scratch pad.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>Sex</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Embarked</th>\n",
       "      <th>Name</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Ticket</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>22.0</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>1</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>NaN</td>\n",
       "      <td>A/5 21171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>2</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>C85</td>\n",
       "      <td>PC 17599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>26.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>1</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>NaN</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>C123</td>\n",
       "      <td>113803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>35.0</td>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>1</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>NaN</td>\n",
       "      <td>373450</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived  Pclass   Age  Sex  SibSp  Parch     Fare  Embarked  \\\n",
       "0         0       3  22.0   -1      1      0   7.2500         1   \n",
       "1         1       1  38.0    1      1      0  71.2833         2   \n",
       "2         1       3  26.0    1      0      0   7.9250         1   \n",
       "3         1       1  35.0    1      1      0  53.1000         1   \n",
       "4         0       3  35.0   -1      0      0   8.0500         1   \n",
       "\n",
       "                                                Name Cabin            Ticket  \n",
       "0                            Braund, Mr. Owen Harris   NaN         A/5 21171  \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...   C85          PC 17599  \n",
       "2                             Heikkinen, Miss. Laina   NaN  STON/O2. 3101282  \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  C123            113803  \n",
       "4                           Allen, Mr. William Henry   NaN            373450  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.optimize as scop\n",
    "import titanic_project as titan\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "features = ['Survived', 'Pclass', 'Age', 'Sex', 'SibSp', 'Parch', 'Fare','Embarked','Name', 'Cabin', 'Ticket']\n",
    "datain = titan.readdata('train.csv', 0.6, 0.6, features)\n",
    "trainset = datain['train']\n",
    "trainset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Survived    0.000000\n",
       "Pclass      0.000000\n",
       "Age         0.207477\n",
       "Sex         0.000000\n",
       "SibSp       0.000000\n",
       "Parch       0.000000\n",
       "Fare        0.000000\n",
       "Embarked    0.000000\n",
       "Name        0.000000\n",
       "Cabin       0.773832\n",
       "Ticket      0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trainset.isnull().sum() / trainset.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Majority of the Cabin information is missing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>Sex</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Embarked</th>\n",
       "      <th>cabclass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Survived</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.270099</td>\n",
       "      <td>-0.094232</td>\n",
       "      <td>0.571729</td>\n",
       "      <td>-0.046940</td>\n",
       "      <td>0.087018</td>\n",
       "      <td>0.205579</td>\n",
       "      <td>0.108864</td>\n",
       "      <td>0.242205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pclass</th>\n",
       "      <td>-0.270099</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.359838</td>\n",
       "      <td>-0.115367</td>\n",
       "      <td>0.101060</td>\n",
       "      <td>0.001775</td>\n",
       "      <td>-0.586986</td>\n",
       "      <td>0.054265</td>\n",
       "      <td>-0.529018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <td>-0.094232</td>\n",
       "      <td>-0.359838</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.091064</td>\n",
       "      <td>-0.353861</td>\n",
       "      <td>-0.238634</td>\n",
       "      <td>0.083645</td>\n",
       "      <td>0.018236</td>\n",
       "      <td>0.137889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex</th>\n",
       "      <td>0.571729</td>\n",
       "      <td>-0.115367</td>\n",
       "      <td>-0.091064</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.070997</td>\n",
       "      <td>0.168163</td>\n",
       "      <td>0.180971</td>\n",
       "      <td>0.115029</td>\n",
       "      <td>0.111086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SibSp</th>\n",
       "      <td>-0.046940</td>\n",
       "      <td>0.101060</td>\n",
       "      <td>-0.353861</td>\n",
       "      <td>0.070997</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.440383</td>\n",
       "      <td>0.181967</td>\n",
       "      <td>-0.041111</td>\n",
       "      <td>-0.065250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Parch</th>\n",
       "      <td>0.087018</td>\n",
       "      <td>0.001775</td>\n",
       "      <td>-0.238634</td>\n",
       "      <td>0.168163</td>\n",
       "      <td>0.440383</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.260505</td>\n",
       "      <td>-0.124586</td>\n",
       "      <td>0.054288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fare</th>\n",
       "      <td>0.205579</td>\n",
       "      <td>-0.586986</td>\n",
       "      <td>0.083645</td>\n",
       "      <td>0.180971</td>\n",
       "      <td>0.181967</td>\n",
       "      <td>0.260505</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.038452</td>\n",
       "      <td>0.325645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Embarked</th>\n",
       "      <td>0.108864</td>\n",
       "      <td>0.054265</td>\n",
       "      <td>0.018236</td>\n",
       "      <td>0.115029</td>\n",
       "      <td>-0.041111</td>\n",
       "      <td>-0.124586</td>\n",
       "      <td>0.038452</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.005776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cabclass</th>\n",
       "      <td>0.242205</td>\n",
       "      <td>-0.529018</td>\n",
       "      <td>0.137889</td>\n",
       "      <td>0.111086</td>\n",
       "      <td>-0.065250</td>\n",
       "      <td>0.054288</td>\n",
       "      <td>0.325645</td>\n",
       "      <td>-0.005776</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Survived    Pclass       Age       Sex     SibSp     Parch  \\\n",
       "Survived  1.000000 -0.270099 -0.094232  0.571729 -0.046940  0.087018   \n",
       "Pclass   -0.270099  1.000000 -0.359838 -0.115367  0.101060  0.001775   \n",
       "Age      -0.094232 -0.359838  1.000000 -0.091064 -0.353861 -0.238634   \n",
       "Sex       0.571729 -0.115367 -0.091064  1.000000  0.070997  0.168163   \n",
       "SibSp    -0.046940  0.101060 -0.353861  0.070997  1.000000  0.440383   \n",
       "Parch     0.087018  0.001775 -0.238634  0.168163  0.440383  1.000000   \n",
       "Fare      0.205579 -0.586986  0.083645  0.180971  0.181967  0.260505   \n",
       "Embarked  0.108864  0.054265  0.018236  0.115029 -0.041111 -0.124586   \n",
       "cabclass  0.242205 -0.529018  0.137889  0.111086 -0.065250  0.054288   \n",
       "\n",
       "              Fare  Embarked  cabclass  \n",
       "Survived  0.205579  0.108864  0.242205  \n",
       "Pclass   -0.586986  0.054265 -0.529018  \n",
       "Age       0.083645  0.018236  0.137889  \n",
       "Sex       0.180971  0.115029  0.111086  \n",
       "SibSp     0.181967 -0.041111 -0.065250  \n",
       "Parch     0.260505 -0.124586  0.054288  \n",
       "Fare      1.000000  0.038452  0.325645  \n",
       "Embarked  0.038452  1.000000 -0.005776  \n",
       "cabclass  0.325645 -0.005776  1.000000  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cabinclass = trainset.Cabin.apply(lambda x: str(x)[0])\n",
    "trainset = trainset.assign(cabclass = cabinclass)\n",
    "ckey = cabinclass.unique()\n",
    "cnum = np.arange(0, ckey.size)\n",
    "ckey2num = dict(zip(ckey, cnum))\n",
    "trainset.cabclass = trainset.cabclass.map(ckey2num)\n",
    "trainset.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>Sex</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Embarked</th>\n",
       "      <th>Name</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Ticket</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>34.5</td>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.8292</td>\n",
       "      <td>3</td>\n",
       "      <td>Kelly, Mr. James</td>\n",
       "      <td>NaN</td>\n",
       "      <td>330911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>47.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.0000</td>\n",
       "      <td>1</td>\n",
       "      <td>Wilkes, Mrs. James (Ellen Needs)</td>\n",
       "      <td>NaN</td>\n",
       "      <td>363272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>62.0</td>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>9.6875</td>\n",
       "      <td>3</td>\n",
       "      <td>Myles, Mr. Thomas Francis</td>\n",
       "      <td>NaN</td>\n",
       "      <td>240276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>27.0</td>\n",
       "      <td>-1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.6625</td>\n",
       "      <td>1</td>\n",
       "      <td>Wirz, Mr. Albert</td>\n",
