaRlpKGU8tq9hErDbwuIjIEIIVwVFRVFZGQkQUFBRERElGq9\nq9FtRzNz28xLZqfb7XY2bNiA3W4vdSxWHf8APy4gyell+wwkf/JQWSd5cJBcOJSUC5vNRkxMDGvW\nrCn1cu0d63UkOCiY1QdXA47usB49etC9e/dSF5ETaScstwpvPv8uIDIGIoRwkc1mo3PnzqW+14dS\nigeue+BiN5ar3WH5rDr+AX5cQMp6F1ZZ6e8uieTBQXLh4OlcDG81nEV7FnEm/Yxb3WEgXVimKOuD\n6EII57gzPlGU6pWq0yu8F/N3zXerOwzyFlKUAuJdZb0LS/q7c0keHCQXDvm5cHd8ojhDIofwVfxX\ngOvdYZB7X3irriruvwVEzkCEECVwd3yiOLe1uI11h9dx+txpt9o5kHKARtUaGRSVsfy2gMgYyCqz\nQ7AEyYOD5MIhPxfujk8Up3L5ytzS5Ba+2/mdW+0cSDlAo1ApIF6Tv6hacFCwyZEIIazM3fGJkgyO\nHMzc+Lkuvz47J5tDZw4RHhpuXFAG8su1sI7Zj9FuejsSn0o0OyQhRBl2PvM8df5Th13jdrk0jnH4\nzGE6ftzRo99lvnw/EI9IPp9cpruvhBDWEBwUTL/m/Zi3Y55Lrz+QcoDG1RobHJVx/LKAJJ1PKvMD\n6NLfnUvy4CC5cPBmLoZEDWFunGvdWAeSrTv+AX5aQMr6JbxCCOu4ucnN7Dy1k8NnDpf6tVYeQAd/\nLSByCa9c859H8uAguXDwZi7KlytP/xb9+Tr+61K/1sqX8IK/FpB0GQMRQljH4KjBfBX/Valmvdvt\ndn4/+Du1y1tzFjr4aQGRMRDp784neXCQXDh4Oxe9G/XmQPIBOt7S0alZ7/kz5H8/9DvPjH7G0Bny\nRvLLApKSnkJoxVCzwxBCCAACAwLpVr0be4L2ODXrPS4ujrhdcVAJ9m7Za+gMeSP5ZQFJvZBKlQpV\nzA7DVNLfnUvy4CC5cDAjFw90foAKbSs4Nes9KiqKZu2agR0iW0YaOkPeSH5ZQNIy0rBVMHZGqRBC\nuKNPyz5UqVeFL378osRZ7zabjRenvUinpp08MkPeKH5ZQOwZdmzlrZlwb5H+7lySBwfJhYMZuSgX\nUI67Iu5id9BupwpCfFI8N7a80bLFA0wsIEqpakqpn5VSu5VSPymlqhaxX4JS6nel1Dal1G/OtG2/\nYLfkDeiFEGVb/tVYzth0bBMd6nXwcETuMfMM5Flguda6BfALMKGI/XKAXlrr67TWHZ1pWLqwpL87\nn+TBQXLhYFYuutbvSkp6Cjv+2lHsflrr3AJSVwpIUe4APs97/DnQv4j9FKWMU7qwhBBWFKACuCvi\nLr6KK/4s5OCZgwQFBFGvSj0vReYaMwtILa31CQCt9XGgVhH7aWCZUmqTUmq0Mw1LF5b0d+eTPDhI\nLhzMzMU9197D7D9mk6Nzitxn09FNtK/b3otRuSbQk40rpZYBBadRKnILwvOF7F7UuvLXa60TlVI1\nyS0kO7XWa4s6ZnR0NCmHUng37V1qhNWgTZs2F09X8z80sl12tmNjYy0Vj5nbsbGxloqnrG737NmT\nasHVeGvOW3Ss17HQ/Tcd20SNEzVYtWqV4cfPf5yQkIC7TLsfiFJqJ7ljGyeUUlcBK7XWLUt4zUTA\nrrV+u4jndUZWBsGvBpP5QiZKubTEvRBCeNSMLTNYsm8J3w/+vtDnb/j8BsZfP54+Tft4PBZfvR/I\nQiA67/F9wILLd1BKVVJKVc57HALcDMQV16g9w46tgk2KhxDCsoZeO5TVCas5mnr0iudSL6SyLXEb\nHes5dc2QqcwsIG8CNymldgM3Am8AKKXqKKUW5+1TG1irlNoGbAQWaa1/Lq7RtIw0GUBH+rvzSR4c\nJBcOZueicvnKDLt2GP/Z8J8rnpuzfQ43Nr7RJxaE9egYSHG01knA3wr5fSLQL+/xAaBNadqVAXQh\nhC94rsdzRE2L4pEOj9AkrAmQe/nuR1s+4s2/vWlydM7xu5no+V1YZV3+wFlZJ3lwkFw4WCEXV1W+\niie7PMn45eMv/m7zsc2cST/D3xpf8X9rS/K7AiJdWEIIX/FE5yeI/yueh394mC3HtjBm8RjGth9L\ngPKNr2bfiLIUpAsrl9l9vFYheXCQXDhYJRfBQcFsvH8jJ86eoPes3jzU/iGe6vqU2WE5zbQxEE+R\nLiwhhC+pWrEq8+6aR7bOJjDAt76STZsH4glKKT31t6lsP7GdD/p9YHY4Qghheb46D8Qj7BfkDEQI\nIbzB7wqIDKLnskofr9kkDw6SCwfJhTH8roDYM2QQXQghvMHvxkBGzR9Fl/pdeKDtA2aHI4QQlidj\nIAWkZUoXlhBCeIPfFRCZB5JL+nhzSR4cJBcOkgtj+F8BkXkgQgjhFX43BtLmwzbMvH0mbeu0NTsc\nIYSwPBkDKcB+Qe6HLoTwDXa7nQ0bNmC3280OxSX+V0CkCwuQPt58kgcHyYWDFXJht9vp3r07PXr0\noHv37j5ZRPyugKRlpMkguhDC8uLi4oiPjycrK4sdO3YQHx9vdkil5ndjIAEvBpD1Qpbc0lYIYWn5\nZyA7duwgIiKCmJgYbDbv9564MwbiW0s/OiEkKESKhxDC8mw2GzExMcTHxxMZGWlK8XCX33VhSfdV\nLiv08VqB5MFBcuFglVzYbDY6d+7sk8UD/LCAyAC6EEJ4h9+NgbT9qC1bHtxidihCCOETZB5IAdKF\nJYQQ3uF3BSQkKMTsECzBKn28ZpM8OEguHCQXxjCtgCilBiml4pRS2UqpItcdUUr1UUrtUkrtUUqN\nL6nd4KBgYwMVQghRKNPGQJRSLYAc4CPgaa311kL2CQD2ADcCx4BNwBCt9a4i2tTDvxvO7AGzPRe4\nEEL4EZ+cB6K13g2gip+00RHYq7U+mLfvXOAOoNACAhAcKGcgQgjhDVYfA6kHHC6wfSTvd0WqFFTJ\nowH5CunjzSV5cJBcOEgujOHRMxCl1DKgdsFfARp4Tmu9yBPHXPH2CiZtnARAaGgobdq0oVevXoDj\nQyPbZWc7NjbWUvGYuR0bG2upeGTbnO38xwkJCbjL9HkgSqmVwFNFjIF0BiZprfvkbT8LaK31m0W0\npV9a9RIv9HzBozELIYS/8Id5IEUFvwloqpRqqJQqDwwBFhbXkFyFJYQQ3mHmZbz9lVKHgc7AYqXU\nj3m/r6OUWgygtc4GxgE/A/HAXK31zuLalTGQXAVPV8syyYOD5MJBcmEMM6/Cmg/ML+T3iUC/AttL\ngRbOtitXYQkhhHeYPgZiJKWUnrt9LoOjBpsdihBC+AR/GAMxjIyBCCGEd/hdAZExkFzSx5tL8uAg\nuXCQXBjD7wqIjIEIIYR3+N0YyNZjW7muznVmhyKEED5BxkAKkC4sIYTwDr8rIDKInkv6eHNJHhwk\nFw6SC2P4XQGRMxAhhPAOvxsDSbuQRkh5uSuhEEI4Q8ZACpAuLCGE8A6/KyAByu/ekkukjzeX5MFB\ncuEguTCGfNsKIYRwid+NgfjT+xFCCE+TMRAhhBBeJwXET0kfby7Jg4PkwkFyYQwpIEIIIVwiYyBC\nCFGGyRiIEEIIr5MC4qekjzeX5MFBcuEguTCGFBAhhBAukTEQIYQow2QMRAghhNeZVkCUUoOUUnFK\nqWylVNti9ktQSv2ulNqmlPrNmzH6MunjzSV5cJBcOEgujGHmGch2YACwuoT9coBeWuvrtNYdPR+W\nf4iNjTU7BEuQPDhILhwkF8YINOvAWuvdAEqpkvreFNLVVmopKSlmh2AJkgcHyYWD5MIYvvDFrIFl\nSqlNSqnRZgcjhBAil0fPQJRSy4DaBX9FbkF4Tmu9yMlmrtdaJyqlapJbSHZqrdcaHau/SUhIMDsE\nS5A8OEguHCQXxjD9Ml6l1ErgKa31Vif2nQjYtdZvF/G8XMMrhBCl5OplvKaNgVym0OCVUpWAAK11\nmlIqBLgZeLGoRlxNghBCiNIz8zLe/kqpw0BnYLFS6se839dRSi3O2602sFYptQ3YCCzSWv9sTsRC\nCCEKMr0LSwghhG/yhauwLqGU6qOU2qWU2qOUGl/EPu8ppfYqpWKVUm28HaO3lJQLpdQ9eZMwf1dK\nrVVKXWtGnN7gzOcib78OSqlMpdRAb8bnTU7+jfTKm5wblzcO6Zec+BupopRamPddsV0pFW1CmF6h\nlJqplDqhlPqjmH1K992ptfaZH3IL3j6gIRAExALXXLbPrcAPeY87ARvNjtvEXHQGquY97lOWc1Fg\nvxXAYmCg2XGb+LmoCsQD9fK2a5gdt4m5mAC8np8H4DQQaHbsHspHN6AN8EcRz5f6u9PXzkA6Anu1\n1ge11pnAXOCOy/a5A5gFoLX+FaiqlKqN/ykxF1rrjVrrM3mbG4F6Xo7RW5z5XAA8CswDTnozOC9z\nJhf3AN9qrY8CaK1PeTlGb3EmFxqw5T22Aae11llejNFrdO70h+Ridin1d6evFZB6wOEC20e48kvx\n8n2OFrKPP3AmFwU9APzo0YjMU2IulFJ1gf5a6w8o4qo/P+HM56I5EKaUWpk3Qfder0XnXc7k4n0g\nQil1DPgd+IeXYrOiUn93WuUyXuFBSqkbgJHknsKWVe8ABfvA/bmIlCQQaAv0BkKADUqpDVrrfeaG\nZYpbgG1a695KqSbkTlZupbVOMzswX+BrBeQo0KDA9tV5v7t8n/ol7OMPnMkFSqlWwHSgj9a6uNNX\nX+ZMLtoDc/PWXqsB3KqUytRaL/RSjN7iTC6OAKe01ulAulJqDdCa3PECf+JMLkYCrwNorfcrpQ4A\n1wCbvRKhtZT6u9PXurA2AU2VUg2VUuWBIcDlXwALgREASqnOQIrW+oR3w/SKEnOhlGoAfAvcq7Xe\nb0KM3lJiLrTWjfN+GpE7DvKwHxYPcO5vZAHQTSlVLm+ybidgp5fj9AZncnEQ+BtAXn9/c+BPr0bp\nXYqiz75L/d3pU2cgWutspdQ44Gdyi99MrfVOpdSY3Kf1dK31EqXU35VS+4Cz5P4Pw+84kwvgBSAM\nmJb3P+9M7YdL4juZi0te4vUgvcTJv5FdSqmfgD+AbGC61nqHiWF7hJOfi1eAzwpc2vp/Wuskk0L2\nKKXUHKAXUF0pdQiYCJTHje9OmUgohBDCJb7WhSWEEMIipIAIIYRwiRQQIYQQLpECIoQQwiVSQIQQ\nQrhECogQQgiXSAERQgjhEikgQgghXCIFRAgPUUq1z7uZV3mlVEjezZsizI5LCKPITHQhPEgp9RIQ\nnPdzWGv9pskhCWEYKSBCeJBSKojcRf3OA121/MEJPyJdWEJ4Vg2gMrl3u6tocixCGErOQITwIKXU\nAuBLoBFQV2v9qMkhCWEYn1rOXQhfkner2Ayt9VylVACwTinVS2u9yuTQhDCEnIEIIYRwiYyBCCGE\ncIkUECGEEC6RAiKEEMIlUkCEEEK4RAqIEEIIl0gBEUII4RIpIEIIIVwiBUQIIYRL/h8p4rGk+iqE\nugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1638f470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Performace a ridge fit of a deg 16 polynomial using a very large penalty**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning 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, 16, l2_penalty=100)\n",
    "print_coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x166eb710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning 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",
      "Learning 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",
      "Learning 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",
      "Learning 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",
      "Learning 