Gradient Boosting Machines Out of Bag - Sklearn.ipynb

Gradient Boosting Machines v.s Decision Tree Demo 99.30% Acc - Sklearn.ipynb

{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Gradient Boosting Machines OOB v.s  Decision Tree Demo 99.30% Acc - Sklearn\n\n\nby John Ryan\n\n<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">**Note:** Citation:  Data Source: Lichman, M. (2013). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science. UCI Machine learning Repository http://archive.ics.uci.edu/ml/datasets.html.</div>\n\n\nFor the purpose of this analysis we will look to machine learning as a method to predict diagnosis of cancers.\n\n**Question:** How do we predict the cancer status of a patient given their health measurements?\n\n\n#### Decision Trees & Gradient Boosting Machines - Ensemble Methods\n\nDecision Trees are a machine learning method that classifies data heuristically.  The method divides data into increasingly smaller portions to identify patterns for prediction. It can be applied to a complex dataset and produce a series of specific choices that produce logical decisions. A decision tree can be viewed as flowchart where the data is constantly divided according to a new criterion to provide further tree nodes/choices. Decision trees can be problematic if they become ‘too’ big as accuracy is lost as more stringent rules are applied to the date. The use of bagging or boosting aims to minimize this issue by finding the optimal tree size that can be applied to the test data.\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### Import Required Libaries"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "import os\nimport warnings\nimport pandas as pd\nimport numpy as np\nwarnings.filterwarnings(\"ignore\", category=DeprecationWarning,\n                       module=\"pandas, lineno=570\")\nfrom __future__ import print_function\nimport requests\nimport seaborn as sns\nimport matplotlib.pyplot as plt\nsns.set_style('whitegrid')\n%matplotlib inline\nfrom sklearn import preprocessing\nfrom sklearn.metrics import log_loss, auc, roc_auc_score\nfrom sklearn.preprocessing import LabelEncoder\nfrom sklearn.cross_validation import train_test_split\nfrom sklearn.ensemble import RandomForestClassifier \nfrom sklearn import metrics\nfrom matplotlib import pyplot",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": "C:\\Users\\IBM_ADMIN\\Anaconda2\\lib\\site-packages\\sklearn\\cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n  \"This module will be removed in 0.20.\", DeprecationWarning)\n",
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### Load the data"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Load the data\n# Make dataset a Pandas DataFrame\ndf = pd.read_csv(\"C:\\\\data\\\\wisc_bc_data.csv\")\ndf.head()",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>id</th>\n      <th>diagnosis</th>\n      <th>radius_mean</th>\n      <th>texture_mean</th>\n      <th>perimeter_mean</th>\n      <th>area_mean</th>\n      <th>smoothness_mean</th>\n      <th>compactness_mean</th>\n      <th>concavity_mean</th>\n      <th>concave points_mean</th>\n      <th>...</th>\n      <th>radius_worst</th>\n      <th>texture_worst</th>\n      <th>perimeter_worst</th>\n      <th>area_worst</th>\n      <th>smoothness_worst</th>\n      <th>compactness_worst</th>\n      <th>concavity_worst</th>\n      <th>concave points_worst</th>\n      <th>symmetry_worst</th>\n      <th>fractal_dimension_worst</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>842302</td>\n      <td>M</td>\n      <td>17.99</td>\n      <td>10.38</td>\n      <td>122.80</td>\n      <td>1001.0</td>\n      <td>0.11840</td>\n      <td>0.27760</td>\n      <td>0.3001</td>\n      <td>0.14710</td>\n      <td>...</td>\n      <td>25.38</td>\n      <td>17.33</td>\n      <td>184.60</td>\n      <td>2019.0</td>\n      <td>0.1622</td>\n      <td>0.6656</td>\n      <td>0.7119</td>\n      <td>0.2654</td>\n      <td>0.4601</td>\n      <td>0.11890</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>842517</td>\n      <td>M</td>\n      <td>20.57</td>\n      <td>17.77</td>\n      <td>132.90</td>\n      <td>1326.0</td>\n      <td>0.08474</td>\n      <td>0.07864</td>\n      <td>0.0869</td>\n      <td>0.07017</td>\n      <td>...</td>\n      <td>24.99</td>\n      <td>23.41</td>\n      <td>158.80</td>\n      <td>1956.0</td>\n      <td>0.1238</td>\n      <td>0.1866</td>\n      <td>0.2416</td>\n      <td>0.1860</td>\n      <td>0.2750</td>\n      <td>0.08902</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>84300903</td>\n      <td>M</td>\n      <td>19.69</td>\n      <td>21.25</td>\n      <td>130.00</td>\n      <td>1203.0</td>\n      <td>0.10960</td>\n      <td>0.15990</td>\n      <td>0.1974</td>\n      <td>0.12790</td>\n      <td>...</td>\n      <td>23.57</td>\n      <td>25.53</td>\n      <td>152.50</td>\n      <td>1709.0</td>\n      <td>0.1444</td>\n      <td>0.4245</td>\n      <td>0.4504</td>\n      <td>0.2430</td>\n      <td>0.3613</td>\n      <td>0.08758</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>84348301</td>\n      <td>M</td>\n      <td>11.42</td>\n      <td>20.38</td>\n      <td>77.58</td>\n      <td>386.1</td>\n      <td>0.14250</td>\n      <td>0.28390</td>\n      <td>0.2414</td>\n      <td>0.10520</td>\n      <td>...