       "      <td>NaN</td>\n",
       "      <td>315154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>12.2875</td>\n",
       "      <td>1</td>\n",
       "      <td>Hirvonen, Mrs. Alexander (Helga E Lindqvist)</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3101298</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived  Pclass   Age  Sex  SibSp  Parch     Fare  Embarked  \\\n",
       "0       NaN       3  34.5   -1      0      0   7.8292         3   \n",
       "1       NaN       3  47.0    1      1      0   7.0000         1   \n",
       "2       NaN       2  62.0   -1      0      0   9.6875         3   \n",
       "3       NaN       3  27.0   -1      0      0   8.6625         1   \n",
       "4       NaN       3  22.0    1      1      1  12.2875         1   \n",
       "\n",
       "                                           Name Cabin   Ticket  \n",
       "0                              Kelly, Mr. James   NaN   330911  \n",
       "1              Wilkes, Mrs. James (Ellen Needs)   NaN   363272  \n",
       "2                     Myles, Mr. Thomas Francis   NaN   240276  \n",
       "3                              Wirz, Mr. Albert   NaN   315154  \n",
       "4  Hirvonen, Mrs. Alexander (Helga E Lindqvist)   NaN  3101298  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = ['Survived', 'Pclass', 'Age', 'Sex', 'SibSp', 'Parch', 'Fare','Embarked','Name', 'Cabin', 'Ticket']\n",
    "testin = titan.readdata('test.csv', 1, 1, features)\n",
    "testset = testin['train']\n",
    "testset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Survived    1.000000\n",
       "Pclass      0.000000\n",
       "Age         0.205742\n",
       "Sex         0.000000\n",
       "SibSp       0.000000\n",
       "Parch       0.000000\n",
       "Fare        0.002392\n",
       "Embarked    0.000000\n",
       "Name        0.000000\n",
       "Cabin       0.782297\n",
       "Ticket      0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "testset.isnull().sum() / testset.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 5, 'B': 6, 'C': 1, 'D': 4, 'E': 2, 'F': 7, 'G': 3, 'T': 8, 'n': 0}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ckey2num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_predict[y_predict > 0.5] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y_predict[y_predict <= 0.5] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79883381924198249"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(y_predict == y).sum()*1.0/y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "regpara = np.array([0, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]) * 0.5\n",
    "trainerror = np.zeros(shape = (regpara.size, 1))\n",
    "vaderror = np.zeros(shape = (regpara.size, 1))\n",
    "\n",
    "for i in range(0, regpara.size):\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (X, y, regpara[i]))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, X, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvad, yvad, 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0JPbaK7qR0ru7dehQ+bVEpMYpKKR2rFwJTz0F//hHrKO0bl0sonf00XDzzREOhYXa3U2k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\n/x88l0QN9j0g1AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xae69748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(regpara, trainerror, '-b', regpara, vaderror,'-r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "tp = np.linspace(0.2, 0.7, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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koCNxzhURnjAKqmbN4JhjvFrKORc3njAKqmLF4OKLrYSxZ0/Q0TjnigBPGAVZaips2wZT\npwYdiXOuCPCEUZC1awdJSd691jkXF54wCrIyZSxpTJgAhWjEvnMuMXnCKOhSU2H5cli0KOhInHOF\nnCeMgu7ii+33Bx8EG4dzrtDzhFHQHXssXHQRDB4MK1YEHY1zrhDzhFEYPPccZGRA797eluGcixlP\nGIVBcjI8+qiNyXjrraCjcc4VUp4wCovbboMWLeD222HduqCjcc4VQp4wCovixeHll2H7dksazjkX\nZZ4wCpN69eDee2H0aB/M55yLOk8Yhc0//gGnnQZ9+sDWrUFH45wrRDxhFDalSlnV1P/+Z8nDOeei\nxBNGYdSsGdxxB7zwAkyZEnQ0zrlCwhNGYfXQQ1C7NvTqBTt3Bh2Nc64Q8IRRWJUpAy+9BEuXwqBB\nQUfjnCsEPGEUZueeayWM//wH5swJOhrnXAHnCaOw+/e/oVo1uPFG2Ls36GiccwWYJ4zC7uij4fnn\nYeFCSx7OOZdHnjCKgtRU6NrVGsLT0oKOxjlXQHnCKCqefhrKlbOqqX37go7GOVcAecIoKqpWhaee\ngpkzYdiwoKNxzhVAnjCKkquussWW7r7blnV1zrlc8IRRlIhYA7gI3HyzL7bknMsVTxhFzQknwOOP\nw6efwmuvBR2Nc64AiWnCEJH2IvKjiCwVkYHZPN9GRLaKyILQz/2hx48Xka9EZLGI/CAivsBDNPXp\nA61a2XxTa9cGHY1zroCIWcIQkeLAc8BFQD3gShGpl82m01S1UejnodBj6cCdqloPaAHceojXurwo\nVsxmtN25E/r2DToa51wBEcsSRnNgqaouU9U9wGjgkkheqKr/U9V5odvbgTSgeswiLYpOOQUeeADe\nfRfGjg06GudcARDLhFEdWBl2fxXZf+mfKSILRWSSiNTP+qSI1AIaA7NiEWSR9ve/Q6NGcMstsHlz\n0NE45xJc0I3e84CaqtoQeAYYF/6kiJQD3gf6q+q27HYgIjeJyBwRmbN+/fqYB1yolCxpVVPr11t7\nhnPOHUYsE8Zq4Piw+zVCj+2nqttUdUfo9kSgpIhUBhCRkliyeFNVPzjUQVT1RVVNUdWUKlWqRPsc\nCr8mTeCf/4RXX7XqKeecO4RYJozZwEkikiwipYBuwITwDUSkmohI6HbzUDwbQ4+9DKSp6pAYxugA\n7rsPmjeHm26ClStz3t45VyTFLGGoajpwG/AJ1mg9RlV/EJHeItI7tFkXYJGIfAc8DXRTVQVaAdcA\nbcO63HaIVaxFXsmS8OabNv35tdf6XFPOuWyJFqLRvikpKTrHFwrKu1Gj4IYb4IknYMCAoKNxzsWB\niMxV1ZRItg260dslkh49oEsXuPdemDcv6GiccwnGE4Y7QAReeMFmtu3e3Qb2OedciCcMd7CKFW2O\nqZ9+gjvvDDoa51wC8YTh/qptWxvUN3w4TJiQ8/bOuSLBE4bL3sMP2yjwG2+E338POhrnXALwhOGy\nV7o0vPUW7NhhjeEZGUFH5JwLmCcMd2h168KQIfDJJ/Dss0FH45wLWI4JQ0SKi4hPNFRU9e4NF19s\n4zIWLQo6GudcgHJMGKq6D7gyDrG4RCRiExQedZR1td29O+iInHMBibRK6hsReVZEzhaRJpk/MY3M\nJY6qVeGVV+D77+Huu4OOxjkXkBIRbtco9PuhsMcUaBvdcFzCuugiW51v6FC7fcEFQUfknIszn0vK\nRW7XLmjWDDZutNJG5cpBR+Scy6eozyUlIkeJyJDMhYpE5D8iclT+wnQFzhFH2Ky2mzZBz54Q1MXG\nnj3w7bfw5JNwySVQpYqvTe5cHETahjES2A78LfSzDRgVq6BcAjv9dHj8cRg/HkaMiM8xt22zrr33\n3Qdt2lgDfMuW1nMrLQ2qV7c5sNasiU88zhVREVVJicgCVW2U02NB8yqpOMnIgAsvhBkzbFbbU06J\n7v7/9z+YNg2mT7ef776zYxYvDo0bw1lnHfg55hj45Rc46SS45x4boe6ci1huqqQiTRgzgbtUdXro\nfitgsKq2zFekUeYJI47WrIHTToPkZEscpUrlfh+q1h6yciXMnWvJYdo0WLbMni9TBlq0gLPPtuRw\nxhlQvnz2++rcGb75BlassKoz51xEcpMwIu0l1Rt4LazdYjNwXV6Cc4XEccfBSy/BZZfBAw/AY48d\n/HxmMli1yhJCdr9XrTp4XEeVKpYYbrvNfjdqZKsBRqJ/f6sme+stm//KORd1OZYwRKQY0EVVx4jI\nkQCqui0eweWWlzAC0KuXDezr2xc2bz44IWQd5FeihLU31KgBxx9/8O/69eHkk22gYF6oWnXVvn2w\ncGHe9+NcEROLKqk5ke4wSJ4wArBjB5xzjrUzZJcMwm9XrWrtELHyyitw/fXw+edw3nmxO45zhUgs\nEsbjwAbgHeCPzMdVdVNeg4wFTxgByciwK/xYJoNI7N4NJ5wAzZvDhx8GG4tzBUQs2jC6hn7fGvaY\nArVzE5grpIolyKTHSUnQpw88+CD8/LP1nHLORU0ks9UWA65W1eQsP54sXOLp3dt6bD39dNCROFfo\nRDJbbQbgiyG4gqFaNbjyShg1CrZsCToa5wqVSOsSvhCRy0W864lLPOnpWWYpuf12+OMP673lnIua\nSBPGzcAY4E8R2SYi20UkIbvWuqLn/POhdWubQQSw7rXnnAPPPGPZxDkXFZEmjKOAHsC/VPVIoD5w\nfqyCci5Sv/4KU6bYIPGLLoLt20NP9O8Pv/1mg/mcc1ERacJ4DmjBgZX3tuPtGi4BTJhgv594AmbN\ngg4dbGgInTrZtCVDhwYan3OFSaQJ4wxVvRXYDaCqm4E8TB7kXHSNHw/16tnEtW+/DTNnQseO8Mfu\n4tCvnxU9fGyOc1ERacLYKyLFsbEXiEgVICNmUTkXgU2bYOpUWxID4Ior4I03LEd06gQ7u91gkxU+\n9VSwgTpXSESaMJ4GxgJVReQRYDrwaMyici4CEyfa1FGdOx94rFs3eO01+PprSL36SNKvvQHeecfX\nynAuCiJKGKr6JjAAeAz4H9BZVd+NZWDO5WTcODj2WEjJMqnBVVfZtFJffgk3LuiLpqfD888HEqNz\nhUnEczqo6hJVfU5Vn1XVtFgG5VxOdu+GyZMhNTX7mUmuuQZGjoTXZ9RhZpVUdPhwW5PcOZdnMZ0E\nSETai8iPIrJURAZm83wbEdkqIgtCP/dH+lpXtH35pY3Ny2y/yE6PHraK7D/X9Uc2bGDvq2/FLT7n\nCqOYJYxQI/lzwEVAPeBKEamXzabTVLVR6OehXL7WFVHjx0O5ctC27eG3u/FG6D78HBZwOqsHDGXP\nnznPzuycy14sSxjNgaWqukxV9wCjgcNcD0btta6Qy8iw8Rft20Pp0jlvf9PNwqZr+lNr+yL+1fZL\n9u6NfYzOFUaxTBjVgZVh91eFHsvqTBFZKCKTRKR+Ll/riqDZs+H33w/uHZWTti92Y2f5qjSbMZRu\n3fCk4VweBL2QwTygpqo2BJ4BxuV2ByJyk4jMEZE569evj3qALvGMG2drNXXokIsXJSVR5v/60ImP\nWPjBz1x1lU8z5VxuxTJhrAaOD7tfI/TYfqq6TVV3hG5PBEqKSOVIXhu2jxdVNUVVU6pUqRLN+F2C\nGj/e5hasUCGXLwytlTHmrKd59124+mpPGs7lRiwTxmzgJBFJFpFSQDdgQvgGIlItc8p0EWkeimdj\nJK91RdPPP0Na2uF7Rx1SaK2MxvNH8dSDW3jnHbjuOhv855zLWcwShqqmA7cBnwBpwBhV/UFEeotI\n79BmXYBFIvIdNpq8m5psXxurWF3BkTn5bJ4SBuxfK6Nf2Zd57DF46y24/npPGs5FQlQLTzfDlJQU\nneMTzRVqZ59tU5gvWJCPnbRpY/Oi//ILjzxRgnvvhRYtbC6qTp18KXBXtIjIXFVNyXnL4Bu9E0Jm\nrxuX2Natgxkzctc7Klv9+8OKFTBuHPfcA8OG2ZTod94JJ58Mp54Kd90F06Z5G4dz4Yp8wti8Gc49\nF265Jcsyny7hfPSRjcHIc3VUpixrZfTpA99/D8uWwdNPw/HH2wS3rVvDMcfYNCNjxsDWrfk/B+cK\nsiKfMCpUgAcegLFj4V2fTjGhjR8PNWtCo0b53FHx0FoZ33xjxcuQ5GTo2xc++ww2bLAk0bEjTJoE\nXbtC5crQrp0lk2XL8hmDcwWQt2Fg1Q5nngnLl8MPP4D3zk08O3faF/aNN9pS3fm2bRvUqGGzF77x\nxmE33bfPFmb68EP7SQtNvVmvnhVWOnWyNpDixaMQl3Nx5m0YuVSihM1sumWLdaJxieezz2yy2XxX\nR2U68ki4IbK1MooXh7POsmVgFy+GpUvh//0/66X7n//YczfcEKW4nEtgnjBCGjSA++6zZT4zu266\nxDF+PBx1lA3Yi5q+fa34MGxYrl5Wp461m3/xhVVd9ehh3XN9ogFX2HnCCDNwIJx+ujWCbt4cdDQu\n0759VhXUoQOULBnFHdepY1VS+Vgr46ij4P/+z6o133knirE5l4A8YYQpWdKqptatsy6WLjHMmGFX\n8vnuTpud/v1h40YrZeSxPe+00+xC47XXohybcwnGE0YWTZrAP/4Bo0bBJ58EHY0Dq44qWdKmM4+6\nc86Bli3h73+3ARhPPmlXDLl0zTXW4erHH2MQo3MJwhNGNu67D+rWhV69rDONC46qJYy2ba2dOupE\n4PPP7QqhShUYMACqV4cuXeyKIcI5Q7p3t6ViX389BjE6lyA8YWQjKcmqplavttKGC05amvVKilrv\nqOyUKWMt19OnW7/qfv1gyhQr0tSuDQ8+CCtXHnYXxx4L559vCSMjI4axOhcgTxiH0KIF3HGHtYd+\n9VXQ0RRdmT3WUlP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dapUqmjlvxe+ntNaBxf+tFyWn6bJfol8/9ccfNvFkjRoHzwAQa7fc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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbde2e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainerror = np.zeros(shape = (tp.size, 1))\n",
    "vaderror = np.zeros(shape = (tp.size, 1))\n",
    "for i in range(0, tp.size):\n",
    "    datain = titan.readdata('train.csv', tp[i], 0.7, features)\n",
    "    X = np.array(datain['train'].ix[:,1:])\n",
    "    y = np.array(datain['train'].ix[:,0])\n",
    "    Xvad = np.array(datain['validation'].ix[:,1:])\n",
    "    yvad = np.array(datain['validation'].ix[:,0])\n",
    "    nfeature = X.shape[1]\n",
    "    theta0 = np.zeros(shape = (nfeature, 1))\n",
    "    regpara = 1.0\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (X, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, X, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvad, yvad, 0.0)\n",
    "plt.plot(tp, trainerror, '-b', tp, vaderror,'-r')\n",