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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zR8wNWvGIBFVjqjK0y1CGdhnKngN7mP/7fBZvXcysDbNIzUzlQO4BBKFO9Tq0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\nvGUlitL1ta6c8845DP1kKD0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DdgIrgOGq+msJbeqIz0bwwRUfBC9wY4yJIhF5HYiqrgeQ\n0i/a6AX8pqpbPNtOAy4Dii0gAHFV7QjEGGNCIdzHQJoD24osb/c8V6KasTWDGlCksD5eN8uDl+XC\ny3IRGEE9AhGReUDTok8BCjysqrOCsc9vX/iWCcsnAFCvXj26d+/OgAEDAO+HxpYrz3JSUlJYxePk\nclJSUljFY8vOLBc+Tk1NpaIcvw5ERBYA95YwBtIbmKCqgzzLDwKqqs+W0JY+vvBxHu3/aFBjNsaY\naBEN14GUFPwKoL2ItBKRasBwYGZpDdlZWMYYExpOnsZ7uYhsA3oDs0XkK8/zJ4rIbABVzQfGAd8A\nKcA0VV1XWrs2BuJW9HC1MrM8eFkuvCwXgeHkWVgzgBnFPJ8GDC6yPBfo5Gu7dhaWMcaEhuNjIIEk\nIjptzTSGJQxzOhRjjIkI0TAGEjA2BmKMMaERdQXExkDcrI/XzfLgZbnwslwERtQVEBsDMcaY0Ii6\nMZBVO1dx2omnOR2KMcZEBBsDKcK6sIwxJjSiroDYILqb9fG6WR68LBdelovAiLoCYkcgxhgTGlE3\nBpJ9OJta1eyuhMYY4wsbAynCurCMMSY0oq6AxEjUvSW/WB+vm+XBy3LhZbkIDPu2NcYY45eoGwOJ\npvdjjDHBZmMgxhhjQs4KSJSyPl43y4OX5cLLchEYVkCMMcb4xcZAjDGmErMxEGOMMSFnBSRKWR+v\nm+XBy3LhZbkIDCsgxhhj/GJjIMYYU4nZGIgxxpiQc6yAiMhQEUkWkXwROb2U7VJF5GcRWS0iP4Yy\nxkhmfbxulgcvy4WX5SIwnDwCWQNcAXxfxnYFwABVPU1VewU/rOiQlJTkdAhhwfLgZbnwslwERlWn\ndqyq6wFEpKy+N8G62sotMzPT6RDCguXBy3LhZbkIjEj4YlZgnoisEJGbnQ7GGGOMW1CPQERkHtC0\n6FO4C8LDqjrLx2bOUdU0EWmMu5CsU9XFgY412qSmpjodQliwPHhZLrwsF4Hh+Gm8IrIAuFdVV/mw\n7XjApaovlLDezuE1xphy8vc0XsfGQI5TbPAiUhOIUdVsEakFXAA8VlIj/ibBGGNM+Tl5Gu/lIrIN\n6A3MFpGvPM+fKCKzPZs1BRaLyGpgOTBLVb9xJmJjjDFFOd6FZYwxJjJFwllYxxCRQSLyq4hsEJEH\nStjmZRH5TUSSRKR7qGMMlbJyISLXei7C/FlEFovIKU7EGQq+fC482/UUkVwRGRLK+ELJx9+RAZ6L\nc5M945BRyYffkToiMtPzXbFGREY5EGZIiMjbIrJbRH4pZZvyfXeqasT84C54G4FWQCyQBJx83DYX\nAV96Hp8JLHc6bgdz0Ruo63k8qDLnosh23wKzgSFOx+3g56IukAI09yw3cjpuB3PxEPB0YR6AfUBV\np2MPUj76AN2BX0pYX+7vzkg7AukF/KaqW1Q1F5gGXHbcNpcBUwBU9Qegrog0JfqUmQtVXa6q+z2L\ny4HmIY4xVHz5XADcCUwH9oQyuBDzJRfXAp+q6g4AVd0b4hhDxZdcKBDveRwP7FPVvBDGGDLqvvwh\no5RNyv3dGWkFpDmwrcjydv78pXj8NjuK2SYa+JKLom4CvgpqRM4pMxci0gy4XFVfp4Sz/qKEL5+L\njkADEVnguUD3+pBFF1q+5OIVoIuI7AR+Bv4nRLGFo3J/d4bLabwmiETkXGA07kPYyupFoGgfeDQX\nkbJUBU4HBgK1gGUiskxVNzobliMuBFar6kARaYf7YuVTVTXb6cAiQaQVkB1AyyLLJ3meO36bFmVs\nEw18yQUiciowCRikqqUdvkYyX3JxBjDNM/daI+AiEclV1ZkhijFUfMnFdmCvquYAOSKyCOiGe7wg\nmviSi9HA0wCquklENgMnAz+FJMLwUu7vzkjrwloBtBeRViJSDRgOHP8FMBMYCSAivYFMVd0d2jBD\nosxciEhL4FPgelXd5ECMoVJmLlS1reenDe5xkNujsHiAb78jXwB9RKSK52LdM4F1IY4zFHzJxRbg\nLwCe/v6OwO8hjTK0hJKPvsv93RlRRyCqmi8i44BvcBe/t1V1nYiMda/WSao6R0T+KiIbgQO4/8KI\nOr7kAngUaAC85vnLO1ejcEp8H3NxzEtCHmSI+Pg78quIfA38AuQDk1R1rYNhB4WPn4sngfeKnNr6\nv6qa7lDIQSUiU4EBQEMR2QqMB6pRge9Ou5DQGGOMXyKtC8sYY0yYsAJijDHGL1ZAjDHG+MUKiDHG\nGL9YATHGGOMXKyDGGGP8YgXEGGOMX6yAGGOM8YsVEGOCRETO8NzMq5qI1PLcvKmL03EZEyh2Jbox\nQSQijwNxnp9tqvqswyEZEzBWQIwJIhGJxT2p3yHgbLVfOBNFrAvLmOBqBNTGfbe7Gg7HYkxA2RGI\nMUEkIl8AHwFtgGaqeqfDIRkTMBE1nbsxkcRzq9gjqjpNRGKAJSIyQFUXOhyaMQFhRyDGGGP8YmMg\nxglkDnMAAAA4SURBVBhj/GIFxBhjjF+sgBhjjPGLFRBjjDF+sQJijDHGL1ZAjDHG+MUKiDHGGL9Y\nATHGGOOX/we5glTOg4GIMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x230afef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RjMbVGxMRHkGV8lWoFFaJM5lnSD+XzolzJ9ifsZ8daTvYnrad/Rn7aVW7FZ2i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\neUQLiFJKKY/8f1XEtHQUpJzeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23214208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ILHf//MUfz9uuXTvatW1H1DdRSHehcoPIm97EWwdPHOSuaXdx65e38kzfZ5g2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2354d5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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CzSZTrKQWLVrE3r17KSwsZMKECaxevZr09HSnw4oqNtbtZbnwslyEhp2FFcPWr1/PiBEj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\nPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x234f74e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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46YSfcsVRVxTMtbbS2kQ3s6uAP7v7hmQ2kEnpbKIH9UecbAN1tn7vAFAeohVq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\nFu8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23732748>"
      ]
     },
     "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, 16, l2_penalty=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)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform a ridge fit of a degree polynimial using a \"good\" penalty strength ###\n",
    "\n",
    "We use the leave one out (LOO) cross validation to choose the penalty value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def loo(data, deg, penalty_values):\n",
    "    polynomial_features(data, deg)\n",
    "    \n",
    "    num_folds = len(data)\n",
    "    folds = gl.cross_validation.KFold(data, num_folds)\n",
    "    \n",
    "    #for each value of penalty, fit a model for each fold and compute avg MSE\n",
    "    l2_penalty_mse = []\n",
