notebooks/12_titanic_confusion.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression exercise with Titanic data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "- Data from Kaggle's Titanic competition: [data](https://github.com/justmarkham/DAT8/blob/master/data/titanic.csv), [data dictionary](https://www.kaggle.com/c/titanic/data)\n",
    "- **Goal**: Predict survival based on passenger characteristics\n",
    "- `titanic.csv` is already in our repo, so there is no need to download the data from the Kaggle website"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Read the data into Pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "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>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PassengerId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Survived  Pclass  \\\n",
       "PassengerId                     \n",
       "1                   0       3   \n",
       "2                   1       1   \n",
       "3                   1       3   \n",
       "4                   1       1   \n",
       "5                   0       3   \n",
       "\n",
       "                                                          Name     Sex  Age  \\\n",
       "PassengerId                                                                   \n",
       "1                                      Braund, Mr. Owen Harris    male   22   \n",
       "2            Cumings, Mrs. John Bradley (Florence Briggs Th...  female   38   \n",
       "3                                       Heikkinen, Miss. Laina  female   26   \n",
       "4                 Futrelle, Mrs. Jacques Heath (Lily May Peel)  female   35   \n",
       "5                                     Allen, Mr. William Henry    male   35   \n",
       "\n",
       "             SibSp  Parch            Ticket     Fare Cabin Embarked  \n",
       "PassengerId                                                          \n",
       "1                1      0         A/5 21171   7.2500   NaN        S  \n",
       "2                1      0          PC 17599  71.2833   C85        C  \n",
       "3                0      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "4                1      0            113803  53.1000  C123        S  \n",
       "5                0      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "url = 'https://raw.githubusercontent.com/justmarkham/DAT8/master/data/titanic.csv'\n",
    "titanic = pd.read_csv(url, index_col='PassengerId')\n",
    "titanic.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Create X and y\n",
    "\n",
    "Define **Pclass** and **Parch** as the features, and **Survived** as the response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "feature_cols = ['Pclass', 'Parch']\n",
    "X = titanic[feature_cols]\n",
    "y = titanic.Survived"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 3: Split the data into training and testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Fit a logistic regression model and examine the coefficients\n",
    "\n",
    "Confirm that the coefficients make intuitive sense."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Pclass', -0.88188860564511296), ('Parch', 0.34239215857498861)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "logreg = LogisticRegression(C=1e9)\n",
    "logreg.fit(X_train, y_train)\n",
    "zip(feature_cols, logreg.coef_[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5: Make predictions on the testing set and calculate the accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# class predictions (not predicted probabilities)\n",
    "y_pred_class = logreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.668161434978\n"
     ]
    }
   ],
   "source": [
    "# calculate classification accuracy\n",
    "from sklearn import metrics\n",
    "print metrics.accuracy_score(y_test, y_pred_class)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 6: Compare your testing accuracy to the null accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.573991\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this works regardless of the number of classes\n",
    "y_test.value_counts().head(1) / len(y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5739910313901345"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this only works for binary classification problems coded as 0/1\n",
    "max(y_test.mean(), 1 - y_test.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confusion matrix of Titanic predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[105  23]\n",
      " [ 51  44]]\n"
     ]
    }
   ],
   "source": [
    "# print confusion matrix\n",
    "print metrics.confusion_matrix(y_test, y_pred_class)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# save confusion matrix and slice into four pieces\n",
    "confusion = metrics.confusion_matrix(y_test, y_pred_class)\n",
    "TP = confusion[1][1]\n",
    "TN = confusion[0][0]\n",
    "FP = confusion[0][1]\n",
    "FN = confusion[1][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True Positives: 44\n",
      "True Negatives: 105\n",
      "False Positives: 23\n",
      "False Negatives: 51\n"
     ]
    }
   ],
   "source": [
    "print 'True Positives:', TP\n",
    "print 'True Negatives:', TN\n",
    "print 'False Positives:', FP\n",
    "print 'False Negatives:', FN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.463157894737\n",
      "0.463157894737\n"
     ]
    }
   ],
   "source": [
    "# calculate the sensitivity\n",
    "print TP / float(TP + FN)\n",
    "print 44 / float(44 + 51)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8203125\n",
      "0.8203125\n"
     ]
    }
   ],
   "source": [
    "# calculate the specificity\n",
    "print TN / float(TN + FP)\n",
    "print 105 / float(105 + 23)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# store the predicted probabilities\n",
    "y_pred_prob = logreg.predict_proba(X_test)[:, 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x18b15c50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x16746cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# histogram of predicted probabilities\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(y_pred_prob)\n",
    "plt.xlim(0, 1)\n",
    "plt.xlabel('Predicted probability of survival')\n",
    "plt.ylabel('Frequency')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# increase sensitivity by lowering the threshold for predicting survival\n",
    "import numpy as np\n",
    "y_pred_class = np.where(y_pred_prob > 0.3, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[105  23]\n",
      " [ 51  44]]\n"
     ]
    }
   ],
   "source": [
    "# old confusion matrix\n",
    "print confusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[72 56]\n",
      " [32 63]]\n"
     ]
    }
   ],
   "source": [
    "# new confusion matrix\n",
    "print metrics.confusion_matrix(y_test, y_pred_class)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.663157894737\n"
     ]
    }
   ],
   "source": [
    "# new sensitivity (higher than before)\n",
    "print 63 / float(63 + 32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5625\n"
     ]
    }
   ],
   "source": [
    "# new specificity (lower than before)\n",
    "print 72 / float(72 + 56)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}