    "plt.xlabel('proportion of data used for training')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The learning curve suggests at leat 60% of the train.csv dataset is needed to produce a reasonable model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "datain = titan.readdata('train.csv', 0.7, 0.7, features)\n",
    "X = np.array(datain['train'].ix[:,1:])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "Xvad = np.array(datain['validation'].ix[:,1:])\n",
    "yvad = np.array(datain['validation'].ix[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Xq = titan.normdata(titan.xquad(X))\n",
    "Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "\n",
    "nfeature = Xq.shape[1]\n",
    "theta0 = np.zeros(shape = (nfeature, 1))\n",
    "regpara = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fy0r4uzkE1K6wAaiRpWgKfU4bbBYTxgfdVSeCJ2bDGHDb4fc44LCaMdTjYA9gkwnlksDl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\nAgOKB7ASTyOZrq0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cDlCDv4w2iwlbe7vw8jvzOD4Tauix9UIIgUvBaG7ITSFjPu3TrI5O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\nMAxjUNgAMAzDGJT/HwCG8Eixb66uAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbfe16d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara))\n",
    "plt.plot(w[0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above shows the weight of each features used in the 2nd order polynomial model. Some parameters stood out while some have very little contributions to the regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81909547738693467"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict = titan.sigmoid(np.dot(Xq,w[0]))\n",
    "y_predict[y_predict > 0.5] = 1\n",
    "y_predict[y_predict <= 0.5] = 0\n",
    "(y_predict == y).sum()*1.0/y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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58D0wIMJ7cM652DvqKHj4YZtNP3y4je46EmXKZAaWUqUshUzW/GYiFiTq1rWc\nZT172no2detm/qxZ07I6F4BIZ7aPAdKB01S1STB3431VbR/rAkaDz2x3zsXNvn1WW8jL4/ffbahx\nRnDICBS1ahVIkIjazPZAR1VtKyJfAajqryJSKl8ldM65RFCqlD3ymuerCIh0Hsn+YOKgAohIdayG\n4pxzLsFFGkgeBSYDx4rIncAnwF0xK5VzzrkiI6KmLVV9WUTmAz2wEVt9VXVZTEvmnHOuSIh4gLOq\nLgeWx7AszjnniqBIm7acc865sDyQOOecyxcPJM455/LFA4lzzrl88UDinHMuXzyQOOecyxcPJM45\n5/LFA4lzzrl88UDinHMuXzyQOOecyxcPJM455/IlpoFERHqKyAoRWSUiI3I4rr2IpIlI/+B5XRGZ\nJSLfiMhSEfm/kGNHisgGEVkYPHrF8h6cc87lLGar0gfrlzwBnAGsB+aJyFRV/SbMcfcA74fsTgNu\nUNUFIlIRmC8iH4Sc+5Cq3h+rsjvnnItcLGskHYBVqrpGVfcBE4A+YY4bBrwJbMrYoao/qeqCYHsH\nsAyoHcOyOuecy6NYBpLawLqQ5+vJEgxEpDbQDxiT3UVEJBloA3wRsnuYiCwSkXHB+vHOOVeobN0K\n99wDyxJg5aZ4d7Y/DNyoqmGX7RWRClhtZbiqbg92jwEaAK2Bn4AHsjl3iIikikjq5s2bo19y55zL\nxvLl0LEjjBgBTZvC2WfDRx+BarxLFhuxDCQbgLohz+sE+0KlABNEZC3QHxgtIn0BRKQkFkReVtVJ\nGSeo6kZVPRAEn6exJrTDqOpYVU1R1ZTq1atH656ccy5HM2ZAp06wYwdMmwYjR8LcudCtG3ToAK+9\nBmlp8S5ldMUykMwDGopIfREpBQwCpoYeoKr1VTVZVZOBN4BrVHWKiAjwLLBMVR8MPUdEaoU87Qcs\nieE9OOdcxJ58Enr2hLp14csv4ayz4Lbb4Icf7LVt22DQIGjYEB59FHbujHeJoyNmgURV04ChwHSs\ns3yiqi4VkatE5KpcTu8CXAicFmaY770islhEFgHdgetjdQ/OOReJtDT4v/+Dq6+2QPLZZ1CvXubr\nZcvClVdak9eUKVC7th1fty7cfDP89FP8yh4NosW10S5ESkqKpqamxrsYzrliaPt2q2W8+y5cfz3c\ndx8kJeV+3uefwwMPwKRJULIknH8+3HADNGuWt3Ls2mWBatmyQx/PP2/9NXkhIvNVNSW342I2j8S5\nou7tt+HCVm0pAAAacUlEQVS55+zbZKVKcPTRkf0sVSreJXcF5bvvrCN9xQp46ikYMiTyczt3hjfe\ngFWr4OGHYdw4+/d21lnw979D9+4gcvh5W7YcHiyWLbPmswxHHQUnnABNmth2rHmNxLksdu60b5bP\nPGNNEGXK2LfObdtg377czy9TxgJKpUrWdPHPf8KZZ4b/o+CKrs8+g759Yf9+Cwg9euTvelu2wJgx\n8NhjsHkztG0LV11lNY3QgLFlS+Y55cpB48YWMEIff/hDdL7QRFoj8UDiXIi5c+GCC2DNGgsAo0Yd\n+h/y998toGQEltx+zp0La9fat8t77oH27eN2ay6KXn4ZLrsMjj8e/vc/aNQoetfeuxdefNGavVas\nsH1Vqx4eLJo0sS8qJWI4ZCrSQIKqFvtHu3bt1Lmc7NuneuutqklJqvXqqX70UXSu+/vvqo89plq9\nuiqonnuu6rffRufaruAdOKD6r3/ZZ9mtm+qWLbF9r6+/Vt20KXbvkRsgVSP4GxvvCYnOxd2330KX\nLlb7OO88+Ppr6No1OtcuVQqGDoXVq20Y6LRp9k3y6quL/kidRLN7NwwcCHfcAZdfDtOnW00hVkqU\ngJYtoShMg/NA4hKWqnWQtmljHZ4TJ8ILL1inebRVrGgT01avtnbvZ56xztB//9uawVx0/fKL/Y4v\nugj+9S945RVYuBD27Mnb9X76CU49Fd58E+6/H55+2gdVhPI+EpeQNm6EK66w9u0zzrDRMrULMC3o\nqlUWRCZMsG+1//qX1VJKly64MhQ327fDW2/Z7/T9921uR/XqFlQOHLBjRKBBA0tb0qyZ/Wza1Dqs\ny5cPf92vvoLeveHXXy0g9e5dcPcUb97ZHsIDiQv19tvWNLF9u3WADxsW2w7LnMyfb/mYZsywCWx3\n3GHNa3kpj6p9c86YS7B8uY3w6dHD/vgde2z0yx9vu3fDO+9Y8HjnHRsMcfzx1gQ1aJDVNvftg5Ur\n4ZtvDn18+62NuMqQnJwZWDIeP/wAl1xiwf7tt6FVq3jdaXx4IAnhgcSBDeu94QYYOxZat4aXXsr7\n5K9o++ADCygLFtgfq//+12ZIhxsyvH+/1WiWL898ZASOHTsyj6tYESpUsOBSooT1A/XrZ0NW69cv\nuHuLtt9/t/6JCRNg6lQbHluzJgwYYMGjY8fIAvH+/dbUmDXALF9u75GhQwer6dSsGbt7Kqw8kITw\nQOK++MKG9a5ebcN6b7+98DUjpadbP80tt9jw427d4G9/s6aZ0GCxevWhSf9q17YO/MaNM+cUNG4M\ntYKsdF9/DZMn22PxYtvXqlVmUGnZsvDPcUlLgw8/tOAxaZINra5aFc45x4JH166RzSaPxIEDNtHw\nm28sFfygQTYpNRF5IAnhgSRxpaVZc9Edd9gf3BdesE7TwmzfPqs1jRplE9PAZic3bHh4wGjUyGoe\nkVq92nI9TZ5sE+pUrc+gb18LLJ07R+8Pcn6pwpw58OqrNuFvyxab5Nmvn/1x79HDUou42PFAEsID\nSWL67jsYPNhqIxdeaDOGYzEiK1Z27LB8TMnJ1hQV7T+aGzda09DkyTBzpgWwY4+1/pR+/ewPdbxq\nbQsWwPDhFkjKlbMyDRxozX1lysSnTInIA0kIDySJZ9Ys6N/fmoueesraz132tm+3pIOTJ9tclx07\nrH/l7LMtXUxBzcj/+Wdr2nvuOahWzWplF16Y/YgqF1uRBhKfR+KKFVUYPdqG9NaoAfPmeRCJRKVK\n9o1/wgRrTps2zWpz775rnc1nnGHBOVbfO/fuhbvvtua7F1+0QRErV9qcGw8ihZ8HElds7NtnczGu\nvdYyqM6da5P+3JEpXdp+f2PH2vDXe++1TvrTTrORX//7X/QCiqpN8mvaFG66yZrTli61VOxFqRky\n0XkgccXC5s32rfmpp+wP0pQp9i3b5U/FivCPf1jiydGj4ccfrbmrdWurvWRM9MuLhQstmWX//lbr\nmDHDPreGDaNWfFdAYhpIRKSniKwQkVUiMiKH49qLSJqI9M/tXBGpIiIfiMjK4GflWN6DK/wWLbI2\n/C+/tJnHd91VeEYeFRdlylhtb+VKGD/ean+DB9vosWefjSy9foaNG+Gvf7U06UuXWur0r77Kfxp2\nFz8xCyQikgQ8AZwFNAUGi0jTbI67B3g/wnNHADNVtSEwM3juEtSkSXDSSTbMd84c++PmYqdkSctf\ntXSpNUlVqmSpZv7wB3jkEZscmJ3ff7cmq4YNbdW+66/P7AcpiMWXXOzEskbSAVilqmtUdR8wAegT\n5rhhwJvApgjP7QOMD7bHA31jUXiXdz/8AE88YYs5NWtmNYSNG6P7HunpNqnwnHOgeXPrVE/JfdUE\nFyUlSsBf/gKpqfDeezYXZfhwG6p8113w22+Zx6pak1WzZjYZtFs3C0QPPADHHBOvO3DRFMtAUhtY\nF/J8fbDvIBGpDfQDxhzBuTVUNSMB989AjXBvLiJDRCRVRFI3Z8zqcjGRnm5/UG691drO69Wz1Onf\nf2+zj2+5xRbgGTQIPvoo/x21u3bZSKyRI+3b8ezZmbO4XcESsS8MH31kNcL27e3zrlcPbr4ZPv4Y\nTj/d5qWUKWOpTaZOhRNPjHfJXTTFu7P9YeBGVU3Py8nBwith/yyp6lhVTVHVlOpFIaF/EbNnjyXJ\nu/JKqFPH/oDceaeNtLn/flvZbfly+0OyfLmNpJo+3b6NNm9ukwO3bTvy9/3+exs5NHmyfaN9/nmf\noFZYnHyyDRtesMCCy913WxaBhQvh8cft5x//GO9SuliIZcvkBqBuyPM6wb5QKcAEsUQ/1YBeIpKW\ny7kbRaSWqv4kIrU4tEnMxdDGjRY83n7b0nTv3m2T1nr2tJnHvXqFX+inUSN46CELNK+9Zp2r111n\nSQrPO886cdu2zf3958yxpqx9+6wcPXtG/x5d/rVpYznDVqywmkr//lClSrxL5WIqkmUU8/LAgtQa\noD5QCvgaaJbD8c8D/XM7F7gPGBFsjwDuza0svtRu3qSnqy5dqvrf/6p27qwqYkuM1q2reu21qtOn\nq+7dm7drp6aqXn65atmyds0OHVSfe0519+7wx48dq1qypOqJJ6ouX57nW3LOHQEiXGo3pmulA72A\nb4HVwC3BvquAq8IcezCQZHdusL8qNlprJTADqJJbOTyQ5M0//2n/QkA1JUV11CjVhQstwETLr7+q\nPvKIapMm9j6VK6tef73qihX2+r59qkOH2mtnnqn6yy/Re2/nXM4iDSSea8uF9cYbcO65cOmlljn3\nuONi+36q1gwyZowN6U1Ls3kFaWm2/4YbrM3dh4k6V3A8aWMIDyRHZsUKG0rbvLn9ES/otal//tkm\nuY0da9tjx8LFFxdsGZxzHkgO4YEkcjt32gpzmzbZbOM6deJXlgMHbBU7H5XlXHxEGki8ocAdpApD\nhthw3fffj28QAUtz4qlOnCv8PJC4g0aPttXo7rzT8x455yIX7wmJrpCYO9dyH/35zza/wznnIuWB\nxLF5s43QqlPH1jQv4f8qnHNHwJu2EtyBAza7fPNmWx+8sifld84dIQ8kCW7kSFtQ6NlnLbWFc84d\nKW/ESGDvvGOTDS+/HC67LN6lcc4VVR5IEtR338EFF1gt5LHH4l0a51xR5oEkAe3da1l0wVKhlC0b\n3/I454o27yNJQMOG2az1t9+2le2ccy4/vEaSYMaNg2eesVXs/vzneJfGOVcceCBJIF99ZSsV9uhh\n650751w0eCBJEL/+aivVVatmaVA8h5VzLlpiGkhEpKeIrBCRVSJyWOINEekjIotEZKGIpIrIycH+\nRsG+jMd2ERkevDZSRDaEvNYrlvdQHKSnWxr2devg9dfBl7B3zkVTzDrbRSQJeAI4A1gPzBORqar6\nTchhM4Gpqqoi0hKYCDRW1RVA65DrbAAmh5z3kKreH6uyFzf33msd6489Bp06xbs0zrniJpY1kg7A\nKlVdo6r7gAlAn9ADVHWnZi6IUh4ItzhKD2C1qn4fw7IWWx9+aB3rgwdb/4hzzkVbLANJbWBdyPP1\nwb5DiEg/EVkOvAOEm189CHg1y75hQZPYOBHx7FDZ2LABBg2Cxo1tlUGReJfIOVccxb2zXVUnq2pj\noC/wn9DXRKQU0Bt4PWT3GKAB1vT1E/BAuOuKyJCg3yV18+bNMSl7YbZnD/TrZz/ffBMqVIh3iZxz\nxVUsA8kGoG7I8zrBvrBU9WOggYhUC9l9FrBAVTeGHLdRVQ+oajrwNNaEFu56Y1U1RVVTqidY77Iq\n/PWvMG8evPSS1Uiccy5WYhlI5gENRaR+ULMYBEwNPUBEThCxBhcRaQuUBraGHDKYLM1aIlIr5Gk/\nYEkMyl6k3XcfvPyyJWTs0yf3451zLj9iNmpLVdNEZCgwHUgCxqnqUhG5Knj9SeAc4CIR2Q/sAQZm\ndL6LSHlsxNeVWS59r4i0xjrm14Z5PaG9846tcDhwINx8c7xL45xLBJI5aKr4SklJ0dTU1HgXI+a+\n+caG9zZsCHPmQLly8S6Rc64oE5H5qpqS23Fx72x30fHLL9C7twWPKVM8iDjnCo5n/y0G0tJgwACb\nuT57NtStm+spzjkXNR5IioEbboCZM+H556Fz53iXxjmXaLxpq4h75hl49FH4298sn5ZzzhU0DyRF\n2Jw5cM01cOaZcM898S6Ncy5ReSApor7/3pbLrV8fJkyAo7yR0jkXJx5IiqCdO22i4b59MHUqHHNM\nvEvknEtk/j22iElPh0sugcWLYdo0aNQo3iVyziU6DyQ5uPdeeO89OOUUe3TqFP/kh//5jyVhfOAB\n6xtxzrl480CSg4oV4bffLGdVerotT9umTWZgOfnkgl1t8M03YeRIq5Fcf33Bva9zzuXEU6REYPt2\n+Owz+OQTGyn1xRfw++/2WqNGmYHllFMgOTk2634sXAhdukCrVjBrFpQuHf33cM65UJGmSPFAkge/\n/w6pqZmB5dNPreYCULu21VQyAkvz5lAin0MaNm2C9u2tVjRvHtSsmf97cM653HggCRHrpI3p6bBk\niQWVjOCyIVh5pVw5aNDAHn/4w6E/k5Nzr1ns2wc9esD8+Xbttm1jdhvOOXeISAOJ95FEQYkS0LKl\nPa691haWWrvWAspXX8GaNbB6NXzwga1YmEEE6tQ5PMBk/KxSxSYcfvKJzRXxIOKcK4w8kMSAiE0U\nrF8fLrooc78q/PxzZmAJ/fnOO7Bx46HXqVgRduyAW26x9UWcc64w8kBSgESgVi17dOly+Ou7dllQ\nyXisXm39Ib5AlXOuMItpIBGRnsAj2AqJz6jq3Vle7wP8B0gH0oDhqvpJ8NpaYAdwAEjLaKcTkSrA\na0AytkLiAFX9NZb3UVDKl4cWLezhnHNFRcxSpIhIEvAEcBbQFBgsIk2zHDYTaKWqrYHLgGeyvN5d\nVVtn6ewZAcxU1YbB+SNicgPOOeciEstcWx2AVaq6RlX3AROAPqEHqOpOzRw2Vh5bhz03fYDxwfZ4\noG+Uyuuccy4PYhlIagPrQp6vD/YdQkT6ichy4B2sVpJBgRkiMl9EhoTsr6GqPwXbPwM1wr25iAwR\nkVQRSd28eXN+7sM551wO4p79V1Unq2pjrGbxn5CXTg6avM4CrhWRrmHOVbKpxajqWFVNUdWU6gWZ\nx8Q55xJMLAPJBiB09fA6wb6wVPVjoIGIVAuebwh+bgImY01lABtFpBZA8HNT9IvunHMuUrEMJPOA\nhiJSX0RKAYOAqaEHiMgJIpaZSkTaAqWBrSJSXkQqBvvLA38ElgSnTQUyFpW9GHgrhvfgnHMuFzEb\n/quqaSIyFJiODf8dp6pLReSq4PUngXOAi0RkP7AHGKiqKiI1gMlBjDkKeEVV3wsufTcwUUQuB74H\nBsTqHpxzzuXOc20555wLy5M2hhCRzVjtJS+qAVuiWJyiwO85Mfg9J4b83HM9Vc11tFJCBJL8EJHU\nSCJyceL3nBj8nhNDQdxz3If/OuecK9o8kDjnnMsXDyS5GxvvAsSB33Ni8HtODDG/Z+8jcc45ly9e\nI3HOOZcvHkgCItJTRFaIyCoROSw1vYicLyKLRGSxiHwmIq3iUc5oiuCe+wT3vDBIgHlyPMoZTbnd\nc8hx7UUkTUT6F2T5oi2Cz7ibiGwLPuOFInJrPMoZTZF8xsF9LxSRpSLyUUGXMdoi+Jz/EfIZLxGR\nA8HaTtGhqgn/wGberwYaAKWAr4GmWY45CagcbJ8FfBHvchfAPVcgs/mzJbA83uWO9T2HHPchMA3o\nH+9yx/gz7gb8L95lLeB7