    "    min_mse=None\n",
    "    best_l2_penalty = None\n",
    "    \n",
    "    for l2_penalty in penalty_values:\n",
    "        next_mse=0.0\n",
    "        for train, validation in folds:\n",
    "            #train model\n",
    "            model = gl.linear_regression.create(train, target='Y',\n",
    "                                               l2_penalty=l2_penalty, \n",
    "                                               validation_set=None, verbose=False)\n",
    "            y_pred = model.predict(validation)\n",
    "            next_mse = next_mse+ ((y_pred -validation['Y'])**2).sum()\n",
    "            \n",
    "        #save sqrd error in list of MSE\n",
    "        next_mse = next_mse/num_folds  #taking avg of mse\n",
    "        l2_penalty_mse.append(next_mse)\n",
    "        #finding out the min and best mse\n",
    "        \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\n",
    "        \n",
    "    \n",
    "    "
   ]
  },
  {
   "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 = np.logspace(-4, 10, num=10)\n",
    "l2_penalty_mse, best_l2_penalty = loo(data, 16, l2_penalty_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot result of estimating LOO for each value lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x23214390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(l2_penalty_values, l2_penalty_mse, 'k-')\n",
    "plt.xlabel('$\\L2_penalty$')\n",
    "plt.ylabel('LOO Cross validation error')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finding the best L2 penalty"
   ]
  },
  {
   "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": [
      "Learning 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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EN43H1a2uxtWtrkadvXUwevhodGjWAWF1wgyLJRDx98PBkwJi+nkgRGY5feE0dpzYgR3H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\nYpbOtUHiOb4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x23237208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_poly_predictions(data, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:gl-env]",
   "language": "python",
   "name": "conda-env-gl-env-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}