Pgb4Bjg+eH5svMsd63vOcvzZwIfRLIPXSEwka6d8ppkrMc7FklAWZbFa\nL6Ywy/WeA8OANyn6CUEjvd/iJJJ7Pg+YpKo/wMHEsEXZkX7Og4FXo1kADyQmorVTQlwOvBvTEsVe\nfteLKYpyvWcRqQ30A8YUYLliJdJ/1ycFTZjvikizgilazERyzycClUVkdrDe0UUFVrrYiPjvl4iU\nA3piX5SiJqZrthdHItIdCyRFvr8gEqo6GUug2RVbL+b0OBcp1h4GblTV9CBpaHG3AGvi2SkivYAp\nQMM4lynWjgLaAT2AssDnIjJXVb+Nb7EKxNnAp6r6SzQv6oHERLR2ioi0xNaVP0tVtxZQ2WLliNeL\nEZEGIlJNVYtqrqJI7jkFmBAEkWpALxFJU9UpBVPEqMr1flV1e8j2NBEZnQCf8Xpgq6ruAnaJyMdA\nK6CoBpIj+b88iCg3awHe2R50ARwFrAHqk9lZ1SzLMccDq4CT4l3eArznE8jsbG8b/OOUeJc9lvec\n5fjnKdqd7ZF8xjVDPuMOwA/F/TMGmgAzg2PLYWsdNY932WN5z8FxRwO/AOWjXQavkRDx2im3AlWB\n0cG31TQtwsnfIrznsOvFxK3Q+RThPRcbEd5vf+BqEUnDPuNBxf0zVtVlIvIesAhIB55R1SXZX7Vw\nO4J/1/2A99VqYlHlM9udc87li4/acs45ly8eSJxzzuWLBxLnnHP54oHEOedcvnggcc45ly8eSFyh\nJyKtg1nXGc9755S5N0rveZ2ILBORl3M5braI5DgMXESGB6kp4kpELhGRx8PsLy0iM4LMsAPzeO2+\nItI0D+fl+lmKyHEi8kZeyuUKhs8jcVEhIkmqeiAG1z0KaI3NOJ8GoKpTganRfq8srgFOV9X1UbjW\ncOAlYHcUrhULbQBUtXWkJ4T5vPsC/8Oy6mY99ihVTQt3nUg+S1X9EZvv4gopr5G4HIlIsogsF5GX\ng2/ob2R8uxaRtSJyj4gsAM4Nag5zgwSAk0WkcnDcbBF5JGQthA7B/ioiMiU4fm6QggYRGSkiL4rI\np8CLwChgYMY35tBv1kH5PgyuMVNEjg/2Py8ij4qtHbNGsllXRET+FpRpiYgMD/Y9iaXkfldErs9y\nfFkRmRD8LiZjuZoyXhsjtm7LUhG5Pdh3HXAcMEtEZmV3XJhyHazpiEg1EVkbbDcTkS+D38UiEWkY\n7L8gZP9TIpIU7L9URL4VkS+BLmHe51gsyLUPzv2DiPQQka/E1t4ZJyKlw33eIdc4CegN3Bdyjdki\n8rCIpAL/JyJni8gXwXVniEiN4NzQzzLsZxZ8xktCjp8kIu+JyEoRuTekHJdn3KuIPC1hal8uRuI9\nvd8fhfsBJGPp47sEz8cBfw+21wL/DDl2EXBqsD0KeDjYng08HWx3BZYE248BtwXbpwELg+2RwHyg\nbPD8EuDxkPc5+Bx4G7g42L4MmBJsPw+8jn1Zaoql2c56b+2AxViK/ArAUqBNyL1VC3PO37CZw2Br\ntKQBKcHzKsHPpOCeW4a7VnbHZXmf2SHXrQasDfmdnR9sl8ICWZPg91Ay2D8auAiohaU8qR4c+2no\n7zHkvboRrEkClMEyyZ4YPH8BGB7u885yjecJSScTlH90yPPKZE6AvgJ4IMxnGfYzw/4NLgk5fg2W\n7qMM8D2WZ+q4oHxVgJLAnHD36o/YPLxG4iKxTlU/DbZf4tDMx68BiMjRwDGqmrHa3HgsaGR4FSz5\nI1BJRI4JrvNisP9DoKqIVAqOn6qqeyIoW2fglWD7xSxlm6Kq6ar6DVAjzLknA5NVdZeq7gQmAafk\n8n5dsd8BqroIC54ZBgTf1r8CmmF/DMOJ9LhwPgduFpEbgXrB76gHFhTnicjC4HkDoCMwW1U3q61T\n8VoE128EfKeZmXCzfo6RXCPcsXWA6SKyGPgHdt/h5PaZAcxU1W2quhdrSquH5Qn7SFV/UdX9WEBy\nBcQDiYtE1jw6oc8jzduT0zXCiUY+oN9DtmOaE15E6gN/B3qoakts/ZYyeT0Oq+lk/P88+LqqvoI1\nI+0BponIadi9jVfV1sGjkaqOjNrNHepIPpfQYx/DaggtgCsJf88Q2WcWeswBvK837jyQuEgcLyKd\ng+3zgE+yHqCq24BfRSTjG/2FQOha2AMBxNZ93xYcPwc4P9jfDdiiIWnNQ+wAKmZTts+w1NgE15oT\n4T0RHNtXRMqJSHksqV1u53+M/Q4QkeZY8xZAJewP57ag/f+sbMqf03Gh1mK1DAjpaBaRBsAaVX0U\neCt4/5lA/6C/I6PvqR7wBXCqiFQVkZKE9GvkYAWQLCInBM+zfo7ZyekzAmuKykhtfnEE1ztS87B7\nrSw2QOOcGLyHy4ZHcheJFcC1IjIOa0rIbvXAi4EnxTrj1wCXhry2V0S+wtqvM1ZaHAmME5FF2Iim\n7P7AzAJGBM02/83y2jDgORH5B7A5y3vmSFUXiMjzwJfBrmdU9atcThsTvN8yYBnWl4Oqfh3c33Ks\nj+HTkHPGAu+JyI+q2j2H40LdD0wUkSFYrSXDAOBCsYzMPwN3qeovIvIv4H0RKQHsB65V1bkiMhJr\nDvsNWJjLvaGqe0XkUuD14A/yPCCSrMgTgKeDwQXhBjaMDK75K/AhlvI8alR1g4jchX2Wv2C/323R\nfA+XPc/+63IkIslYR2zzfFxjNtZBnxqlYjl3GBGpoLbS41HAZGxQxOR4lysReNOWc664GBnUWpcA\n32HLBrsC4DUS55xz+eI1Euecc/nigcQ551y+eCBxzjmXLx5InHPO5YsHEuecc/nigcQ551y+/D9g\nbJnm0U8BqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbde2d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainerror = np.zeros(shape = (tp.size, 1))\n",
    "vaderror = np.zeros(shape = (tp.size, 1))\n",
    "for i in range(0, tp.size):\n",
    "    datain = titan.readdata('train.csv', tp[i], 0.7, features)\n",
    "    X = np.array(datain['train'].ix[:,1:])\n",
    "    y = np.array(datain['train'].ix[:,0])\n",
    "    Xvad = np.array(datain['validation'].ix[:,1:])\n",
    "    yvad = np.array(datain['validation'].ix[:,0])\n",
    "    \n",
    "    Xq = titan.normdata(titan.xquad(X))\n",
    "    Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "    Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "    Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "\n",
    "    nfeature = Xq.shape[1]\n",
    "    theta0 = np.zeros(shape = (nfeature, 1))\n",
    "    regpara = 1.0\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, 0.0)\n",
    "plt.plot(tp, trainerror, '-b', tp, vaderror,'-r')\n",
    "plt.xlabel('proportion of data used for training')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The learning curve suggests that with training data more than 50% of the train.csv dataset the model is able to avoid being overfitting, which is a problem with less than 40% of the data used for training. The absolute error for the validation set is smaller compared to the linear model, suggesting adding 2nd order terms improves the performance of the regression. To further reduce the error, we can try more complex set of features or models more advanced than logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81072555205047314"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The 2nd order terms gives an accuracy of 81% in the validation set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WEmXZwlgADJRUKqkdyUXrJ3MXiIjSiBgQEQOAGcDfRsQsklNRYyV1UpImZwIrMqwVpkyB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\nM7OC/H/XEVb8KnWKEgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc99fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regpara = np.array([0, 0.01, 0.03, 0.1, 0.3, 1, 3, 10])\n",
    "trainerror = np.zeros(shape = (regpara.size, 1))\n",
    "vaderror = np.zeros(shape = (regpara.size, 1))\n",
    "\n",
    "for i in range(0, regpara.size):\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara[i]))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, 0.0)\n",
    "plt.plot(regpara, trainerror, '-b', regpara, vaderror,'-r')\n",
    "plt.xlabel('regularization parameter value')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above suggests the optimum regularization parameter to use is 3. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we take Age out of the input features to test the model. A large number of passengers on the list doesn't have age information available. Therefore it is important to find a model works for those passengers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = ['Survived', 'Pclass', 'Sex', 'SibSp', 'Parch', 'Fare','Embarked']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OhUcftbHEnXMuyjxh5ATnn5/9bXTvDh99BOPGwTXXZH97zjl3BO8llSwuucQuSw0efOxl\nnXMuCzxhJIs8eeD222HSJPj556Cjcc4lIU8YyeSWW6z9YsiQoCNxziUhTxjJpFw56NABhg+HHTuC\njsY5l2Q8YSSb7t1h61YYMSLoSJxzScYTRrJp0QLq1rXG7yS6x8Y5FzxPGMlGxM4yZs+GGTOCjsY5\nl0Q8YSSjzp2haFHvYuuciypPGMmoRAm48UYYORL+/DPoaJxzScITRrLq3t2GgR0+POhInHNJwhNG\nsqpf3yraDh58qAS6c85lgyeMZNa9u5VK/+qroCNxziUBTxjJrEMHKFPGG7+dc1HhCSOZFSpk5UI+\n+ABWrw46GudcgvOEkexuvx3277exMpxzLhs8YSS7U06x0uevvAKpqUFH45xLYJ4wcoPu3e2S1Ecf\nBR2Jcy6BecLIDS6/HCpV8sZv51y2eMLIDfLlg65d4YsvrJutc85lgSeM3OLWWy1xvPRS0JE45xKU\nJ4zconx5aNcOhg2DXbuCjsY5l4A8YeQm3btbMcJRo4KOxDmXgDxh5CYtW0LNmt747ZzLEk8YuYkI\ndOsG06fDjz8GHY1zLsF4wshtbroJChf2swznXKZ5wshtjjsOrrsO3n4btmwJOhrnXAKJacIQkdYi\nslhElohIrwyWO1NEUkWkQ9i840RktIgsEpGFItIslrHmKt27w86d8OabQUfinEsgMUsYIpIXGAhc\nCtQGrhOR2kdZ7hlgwhEvPQ+MV9WawOnAwljFmus0bmzT4MGgGnQ0zrkEEcszjCbAElVdqqp7gZFA\n23SW6wGMAdYdmCEiJYFzgVcBVHWvqm6OYay5T/fu8PPPMHly0JE45xJEvhhuuyKwKux5CnBW+AIi\nUhFoB5wPnBn2UjVgPTBMRE4HZgH3qOqOGMabu3TqBP/3f3aWce65QUeTuPbtsxLyM2dC1aqHpmrV\nDj0uVSrQEGMqLc2KWhYrBq1aBR2Ni7FjJozQJaO7VfW/Mdj/AOAhVU0TkSPjagj0UNXpIvI80Av4\nZzrxdQW6AlSuXDkGISapIkWsx9SgQbB2LZxwQtARJZ79++HGG+Hdd+3Lcvly+Ppr2L798OVKljx6\nMqlWDUqUiHfk2acKn30G//iHddEuXBjmz4eTTw46MhdDohFcwxaRH1S1SaY2bI3Uj6nqJaHnDwOo\n6r/DllkGHMgUZYGd2Jf/NGCaqlYNLXcO0EtVL89on40bN9aZM2dmJszcbdEiqFUL+vaF3r2Djiax\nqNqZxSuvwNNPw0MPHZq/aRMsW2YJJHw6MG/HESfKpUrB8cdbEj/WVLhw+vNPO80qEsfDN9/AI4/A\n1KmW8O67zz4/zZrB+PF2v49LGCIyS1UbR7JspJekporIi8C7wMFPu6rOzmCdGUANEakGrAY6AdeH\nL6Cq1cKCfh34WFXHhZ6vEpHTVHUx0Ar4OcJYXaRq1oTzz7eChA89BHnzZm07aWmQJxf10FaFBx+0\nZPHww4eSBdiXZenSNjVqlP66GzcenkCWLbOSLTt32rR9O6xbd+j5gWnPnqPHJGJnOTffbDXDCheO\n9lHDjBmWKL74AipUsMuZt9wCBQrY6z16wIgRcP31GW/HJaxIzzC+Tme2quoFx1jvMuyyU17gNVXt\nKyLdQisPOWLZ17GEMTr0/AxgKFAAWArcrKqbMtqfn2FkwejR0LEj9Oljv1B37LBp+/bD/83o8e7d\nto2334b8+YM+otjr29cuxdxxB7z4Yvx+Ue/fb3/rIxPJ9u12Kez112HFCrsE1qmTfZmfeWb245s/\nH/75Txg3DsqUsSR5xx2HJ6X9+6FFC1i61M5cS5fO3j5d3GTmDCOihJEoPGFkwb59NozrqlWHz8+X\nzxoyixa16cDj9OZt3QpDhtgNgW++mfUzlUTw4ov2S7pzZxg+PGedWaWlwaRJVpF4zBirSly7tp11\ndO4MJ56Yue0tWWI/JEaMgOLF4f77oWdPe5yeefPsrOpvf4NXX8324bj4yEzCQFWPOQElgf7AzND0\nHFAyknXjOTVq1EhdFmzYoLpwoerKlap//qm6Z0/mt/H006qgeuutqmlp0Y8xJxg+3I6xbVvVffuC\njiZjmzervvyyarNmFnPevKpXXKE6Zsyx39+VK1Vvu83WKVxY9aGH7DMSiYcesv19/XW2D8HFBzBT\nI/yOjTRhjAH+BZwcmvoAYyPdSbwmTxgB693bPlL33pt8SWPsWNU8eVRbtVLdtSvoaDJn4UL7Ii9f\n3t6fsmVV77lHdc6cw5f74w+bX6CAav78qnfdpbpmTeb2tWOH6sknq556auL9nXKpWCSMOZHMC3ry\nhBGwtDTVHj3sY9WnT9DRRM+ECfYl2rSp6rZtQUeTdfv2qX7yiWqHDpYQQLVhQ9UXXrBkX6SIJcWb\nb1Zdtizr+5kwwbb96KNRC93FTiwSxvfA2WHPWwDfR7qTeE2eMHKA/ftVu3Sxj1a/fkFHk33ffWdf\npPXr2+W6ZLFhgyWKBg3svQLVa69VXbQoOtvv3NmS0oIF0dmei5nMJIxIe0mdDrwRassA2ATcpKrz\nImooiRNv9M4h9u+3BvD33rMuu127Bh1R1syda4NOlS0LU6Yk782N8+dbJ4eaNaO3zfXrbXu1a9t9\nGzmpc4A7TFTvwxCRPMBpqnq6iJQAUNWt2YzRJbO8eeGtt6zLbbdu1pPqhhtit7/Jk62313nnRa+H\n1i+/wMUXW4+giROTN1kA1K0b/W2WKwf9+lnX3ldfhdtui/4+XNwdM+2rahrwYOjxVk8WLiIFCtg9\nHuedZyVIPvgg+vv45Re4/HKrhdWqld1Hcs89MG1a9qrwrlwJF15o2/jiC6hSJXox5yZdutgZ2gMP\nwB9/BB2Ni4JIzxMnisj9InKSiJQ+MMU0Mpf4CheGDz+0UurXXGNfvtGwZYvdE1Cnjl0qeu45u/zV\nvLldAmvWzO4t6d3bLrdkxtq1liy2boUJE6zkhssaEXs/du+2+zdc4oukoQNYls60NNKGknhN3uid\nQ23caI3GRYqoTpmS9e3s3686dKjq8ceritg9H3/8cfgymzerDhumevHFdh8BqNatq9q3r+rSpRlv\n/88/VU8/3eKcOjXrcbrDPf64vQ+ffBJ0JC4dRLOXFHYW0iLSDQY5ecLIwf74w/rmlyihOmtW5tef\nMkW1USP7yLZooTpz5rHXWbtW9cUXbfkDPYGaNlV9/nnV338/fNlt2+wmtwIFrFuoi549e1Rr11at\nUkV1+/ago3FHyEzCiLSX1I+q2iBGJzlR472kcrhVq+Dss60x/NtvoXZtVK2qyMknwyWXpLNOSooV\n+hsxAipWhGeftTpJma2PtGIFjBxp25k713rtnH++9ea64gornfHVV9bu0q5dVA7XhZkyBc45x8Zg\n6dcv6GjMjh1Won30aGsPK1Qo46lw4aO/dsYZUKNG0EeUJVGvJSUi/bB7McZqJCsExBNGAliyxL44\n8uSByZN5dszJPPiglaX66ScbIgKwOkjPPQf//rd1033wQasKW7Ro9mNYuNASx4gRFs8Br79uDfQu\nNrp1swq/M2ZAw4bBxLBjB3zyibV5ffqpFW88/nhrZ9u3z9pbwqdduw5/npqa/nYLF7Y6Xk0yNQpE\njhCLhLENKALsB3ZjY1ioquaokV88YSSI+fPhvPPYnqcEp22YQsMrKvLtt/Yd8uVEJc+4sdaovXw5\ndOhgZxUHM0kUqcKsWTBqFNSrZ4MhudjZvNnGX6lY0Xqy5YvlgJ9htm8/PEns2mXdpNu3tyrL554b\neXfs1FQrMx+eRDZvtk4d27bB999bh4sEEovig3mAG4FHQ88rA2dFet0rXpO3YSSOqc/P0C0U1+VF\naurulWv11VdV6zFXV1VvaW0N9eqpfvVV0GG6aHv3XXt/+/eP7X62blUdMUK1fXvVQoVsnyecoHrH\nHVYYMTU1uvtbvFi1TBnV6tVV162L7rZjjBiUBhkMDAQWhp6XAmZEupN4TZ4wEsP06dYR6ZYa32pa\n4cKqZ5yhad26ayp5dAOl9Y8+g3J+NViXNWlpqpdfrlq0qOqKFdHd9tatqm+/rXrVVYeSRPnyVkTx\nm2+inySONHWq7bdpUyvCmCBikTBmh/79MWze3Eh3Eq/JE0bOt3ixFUutVi3UUWn8eKs5lDevbrul\nh1YruVGbNYv9/20XoOXL7RfD5Zdnv6pxSop1o27bVrVgQftKq1DBimB++611xY6nsWOty/dVVyXM\nhzgWCWM6NmregcRRLjx55JTJE0bOtmaNatWqquXKqf76a9gLs2ZZCW5Vfest+1T+5z/BxOji5Lnn\n7I0eNSpz6+3caT8y7rtPtU4dPdhdumJF1bvvVp08Of5J4kgvvGAx3XlnQpT5j0XCuAH4EEgB+gKL\ngY6R7iRekyeMnGvzZrsnrmhR1Rkzjr5cWppqu3Z2O8T8+fGLz8XZvn1WWv3EE1U3bTr6cmlpqvPm\nqT77rOpFFx06iyhYUPXCC+2XxZw5Oe+L+f77E+aXT2YSRsRDtIpITaAV1kPqS1VdGNGKceS9pHKm\nPXugdWvriv/JJ1bTLyPr1lnVjypVrNNJbhgmPFeaPdvGHL/tNrsZ54B166zg4+efW3mWA3Woate2\nm3Uuvth6NhUpEkzckUhLg+uvh3ffte7bnToFHdFRRbVa7QGqughYlOWoXK60f7/1Vp00yQrYHitZ\ngHWLHzLEetQ+/TT8858xD9MFoWFDqzHVvz80aGDdqD//HH780V4vXRouusiSxEUXWXHJRJEnj93X\n8/vvdm9P+fJWiDPBRXyGkQj8DCNnUYW774YXX7R78O67L3PrX3+9dZ2fMcNupHVJaPt2O51cudLu\ny2je3H5VXHKJJZFolasPyqZN0KKFJY4pU+xYc5io37iXKDxh5CxPPQWPPGL34D37bObX//NP+/91\n/PGWNAoUiH6MLgf45Rf49Ve7zFS8eNDRRN+KFdC0qV1bnTYNKlQIOqLDZCZh+DBYLiZee82SRefO\n8MwzWdtG6dJWSWLePHj88ejG53KQU0+1cU2SMVmANcZ9+qmdbVx2mZXOT1CeMFzUffyxjcp6ySWW\nOLIzOucVV8DNN1tJqR9+iF6MzsVVgwZW5HD+fGuc27cv6IiyxBOGi6rvv7eyOg0b2v+PaPRw+u9/\nrfzQTTdZGSDnEtIll9gp8xdfWM+wBGwO8IThombhQjsjqFTJus8WKxad7ZYsacNCL1rkPaZcgrv5\nZvjXv2D4cOjTJ+hoMs0ThouKlBT7AVWggPWMLFcuutu/6CKrjt2/v3U2cS5h/fOf8Pe/wxNPwNCh\nQUeTKd5LyjF8uDUsFy2aualQIRvHaNMmG+Ji5UobFylWXWC3b4f69a1NZO7c6AyN4Vwg9u2DNm3s\n8tRHH8GllwYWinerdRFbsgROO826wO/bl7nLqnny2M22InY39/jxNohdLH3zje3jjjvs/g7nEta2\nbXYz3y+/2Ae7UaNAwojJnd4uOf3nP9YwvWwZnHiiNSrv2JG5aedO6/gR62QB9v/rnntgwAAbSbVV\nq9jv07mYKF7cGvuaNbMbFtu0gS5d7NpuvAaXyiQ/w8jFUlJsLO1bb4VBg4KOJnK7dtllr927bVjX\nEjlq3EfnMmnlSusK+NZbsGGDlRG58UZrIK9ZM+a79xv3XET69bMaaQ88EHQkmVO4sLW7pKRkvtyI\nczlO5cqWMFavhrFjbXzx556z4WybNYOXX4YtW4KOEvCEkWutX2+fwxtugGrVgo4m85o2tUT36qt2\nE61zCa9AAbvO+uGH9muoXz9r57j9drtefMMNVsU3LS2wEP2SVC71yCN29/SCBfZDJhHt2WPthJs2\n2Q20pUoFHZFzUaYKM2fCsGFWJn3zZjsjuekma+84+eRs78IvSbkMbdliPYzat0/cZAFQsKBdmlq3\nztoLlywJOiLnokzExgwZNMgq3o4YYe0aTz4Jp5wCLVvaf4IdO+ISjieMXGjgQKt/9sgjQUeSfY0a\n2bAD8+ZBvXp21pSgZXqcy1ihQjYQ0+efWwXcvn2t3aNLF7uuvHdvzEPwS1K5zI4dULWq/WhJpmv/\na9bY2BtjxljieOUVOOusoKNyLsZUYepU+Plnq/iZBTnmkpSItBaRxSKyRER6ZbDcmSKSKiIdjpif\nV0R+FJEWwN/kAAAZj0lEQVSPYxlnbjJ0qPXc69076Eiiq0IFK3Y4bpyNo9GsmSWQbduCjsy5GBKB\ns8/OcrLIrJglDBHJCwwELgVqA9eJSO2jLPcMMCGdzdwD5LixwxPVnj02kNG559pnLBm1bWs/tu66\ny9ppate2TifOueyL5RlGE2CJqi5V1b3ASKBtOsv1AMYA68Jnikgl4HIgsapz5WBvvGGXPJOh7SIj\nJUrACy9YqfVSpSyJdOhgbYbOuayLZcKoCKwKe54SmneQiFQE2gGD01l/APAgEFyn4ySSmmoj3zVq\nZJVfc4OzzoJZs2yo2I8/th5hL70UaDd2lwNt3GjNAHPnwm+/Wa+7XbsScriKmAu6YMkA4CFVTROR\ngzNF5ApgnarOEpGWGW1ARLoCXQEqV64cw1AT26hR9p9h7Fi77Jlb5M8PDz9sZxjdutn05pt202Lt\nv1wgdbnJ7t12Jtq3b/qjpubNa+WeDkzFih3+PHyqWhVat4YyZeJ+GHEVs15SItIMeExVLwk9fxhA\nVf8dtswy4MDXV1lgJ/blfxZwI5AKFAJKAGNVtXNG+/ReUulLS4PTT7d/f/ope0OmJjJVuyx3333W\nGP7wwzYVKhR0ZC6eVK2DxEMPWdHNK6+0NuM9e+xzsX27/ZvelN5rB7px581rbYNt29p9QaecEuxx\nRiozvaRQ1ZhM2NnLUqAaUACYC9TJYPnXgQ7pzG8JfBzJPhs1aqTur8aNUwXVN98MOpKcYd061c6d\n7W9y2mmq33wTdEQuXqZPV23e3N77+vVVv/gi+9vcvVv1hx9UH3lEtV492zao1qmj+vDDqtOmqe7f\nn/39xAowUyP8Xo/Zb01VTQXuAj7HejqNUtUFItJNRLrFar/ucKp2yl2tmt3z42w0wDfftPuf9u61\nkulPPRV0VMGZMgW++y7oKGJr1Sro3NnatX77ze7TmT0bLrww+9suWNDua3rySbuB9LffrJbg8cfb\n8AFNm9qY9F27WltaQo9LH2lmSYTJzzD+6osv7NfOkCFBR5Iz7dih2r69av78qsuWBR1NfG3dqnr7\n7fb5KFhQdfLkoCOKvm3bVP/xD9VChewYe/e2446XjRtV33pLtWNH1WLF7G9dpIjqVVepDhumun59\n/GI5GjJxhhH4l3w0J08Yf9WypWqFCnba7NKXkmJfKDfeGHQk8fPll6pVqqiKqPbsqXrqqaqlS6su\nWhR0ZNGRmqr66quqJ55o33LXX6+6fHmwMe3erTp+vOodd6hWqmRx5cmjevbZqv36BRefJwynqqpT\np9o73L9/0JHkfA8+aF+ec+cGHUlsbdumeued9rmoUUN1yhSb/9tvquXKqZ58suratcHGmF1ffaV6\nxhl2jM2aqX7/fdAR/VVamuqsWaqPPqp6+ul6sN3jrLNUn3tOdcWK+MXiCcOpqurll6uWKaO6fXvQ\nkeR8f/6petxxqldcEXQksfPNN5YQDpxV7Nhx+OvTp6sWLqzapMlfX0sEixertmlj32pVqqiOHGlf\nzIlgyRLVf/9btUGDQ8mjaVP7sbdyZWz3nZmE4cUHk9ScOdCgATzxBPzjH0FHkxieftq62U6enFyl\nU3butNphL7xgnR+GDbPyMOn54AMbw6dtW+t6mjdvbGPbt8/+5l98YSMpFimS+alwYSs6OXCgPe7d\nG3r2TNzu0kuWwHvv2b1Tc+bYvGbN4Jpr7H6iSpWiu78c0a02iMnPMA655hrV4sVVN20KOpLEsWOH\ntfc0b544v0yPZepUu/QEqnfdFdnZ5gsv2PI9esT277B5s+rFF9u+LrxQ9ZJLVM85R7VRI9Vatews\noVw51aJF7azowC/v9KY8eawB/48/YhdvEH75RbVv30OX2MA+nwMGWNtbNOCXpHK3RYvsP1ivXkFH\nknheesn+V3z4YdCRZM/Onar332+fgypVrJE7M+67T2Pa/rV8ud2nkC+fNU4fS1qa6q5ddukwJcW+\nSOfMUf3uO9WJE+15slu8WPXJJw9v82jRQvX557OXPDxh5HJdulivn0RvvAzC3r32i7xOHetpk4im\nTVOtWdP+d99+e9a6ke7fr3r11ZZwRo+ObnzTp6uecIJqyZL2Ze8yb9Ei1SeesJsPwf6We/dmbVue\nMHKx5cvtV1uPHkFHkrhGjbL/Ga+/HnQkmbN7t51V5smjetJJqp9/nr3t7dxpvYwKFbJf8tEwerQ1\nrFerpvrzz9HZZm63cKHq2LFZX98TRi525512E1qse1Yks7Q0u45euXLi3L8yY4adFYHq3/9u7QPR\nsH69avXq1tsuO5d90tJU//MfPdjV1c9+c47MJIxcWoYuOf3xh42o97e/wUknBR1N4hKxHlMrV8Lg\n9Arv5yC7d1svuKZNYdMmG3Z36FAoWTI62y9bFj77zP4ml10G69dnfhv79sHtt8ODD8K118KXX1rZ\nDJd4PGEkkf/+1/5zPvRQ0JEkvgsvtOlopa9zgq+/hvr1LcbOnWH+fLj00ujvp3p1G7UwJcWqsGam\nFtKWLXD55Va7qXdveOcd6/rqEpMnjCTx558waJD11a5RI+hoksO//23jnz/3XNCRHG7jRrjlFrjg\nAti/3+5heP11G10wVpo1g7ffhunTLTnt33/sdZYvh+bNLbG99polttxaWj9Z+NuXA+zebVN2vPii\n1ep/+OHoxOSgcWPo2NESxtq1QUdjHSnfecdGDnzjDejVy8Y3iUbF1Ui0bw/9+9sgXA88kPGy06db\nZdg1a2DCBLj55vjE6GIr6BH3cr29e+0LYPlyOPFEqFLFRu+qUuWvj4sVS38b27fD88/bQDD168cx\n+FzgySftC7JvX7tTOihLl0L37vbl26QJTJwYzHvds6cNOvTf/9pn8+67/7rM6NFw441QoQJ88gnU\nrBn3MF2MeMII2PvvW7Lo2tVO85cvt3Go33/fkkm4MmXSTyjff2+XpB55JP7xJ7tTT4Vbb4UhQ+zL\n8uST47v/1FT7cu7Tx8p0/O9/ljhiXbIjI/37W4eAnj2hcmW46iqbr2rjP/TqZZeixo2zsUdc8vBa\nUgE791xYvRp+/fXw67tpadbracUKSyIrVhz+ePnywxsfW7WyX50u+tassYbf9u3hrbfit98ZM+yH\nxJw51tj84os5p/fbzp3WhjJ3LkyaBA0bWiJ79VUbqGvYsMSt5ZTbeC2pBDF3rvVLf/bZzK+blmZD\njc6YoTpmjOqaNdGPzx3Sq5fd9TxnTuz3tW2bVZPNk0e1fHl7f3Nibau1a636bblyNu4K2GBFOXk4\nUvdXeLXaxHD77dZ4uXo1lC4ddDQuI5s32+WoZs3sunysfPKJ/VJPSbF/n3oqevdUxMIvv9jfZNs2\n6zp7001BR+QyKzNnGN5LKiCbN9vljeuu82SRCI47zq7Nf/opfPtt9Lf/xx92U9sVV0CJEjbO9sCB\nOTtZgLXxTJ9u7W6eLJKfJ4yADB9u14HvuivoSFykevSAihUtcUTrxHzfPrt/pmZNG4viySdh9mxr\nNE4U1atDvXpBR+HiwRNGANLS7EuiaVNrLHSJoXBheOwx65X24YfZ25aq9SKqVw/uvBMaNYJ586yn\nW4ECUQnXuajzhBGAL7+0a7933hl0JC6zunSB006zMheR3O2cnu++sxH92rWznnEffmg93E49Naqh\nOhd1njACMHCg9U/v2DHoSFxm5ctnN/H9/DO8+Wbm1v3lF7j6amjRwm7Ee/llO6u48kor7udcTucJ\nI85WroSPPrKbwQoWDDoalxXt29vd1o8+GllJl7Vr7Wyydm27U/vxx23c5ttuswTkXKLwhBFnQ4bY\nv926BRuHy7oD5c9XrbK2qKPZsQOeeMIahV9+2bpRL1kC//wnFC0av3idixZPGHG0e7f1Vb/ySiup\n4BLX+efDxRfbfRJbthz+WmqqJYjq1e0s5JJLYMECuxR5wgnBxOtcNHjCiKP33rNy2d6VNjk8/bSV\nGu/Xz56rWgN2vXp2NnHKKTB1qhXj8wZtlww8YcTRwIHWw6ZVq6AjcdHQoIHVTerf39qlzjsP2ra1\nbtPvvw+TJyfW/RTOHYsnjDiZNcvuiL3jDu8Rk0yeeMKqCrdpY72gBg+2ke+uusrfZ5d8vI9GnAwc\naA2dXj4huVSvbg3f69bZ2BDFiwcdkXOx4wkjDjZuhBEjLFnk9NpALvNuuy3oCJyLD78kFQfDhlkP\nKb+z2zmXyDxhxNj+/XbJ4pxzvECbcy6xecKIsfHjbQxk70rrnEt0njBibOBAKF/eCs0551wi84QR\nQ7/9ZmcYXbtC/vxBR+Occ9njCSOGBg+GvHktYTjnXKKLacIQkdYislhElohIrwyWO1NEUkWkQ+j5\nSSLytYj8LCILROSeWMYZCzt3wmuv2aWoChWCjsY557IvZglDRPICA4FLgdrAdSJS+yjLPQNMCJud\nCvyfqtYGmgJ3prduTjZyJGza5F1pnXPJI5ZnGE2AJaq6VFX3AiOBtuks1wMYA6w7MENVf1fV2aHH\n24CFQMUYxhpVqvDii1CnDpx7btDROOdcdMQyYVQEVoU9T+GIL30RqQi0AwYfbSMiUhVoAEyPeoQx\nMm0a/PijdaX1ekLOuWQRdKP3AOAhVU1L70URKYadffRU1a1HWaariMwUkZnr16+PYaiRGzgQSpSA\nzp2DjsQ556InlrWkVgMnhT2vFJoXrjEwUuxneFngMhFJVdVxIpIfSxZvq+rYo+1EVV8GXgZo3Lix\nRjH+LFm3zsa9uP12KFYs6Giccy56YpkwZgA1RKQalig6AdeHL6Cq1Q48FpHXgY9DyUKAV4GFqto/\nhjFG3dChVu76jjuCjsQ556IrZpekVDUVuAv4HGu0HqWqC0Skm4gca0TrFsCNwAUiMic0XRarWKMl\nNdXG7G7VCmrWDDoa55yLrpiWN1fVT4FPj5g35CjLdgl7PAVIuObijz+GVavg+eeDjsQ556Iv6Ebv\npDJwIJx0Elx5ZdCROOdc9HnCiJJFi2DiRGvszufDUjnnkpAnjCgZNAgKFPDR15xzycsTRhRs3w7D\nh0PHjnD88UFH45xzseEJIwreegu2bvW6Uc655OZX27Nh61YYPRqeegoaNICmTYOOyDnnYscTRial\npcFXX9klqDFjYNcuOPVUGDDA60Y555KbJ4wI/fqrJYk33rB7LUqWhL/9Dbp0gbPO8mThnEt+njAy\nsGULjBpliWLqVMiTBy6+GJ59Ftq0gcKFg47QOefixxPGEfbvhy+/tCQxdizs3g21asEzz1j1WR89\nzzmXW3nCCFm8+NAlp9WroVQpuOUWu+TUuLFfcnLOuVyfMLZvh4suskGP8uaF1q2tAfvKK6FgwaCj\nc865nCPXJ4xixeCUU+Dqq+GGG6B8+aAjcs65nCnXJwywG++cc85lzO/0ds45FxFPGM455yLiCcM5\n51xEPGE455yLiCcM55xzEfGE4ZxzLiKeMJxzzkXEE4ZzzrmIiKoGHUPUiMh6YEUWVy8LbIhiOInA\njzn55bbjBT/mzKqiquUiWTCpEkZ2iMhMVW0cdBzx5Mec/HLb8YIfcyz5JSnnnHMR8YThnHMuIp4w\nDnk56AAC4Mec/HLb8YIfc8x4G4ZzzrmI+BmGc865iOSqhCEirUVksYgsEZFe6bx+g4jME5GfROQ7\nETk9iDijKYJjbhs65jkiMlNEzg4izmg61jGHLXemiKSKSId4xhcLEbzPLUVkS+h9niMijwYRZzRF\n8j6HjnuOiCwQkW/iHWO0RfA+PxD2Hs8Xkf0iUjpqAahqrpiAvMBvwMlAAWAuUPuIZZoDpUKPLwWm\nBx13HI65GIcuTdYHFgUdd6yPOWy5r4BPgQ5Bxx2H97kl8HHQscb5mI8DfgYqh54fH3TcsT7mI5a/\nEvgqmjHkpjOMJsASVV2qqnuBkUDb8AVU9TtV3RR6Og2oFOcYoy2SY96uoU8XUBRI9EatYx5zSA9g\nDLAunsHFSKTHnEwiOebrgbGquhJAVRP9vc7s+3wdMCKaAeSmhFERWBX2PCU072j+DnwW04hiL6Jj\nFpF2IrII+AS4JU6xxcoxj1lEKgLtgMFxjCuWIv1sNw9dfvxMROrEJ7SYieSYTwVKicgkEZklIn+L\nW3SxEfF3mIgUAVpjP4qixsf0ToeInI8ljIS/nh8JVX0feF9EzgWeAC4MOKRYGwA8pKppIhJ0LPEy\nG7s0s11ELgPGATUCjinW8gGNgFZAYeB7EZmmqr8EG1ZcXAlMVdU/o7nR3JQwVgMnhT2vFJp3GBGp\nDwwFLlXVjXGKLVYiOuYDVPVbETlZRMqqaqLW4onkmBsDI0PJoixwmYikquq4+IQYdcc8ZlXdGvb4\nUxEZlAve5xRgo6ruAHaIyLfA6UCiJozM/H/uRJQvRwG5qtE7H7AUqMahBqM6RyxTGVgCNA863jge\nc3UONXo3DH0AJejYY3nMRyz/Oonf6B3J+3xi2PvcBFiZ7O8zUAv4MrRsEWA+UDfo2GN5zKHlSgJ/\nAkWjHUOuOcNQ1VQRuQv4HOtt8JqqLhCRbqHXhwCPAmWAQaFfn6mawEXMIjzmq4G/icg+YBdwrYY+\ndYkowmNOKhEecwegu4ikYu9zp2R/n1V1oYiMB+YBacBQVZ0fXNTZk4nPdjtggtqZVVT5nd7OOeci\nkpt6STnnnMsGTxjOOeci4gnDOedcRDxhOOeci4gnDOeccxHxhOFyDBE5I3QX8oHnbTKqNhulfd4t\nIgtF5O1jLDdJRDLsYi0iPUMlGQIlIl1E5MV05hcUkYmhSqbXZnHbV4lI7Sysd8z3UkQqiMjorMTl\n4iPX3IfhokNE8qrq/hhsNx9wBnYX9qcAqvoh8GG093WEO4ALVTUlCtvqCbwF7IzCtmKhAYCqnhHp\nCum831cBH2NVYI9cNp+qpqa3nUjeS1Vdg90v4nIoP8NwAIhIVRFZJCJvh35xjz7wa1lElovIMyIy\nG+gYOhOYFipk976IlAotN0lEng+rxd8kNL+0iIwLLT8tVH4FEXlMRN4UkanAm8DjwLUHfgGH/1IO\nxfdVaBtfikjl0PzXReQFsfFLlspRxrYQkftCMc0XkZ6heUOwUtGfici9RyxfWERGhv4W72O1iA68\nNlhs7JAFIvKv0Ly7gQrA1yLy9dGWSyeug2cuIlJWRJaHHtcRkR9Cf4t5IlIjNL9z2PyXRCRvaP7N\nIvKLiPwAtEhnP8djyezM0LqniEgrEflRbPyX10SkYHrvd9g2mgNtgGfDtjFJRAaIyEzgHhG5UkSm\nh7Y7UUROCK0b/l6m+56F3uP5YcuPFZHxIvKriPwnLI6/HzhWEXlF0jmbcjES9O3uPuWMCaiKlTZv\nEXr+GnB/6PFy4MGwZecB54UePw4MCD2eBLwSenwuMD/0+H9An9DjC4A5ocePAbOAwqHnXYAXw/Zz\n8DnwEXBT6PEtwLjQ49eB97AfP7Wx8s9HHlsj4CesfHsxYAHQIOzYyqazzn3YnbRg44SkAo1Dz0uH\n/s0bOub66W3raMsdsZ9JYdstCywP+5vdEHpcAEtYtUJ/h/yh+YOAvwHlsVIf5ULLTg3/O4btqyWh\nMTGAQljl01NDz98Aeqb3fh+xjdcJK6USin9Q2PNSHLoh+FbguXTey3TfM+wzOD9s+aVYmYtCwAqs\njlKFUHylgfzA5PSO1afYTH6G4cKtUtWpocdvcXi13ncBRKQkcJyqHhi9bDiWHA4YAVbIECghIseF\ntvNmaP5XQBkRKRFa/kNV3RVBbM2Ad0KP3zwitnGqmqaqPwMnpLPu2cD7qrpDVbcDY4FzjrG/c7G/\nAao6D0uSB1wT+vX9I1AH+9JLT6TLped7oLeIPARUCf2NWmHJb4aIzAk9Pxk4C5ikquvVxkl4N4Lt\nnwYs00OVW498HyPZRnrLVgI+F5GfgAew407Psd4zgC9VdYuq7sYugVXB6mB9o6p/quo+LPG4OPGE\n4cIdWScm/HmkdWky2kZ6olHvZk/Y45jWKxeRasD9QCtVrY+NIVIoq8thZy4H/h8efF1V38Eu/+wC\nPhWRC7BjG66qZ4Sm01T1sagd3OEy876EL/s/7Bd/PeB20j9miOw9C19mP97mGjhPGC5cZRFpFnp8\nPTDlyAVUdQuwSUQO/EK/EQgfK/laALGxwbeElp8M3BCa3xLYoGHltsNsA4ofJbbvsJLNhLY1OcJj\nIrTsVSJSRESKYsXZjrX+t9jfABGpi12WAiiBfUFuCV2fv/Qo8We0XLjl2FkDhDX4isjJwFJVfQH4\nILT/L4EOofaIA21DVYDpwHkiUkZE8hPW7pCBxUBVEakeen7k+3g0Gb1HYJeQDpTcvimC7WXWDOxY\nS4l1lLg6BvtwR+EZ24VbDNwpIq9hlwCONiLdTcAQsUbxpcDNYa/tFpEfsevLB0bvewx4TUTmYT2I\njvZF8jXQK3S55d9HvNYDGCYiDwDrj9hnhlR1toi8DvwQmjVUVX88xmqDQ/tbCCzE2lpQ1bmh41uE\ntQFMDVvnZWC8iKxR1fMzWC5cP2CUiHTFzkIOuAa4UayK8B/AU6r6p4j8A5ggInmAfcCdqjpNRB7D\nLmNtBuYc49hQ1d0icjPwXuiLdwYQSSXfkcAroUb+9DoYPBba5iZszPRqEWwzYqq6WkSewt7LP7G/\n75Zo7sMdnVerdYD1UMEaROtmYxuTsIbymVEKy7m/EJFiaiMH5gPexzonvB90XLmBX5JyziWax0Jn\nofOBZdhwsy4O/AzDOedcRPwMwznnXEQ8YTjnnIuIJwznnHMR8YThnHMuIp4wnHPORcQThnPOuYj8\nP/v6NNMH/7nFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xac65160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainerror = np.zeros(shape = (tp.size, 1))\n",
    "vaderror = np.zeros(shape = (tp.size, 1))\n",
    "for i in range(0, tp.size):\n",
    "    datain = titan.readdata('train.csv', tp[i], 0.7, features)\n",
    "    X = np.array(datain['train'].ix[:,1:])\n",
    "    y = np.array(datain['train'].ix[:,0])\n",
    "    Xvad = np.array(datain['validation'].ix[:,1:])\n",
    "    yvad = np.array(datain['validation'].ix[:,0])\n",
    "    \n",
    "    Xq = titan.normdata(titan.xquad(X))\n",
    "    Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "    Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "    Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "    \n",
    "    nfeature = Xq.shape[1]\n",
    "    theta0 = np.zeros(shape = (nfeature, 1))\n",
    "    regpara = 1.0\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, 0.0)\n",
    "plt.plot(tp, trainerror, '-b', tp, vaderror,'-r')\n",
    "plt.xlabel('proportion of data used for training')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the error increased without Age information. But still close to the original model. The learning curve suggests adding more data improves the performance on training and validation set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "datain = titan.readdata('train.csv', 0.6, 0.6, features)\n",
    "X = np.array(datain['train'].ix[:,1:])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "Xvad = np.array(datain['validation'].ix[:,1:])\n",
    "yvad = np.array(datain['validation'].ix[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Xq = titan.normdata(titan.xquad(X))\n",
    "Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "\n",
    "nfeature = Xq.shape[1]\n",
    "theta0 = np.zeros(shape = (nfeature, 1))\n",
    "regpara = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MpMy9h+XLw/IGDaBvX/jGN4oConPnCp9SRGopBYYUs38/LFlSPCA+/DA81qJF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\n2NCjHAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc0ba5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regpara = np.array([0, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]) * 0.1\n",
    "trainerror = np.zeros(shape = (regpara.size, 1))\n",
    "vaderror = np.zeros(shape = (regpara.size, 1))\n",
    "\n",
    "for i in range(0, regpara.size):\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara[i]))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, 0.0)\n",
    "plt.plot(regpara, trainerror, '-b', regpara, vaderror,'-r')\n",
    "plt.xlabel('regularization parameter value')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure above sugests that the optimum regularization parameter to use is 0.3. Using this value and the optimum training data set size (60% of total data), we estimate the accuracy of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, 0.3))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79551820728291311"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,theta))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without Age the model accuracy drops by 2-3% in the validation dataset. We try to recover the age information from other information available. After carefully examining the data, it seems a person's title is loosely correlated to the person's age. For example, those with the title 'Master' are usually children and have younger ages. Here I group passengers by sex, social class, and title. For those without age i the data base I assign the median age of the group they belong to as their age.\n",
    "\n",
    "The first step is to parse the name to get titles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = ['Survived', 'Pclass', 'Age', 'Sex', 'SibSp', 'Parch', 'Fare','Embarked','Name']\n",
    "datain = titan.readdata('train.csv', 0.6, 0.6, features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0                                Braund, Mr. Owen Harris\n",
       "1      Cumings, Mrs. John Bradley (Florence Briggs Th...\n",
       "2                                 Heikkinen, Miss. Laina\n",
       "3           Futrelle, Mrs. Jacques Heath (Lily May Peel)\n",
       "4                               Allen, Mr. William Henry\n",
       "5                                       Moran, Mr. James\n",
       "6                                McCarthy, Mr. Timothy J\n",
       "7                         Palsson, Master. Gosta Leonard\n",
       "8      Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg)\n",
       "9                    Nasser, Mrs. Nicholas (Adele Achem)\n",
       "10                       Sandstrom, Miss. Marguerite Rut\n",
       "11                              Bonnell, Miss. Elizabeth\n",
       "12                        Saundercock, Mr. William Henry\n",
       "13                           Andersson, Mr. Anders Johan\n",
       "14                  Vestrom, Miss. Hulda Amanda Adolfina\n",
       "15                      Hewlett, Mrs. (Mary D Kingcome) \n",
       "16                                  Rice, Master. Eugene\n",
       "17                          Williams, Mr. Charles Eugene\n",
       "18     Vander Planke, Mrs. Julius (Emelia Maria Vande...\n",
       "19                               Masselmani, Mrs. Fatima\n",
       "20                                  Fynney, Mr. Joseph J\n",
       "21                                 Beesley, Mr. Lawrence\n",
       "22                           McGowan, Miss. Anna \"Annie\"\n",
       "23                          Sloper, Mr. William Thompson\n",
       "24                         Palsson, Miss. Torborg Danira\n",
       "25     Asplund, Mrs. Carl Oscar (Selma Augusta Emilia...\n",
       "26                               Emir, Mr. Farred Chehab\n",
       "27                        Fortune, Mr. Charles Alexander\n",
       "28                         O'Dwyer, Miss. Ellen \"Nellie\"\n",
       "29                                   Todoroff, Mr. Lalio\n",
       "                             ...                        \n",
       "505           Penasco y Castellana, Mr. Victor de Satode\n",
       "506        Quick, Mrs. Frederick Charles (Jane Richards)\n",
       "507        Bradley, Mr. George (\"George Arthur Brayton\")\n",
       "508                             Olsen, Mr. Henry Margido\n",
       "509                                       Lang, Mr. Fang\n",
       "510                             Daly, Mr. Eugene Patrick\n",
       "511                                    Webber, Mr. James\n",
       "512                            McGough, Mr. James Robert\n",
       "513       Rothschild, Mrs. Martin (Elizabeth L. Barrett)\n",
       "514                                    Coleff, Mr. Satio\n",
       "515                         Walker, Mr. William Anderson\n",
       "516                         Lemore, Mrs. (Amelia Milley)\n",
       "517                                    Ryan, Mr. Patrick\n",
       "518    Angle, Mrs. William A (Florence \"Mary\" Agnes H...\n",
       "519                                  Pavlovic, Mr. Stefo\n",
       "520                                Perreault, Miss. Anne\n",
       "521                                      Vovk, Mr. Janko\n",
       "522                                   Lahoud, Mr. Sarkis\n",
       "523      Hippach, Mrs. Louis Albert (Ida Sophia Fischer)\n",
       "524                                    Kassem, Mr. Fared\n",
       "525                                   Farrell, Mr. James\n",
       "526                                 Ridsdale, Miss. Lucy\n",
       "527                                   Farthing, Mr. John\n",
       "528                            Salonen, Mr. Johan Werner\n",
       "529                          Hocking, Mr. Richard George\n",
       "530                             Quick, Miss. Phyllis May\n",
       "531                                    Toufik, Mr. Nakli\n",
       "532                                 Elias, Mr. Joseph Jr\n",
       "533               Peter, Mrs. Catherine (Catherine Rizk)\n",
       "534                                  Cacic, Miss. Marija\n",
       "Name: Name, dtype: object"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datain['train'].Name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The name entry has a fixed format: First name, comma, title, period, last name, then other names.\n",
    "The split() method for string in Python provides an easy way to split the different parts and retain the title. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "' Mr'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datain['train'].Name[0].split(',')[1].split('.')[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def name2title(name):\n",
    "    return name.split(',')[1].split('.')[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "title = datain['train'].Name.apply(name2title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " Mr        302\n",
       " Miss      121\n",
       " Mrs        76\n",
       " Master     26\n",
       " Dr          3\n",
       " Rev         3\n",
       " Ms          1\n",
       " Don         1\n",
       " Mme         1\n",
       " Major       1\n",
       "Name: Name, dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "title.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of the titles are the common Mr., Miss., Mrs., with a small fraction of Master. There are just a handful of others like Dr., Rev., and Don. Due to the small number of those titles compared to the others, it can be misleading to use them as classifier. Mme (according to Wikipedia) is the abbreviation of a female title (likely married since there is another one for unmarried), therefore it to be treated equal to Mrs. Below we look for the correlation of those titles to other features, especially with Age."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Name\n",
       " Don       40.0\n",
       " Dr        44.0\n",
       " Major     52.0\n",
       " Master     3.5\n",
       " Miss      21.0\n",
       " Mme       24.0\n",
       " Mr        30.0\n",
       " Mrs       35.0\n",
       " Ms        28.0\n",
       " Rev       51.0\n",
       "Name: Age, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = datain['train'].groupby(title)['Age'].median()\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is obvious that each title group has a distinct median age. This is what we wanted. We can then filling those missing ages by mapping their title to the median age of each title group. The same treatmean will be applied to the test set. There might be a different set of unique titles in the test set but I assume the correlation of title to age still holds. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import titanic_project as titan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = ['Survived', 'Pclass', 'Age', 'Sex', 'SibSp', 'Parch', 'Fare', 'Embarked','Name']\n",
    "datain = titan.readdata('train.csv', 0.6, 0.6, features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.array(datain['train'].ix[:,1:-1])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "\n",
    "Xvad = np.array(datain['validation'].ix[:,1:-1])\n",
    "yvad = np.array(datain['validation'].ix[:,0])\n",
    "\n",
    "Xq = titan.normdata(titan.xquad(X))\n",
    "Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "\n",
    "nfeature = Xq.shape[1]\n",
    "theta0 = np.zeros(shape = (nfeature, 1))\n",
    "regpara = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83177570093457942"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict = titan.sigmoid(np.dot(Xq,w[0]))\n",
    "y_predict[y_predict > 0.5] = 1\n",
    "y_predict[y_predict <= 0.5] = 0\n",
    "(y_predict == y).sum()*1.0/y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81792717086834732"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the validation set accuracy is improved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2XtPL0sLQWFKSuQ45BJ5/PgxkeO21YUTc226Dm2+GIv9pJP3Url2b7OzsVJchMXRISjKb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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb566ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regpara = np.array([0, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]) * 0.1\n",
    "trainerror = np.zeros(shape = (regpara.size, 1))\n",
    "vaderror = np.zeros(shape = (regpara.size, 1))\n",
    "trainacu = np.zeros(shape = (regpara.size, 1))\n",
    "vadacu = np.zeros(shape = (regpara.size, 1))\n",
    "\n",
    "for i in range(0, regpara.size):\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara[i]))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, regpara[i])\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, regpara[i])\n",
    "    trainacu[i] = titan.getacu(theta, Xq, y)\n",
    "    vadacu[i] = titan.getacu(theta, Xvadq, yvad)\n",
    "plt.semilogx(regpara, trainerror, '-b', regpara, vaderror,'-r')\n",
    "plt.xlabel('regularization parameter value')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SlkiMiWfPPAN798LTTwcdiSnELJEYE69Wr4bBg+GWWyAx81Q/xuQfSyTGxKu+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\nJiL/D1iJs9xCE+S1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9ce3518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogx(regpara, trainacu, '-b', regpara, vadacu,'-r')\n",
    "plt.xlabel('regularization parameter value')\n",
    "plt.ylabel('accuracy')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.82352941176470584"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the optimum regularization parameter the accuracy for the validation set is 82%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I now take a closer look at the features to further improve the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\theya\\Anaconda2\\lib\\site-packages\\ipykernel\\__main__.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  from ipykernel import kernelapp as app\n"
     ]
    }
   ],
   "source": [
    "age_gender = datain['train'].loc[:,'Age']\n",
    "age_gender[datain['train'].Sex == -1] = -age_gender[datain['train'].Sex == -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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peTvwJHAyMA/4PrCqmfF8j3/8SeB7/L7H32qMrW6+x19nbnm8xw98AXge+CXw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\nnje+6gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb948cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(age_gender[y == 0], datain['train'].Pclass[y == 0], 'xr')\n",
    "plt.plot(age_gender[y == 1], datain['train'].Pclass[y == 1], 'ob')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2XNOJyC4AP1fVp0outWzNLj4J4L9nX7dy3a1cmysRiQK4HMBjAC5Q1Zeyl34B\n4IImlVXOn8N8QMkUnGv1mjcAOAPg69lHSF8TkXY0ue5AIydrBSLyKIB/5nJpL8x6vAvAhwB8EMAh\nEXlPA8tzVaXmPTCPNVpOpbpV9TvZNnsBzABINrK2dwIRWQXzfzn7E1X9tYjkrqmqikjL/EiciFwH\n4BVVPSoiH3Zr02o1ZwUAXAHgU6r6mIj8V5hHLznNqPsdF+yqOljumojEAHxLzYOxH4lIBua/+fBz\nmOfYjvXZcw1RrmYR2QrzieGp7G/a9QAeF5FtaHLNQOW1BgAR+QSA6wAMZNccaIG6K2jl2oqIyDKY\nUE+q6reyp18WkQtV9SURuRDAK+VHaLirAewUkWEAKwF0iEgCrV0zYP7W9qKqPpY9/iZMsDe1bj6K\nKfZtmC9QISKXwnwR8iqA7wK4QURWiMgGAJcA+FHTqsxS1R+r6jpVjapqFOYX2RWq+gu0aM0OEbkW\n5q/dO1X1zYJLrVz3EQCXiMgGEVkO4AaYeluKmD/l7wPwrKpOFlz6LoCPZ19/HMB3Gl1bOap6h6qu\nz/46vgFASlVvRgvXDADZ32unRWRj9tQAgGfQ5LrfcZ/YqzgI4KCIHANwHsDHs58kj4vIIZg3bAbA\nf1LV2SbWWZWqtnrNX4b5yZdHsn/b+KGq/sdWrltVZ0Tkj2B+AskP4KCqHm9yWW6uBrAbwI9F5Mns\nuT0A/hTm8eItMD9BdX2T6qvFUqj5UwCS2T/snwfwH2A+NDetbv7LUyIiy/BRDBGRZRjsRESWYbAT\nEVmGwU5EZBkGOxGRZRjsRESWYbATEVmGwU5EZJn/D3/NlIra3n3UAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5664a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pclass_gender = datain['train'].loc[:,'Pclass']\n",
    "pclass_gender[datain['train'].Sex == 0.5] = -pclass_gender[datain['train'].Sex == 0.5]\n",
    "plt.plot(age_gender[y == 0], pclass_gender[y == 0], 'xr')\n",
    "plt.plot(age_gender[y == 1], pclass_gender[y == 1], 'ob')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above the age is multipled with gender (male = -1, female = 1) and the resulting separation for survived (blue dots) and not survived (red x) is much more clearer than before. The figure above is probably the reason why the second order poly model works better than linear model.\n",
    "\n",
    "In the orginal model Sex is mapped with {'female': 1; 'male': 0.5} but that doesnt give enough separation between the two genders when multiplied to other terms. Below I change the mapping to {'female': 1; 'male': -1}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import titanic_project as titan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "features = ['Survived', 'Pclass', 'Age', 'Sex', 'SibSp', 'Parch', 'Fare', 'Embarked','Name']\n",
    "datain = titan.readdata('train.csv', 0.6, 0.6, features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = np.array(datain['train'].ix[:,1:-1])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "\n",
    "Xvad = np.array(datain['validation'].ix[:,1:-1])\n",
    "yvad = np.array(datain['validation'].ix[:,0])\n",
    "\n",
    "Xq = titan.normdata(titan.xquad(X))\n",
    "Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "Xq = np.concatenate((np.ones(shape=(Xq.shape[0], 1)), Xq), axis = 1)\n",
    "Xvadq = np.concatenate((np.ones(shape=(Xvadq.shape[0], 1)), Xvadq), axis = 1)\n",
    "\n",
    "nfeature = Xq.shape[1]\n",
    "theta0 = np.zeros(shape = (nfeature, 1))\n",
    "regpara = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83738317757009351"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_predict = titan.sigmoid(np.dot(Xq,w[0]))\n",
    "y_predict[y_predict > 0.5] = 1\n",
    "y_predict[y_predict <= 0.5] = 0\n",
    "(y_predict == y).sum()*1.0/y.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.82072829131652658"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SYIiIJFFaCv/7v/GQ+PRTaN4cvvrVEBJ/8zfQuHG2a1m7FBgiIpHDh8uGxPbt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\nqAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4832c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regpara = np.array([0, 0.01, 0.03, 0.1, 0.3, 1, 3, 10]) * 0.1\n",
    "trainerror = np.zeros(shape = (regpara.size, 1))\n",
    "vaderror = np.zeros(shape = (regpara.size, 1))\n",
    "trainacu = np.zeros(shape = (regpara.size, 1))\n",
    "vadacu = np.zeros(shape = (regpara.size, 1))\n",
    "\n",
    "for i in range(0, regpara.size):\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, regpara[i]))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xq, y, regpara[i])\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadq, yvad, regpara[i])\n",
    "    trainacu[i] = titan.getacu(theta, Xq, y)\n",
    "    vadacu[i] = titan.getacu(theta, Xvadq, yvad)\n",
    "plt.semilogx(regpara, trainerror, '-b', regpara, vaderror,'-r')\n",
    "plt.xlabel('regularization parameter value')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xq, y, 0.3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8263305322128851"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadq,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model improves slightly. However, the accuracy is still only around 80%. The figure with age and pclass (above) illustates the difficulties even 2nd order polynomial could face: large overlap of data with different results (survivied or not). For example, female with smaller family size and aged between 20 and 40 has a large number of survived and unsurvived passengers. Decision boundary can not separate them apart easily. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.array(datain['train'].ix[:,1:-1])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "\n",
    "Xvad = np.array(datain['validation'].ix[:,1:-1])\n",
    "yvad = np.array(datain['validation'].ix[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "gender = X[:, 2]\n",
    "vadgender = Xvad[:, 2]\n",
    "X[gender == -1, :] = -X[gender == -1, :]\n",
    "Xvad[vadgender == -1, :] = -Xvad[vadgender == -1, :]\n",
    "X[:, 2] = gender\n",
    "Xvad[:, 2] = vadgender\n",
    "\"\"\"\n",
    "\n",
    "regpara = 1.0\n",
    "order = np.arange(1, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Gm+l1770+08sVXZ5IEl3jxnDCCZ5IEkixYlYQ8pNPbB5Emza2Y+NJJ8FNN/lM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\nLiqeSJxzzkXFE4lzzrmo/D/gJRZ07YZlJAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6189048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trainerror = np.zeros(shape = (order.size, 1))\n",
    "vaderror = np.zeros(shape = (order.size, 1))\n",
    "\n",
    "for i in range(0, order.size):\n",
    "    Xp = titan.normdata(titan.polyx(X, order[i]))\n",
    "    Xvadp = titan.normdata(titan.polyx(Xvad, order[i]))\n",
    "    Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "    Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "    theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xp, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadp, yvad, 0.0)\n",
    "plt.plot(order, trainerror, '-b', order, vaderror,'-r')\n",
    "plt.xlabel('order of polynomials')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It suggests that order = 7 is optimum. With polynomial orders higher than 2 the model becomes highly variant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "order = 7\n",
    "Xp = titan.normdata(titan.polyx(X, order))\n",
    "Xvadp = titan.normdata(titan.polyx(Xvad, order))\n",
    "Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.80112044817927175"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadp,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance is not better than the full second order polynomial terms (including cross terms) where the accuracy was 82.6%. The reason is again illustrated in the crossplots of different features above. When gender is considered as an independent feature the separation between survived and not survived is not great. Higher order polynomials can help but ultimately the feature is not good enough. When combining gender and other features the separation is much better. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.array(datain['train'].ix[:,1:-1])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "\n",
    "Xvad = np.array(datain['validation'].ix[:,1:-1])\n",
    "yvad = np.array(datain['validation'].ix[:,0])\n",
    "gender = X[:, 2]\n",
    "vadgender = Xvad[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gender_age = np.copy(X[:, 1])\n",
    "gender_age[X[:,2] == -1] = -gender_age[X[:,2] == -1]\n",
    "X = np.concatenate((X, gender_age.reshape(X.shape[0], 1)), axis = 1)\n",
    "gender_age = np.copy(Xvad[:, 1])\n",
    "gender_age[Xvad[:,2] == -1] = -gender_age[Xvad[:,2] == -1]\n",
    "Xvad = np.concatenate((Xvad, gender_age.reshape(Xvad.shape[0], 1)), axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g5jTExrq1yVu3hmuvdcmkWgE6q/3vf8HvKtaudWtXBKpZ0yWIiy8+NWHUqmVV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\naAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5c16d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regpara = 1.0\n",
    "order = np.arange(1, 10)\n",
    "trainerror = np.zeros(shape = (order.size, 1))\n",
    "vaderror = np.zeros(shape = (order.size, 1))\n",
    "\n",
    "for i in range(0, order.size):\n",
    "    Xp = titan.normdata(titan.polyx(X, order[i]))\n",
    "    Xvadp = titan.normdata(titan.polyx(Xvad, order[i]))\n",
    "    Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "    Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "    theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xp, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadp, yvad, 0.0)\n",
    "plt.plot(order, trainerror, '-b', order, vaderror,'-r')\n",
    "plt.xlabel('order of polynomials')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "order = 2\n",
    "Xp = titan.normdata(titan.polyx(X, order))\n",
    "Xvadp = titan.normdata(titan.polyx(Xvad, order))\n",
    "Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.79271708683473385"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadp,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y2RtmtsrMJmZYPtLMlprZEjMrNLOT0pb90MyWmdlyM7sqzjpFRKRisQWGmeUA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc144f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array(datain['train'].ix[:,1:-1])\n",
    "y = np.array(datain['train'].ix[:,0])\n",
    "Xvad = np.array(datain['validation'].ix[:,1:-1])\n",
    "yvad = np.array(datain['validation'].ix[:,0])\n",
    "\n",
    "Xq = titan.normdata(titan.xquad(X))\n",
    "Xvadq = titan.normdata(titan.xquad(Xvad))\n",
    "\n",
    "regpara = 0.1\n",
    "order = np.arange(1, 10)\n",
    "trainerror = np.zeros(shape = (order.size, 1))\n",
    "vaderror = np.zeros(shape = (order.size, 1))\n",
    "\n",
    "for i in range(0, order.size):\n",
    "    Xp = titan.normdata(titan.polyx(X, order[i]))\n",
    "    Xvadp = titan.normdata(titan.polyx(Xvad, order[i]))\n",
    "    Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "    Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "    Xp = np.concatenate((Xp, Xq[:, 7:]), axis = 1)\n",
    "    Xvadp = np.concatenate((Xvadp, Xvadq[:, 7:]), axis = 1)\n",
    "    theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "    theta = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, regpara))[0]\n",
    "    trainerror[i] = titan.lfCost(theta, Xp, y, 0.0)\n",
    "    vaderror[i] = titan.lfCost(theta, Xvadp, yvad, 0.0)\n",
    "plt.plot(order, trainerror, '-b', order, vaderror,'-r')\n",
    "plt.xlabel('order of polynomials')\n",
    "plt.ylabel('error')\n",
    "plt.legend(['training','validation'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "order = 2\n",
    "Xp = titan.normdata(titan.polyx(Xq, order))\n",
    "Xvadp = titan.normdata(titan.polyx(Xvadq, order))\n",
    "Xp = np.concatenate((np.ones(shape=(Xp.shape[0], 1)), Xp), axis = 1)\n",
    "Xvadp = np.concatenate((np.ones(shape=(Xvadp.shape[0], 1)), Xvadp), axis = 1)\n",
    "Xp = np.concatenate((Xp, Xq[:, 7:]), axis = 1)\n",
    "Xvadp = np.concatenate((Xvadp, Xvadq[:, 7:]), axis = 1)\n",
    "theta0 = np.zeros(shape = (Xp.shape[1], 1))\n",
    "w = scop.fmin_l_bfgs_b(titan.lfCost, theta0, titan.lfGradient, (Xp, y, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8263305322128851"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yvad_predict = titan.sigmoid(np.dot(Xvadp,w[0]))\n",
    "yvad_predict[yvad_predict > 0.5] = 1\n",
    "yvad_predict[yvad_predict <= 0.5] = 0\n",
    "(yvad_predict == yvad).sum()*1.0/yvad.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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