</td>\n      <td>14.91</td>\n      <td>26.50</td>\n      <td>98.87</td>\n      <td>567.7</td>\n      <td>0.2098</td>\n      <td>0.8663</td>\n      <td>0.6869</td>\n      <td>0.2575</td>\n      <td>0.6638</td>\n      <td>0.17300</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>84358402</td>\n      <td>M</td>\n      <td>20.29</td>\n      <td>14.34</td>\n      <td>135.10</td>\n      <td>1297.0</td>\n      <td>0.10030</td>\n      <td>0.13280</td>\n      <td>0.1980</td>\n      <td>0.10430</td>\n      <td>...</td>\n      <td>22.54</td>\n      <td>16.67</td>\n      <td>152.20</td>\n      <td>1575.0</td>\n      <td>0.1374</td>\n      <td>0.2050</td>\n      <td>0.4000</td>\n      <td>0.1625</td>\n      <td>0.2364</td>\n      <td>0.07678</td>\n    </tr>\n  </tbody>\n</table>\n<p>5 rows × 32 columns</p>\n</div>",
            "text/plain": "         id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n0    842302         M        17.99         10.38          122.80     1001.0   \n1    842517         M        20.57         17.77          132.90     1326.0   \n2  84300903         M        19.69         21.25          130.00     1203.0   \n3  84348301         M        11.42         20.38           77.58      386.1   \n4  84358402         M        20.29         14.34          135.10     1297.0   \n\n   smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n0          0.11840           0.27760          0.3001              0.14710   \n1          0.08474           0.07864          0.0869              0.07017   \n2          0.10960           0.15990          0.1974              0.12790   \n3          0.14250           0.28390          0.2414              0.10520   \n4          0.10030           0.13280          0.1980              0.10430   \n\n            ...             radius_worst  texture_worst  perimeter_worst  \\\n0           ...                    25.38          17.33           184.60   \n1           ...                    24.99          23.41           158.80   \n2           ...                    23.57          25.53           152.50   \n3           ...                    14.91          26.50            98.87   \n4           ...                    22.54          16.67           152.20   \n\n   area_worst  smoothness_worst  compactness_worst  concavity_worst  \\\n0      2019.0            0.1622             0.6656           0.7119   \n1      1956.0            0.1238             0.1866           0.2416   \n2      1709.0            0.1444             0.4245           0.4504   \n3       567.7            0.2098             0.8663           0.6869   \n4      1575.0            0.1374             0.2050           0.4000   \n\n   concave points_worst  symmetry_worst  fractal_dimension_worst  \n0                0.2654          0.4601                  0.11890  \n1                0.1860          0.2750                  0.08902  \n2                0.2430          0.3613                  0.08758  \n3                0.2575          0.6638                  0.17300  \n4                0.1625          0.2364                  0.07678  \n\n[5 rows x 32 columns]"
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### One Hot Encoder"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#transform attributes to algortim readable numeric representations of the original data.\nfor feature in df.columns:\n    if df[feature].dtype=='object':\n        le = LabelEncoder()\n        df[feature] = le.fit_transform(df[feature])\ndf.tail(3)",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": "<div>\n<style>\n    .dataframe thead tr:only-child th {\n        text-align: right;\n    }\n\n    .dataframe thead th {\n        text-align: left;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>id</th>\n      <th>diagnosis</th>\n      <th>radius_mean</th>\n      <th>texture_mean</th>\n      <th>perimeter_mean</th>\n      <th>area_mean</th>\n      <th>smoothness_mean</th>\n      <th>compactness_mean</th>\n      <th>concavity_mean</th>\n      <th>concave points_mean</th>\n      <th>...</th>\n      <th>radius_worst</th>\n      <th>texture_worst</th>\n      <th>perimeter_worst</th>\n      <th>area_worst</th>\n      <th>smoothness_worst</th>\n      <th>compactness_worst</th>\n      <th>concavity_worst</th>\n      <th>concave points_worst</th>\n      <th>symmetry_worst</th>\n      <th>fractal_dimension_worst</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>566</th>\n      <td>926954</td>\n      <td>1</td>\n      <td>16.60</td>\n      <td>28.08</td>\n      <td>108.30</td>\n      <td>858.1</td>\n      <td>0.08455</td>\n      <td>0.10230</td>\n      <td>0.09251</td>\n      <td>0.05302</td>\n      <td>...</td>\n      <td>18.980</td>\n      <td>34.12</td>\n      <td>126.70</td>\n      <td>1124.0</td>\n      <td>0.11390</td>\n      <td>0.30940</td>\n      <td>0.3403</td>\n      <td>0.1418</td>\n      <td>0.2218</td>\n      <td>0.07820</td>\n    </tr>\n    <tr>\n      <th>567</th>\n      <td>927241</td>\n      <td>1</td>\n      <td>20.60</td>\n      <td>29.33</td>\n      <td>140.10</td>\n      <td>1265.0</td>\n      <td>0.11780</td>\n      <td>0.27700</td>\n      <td>0.35140</td>\n      <td>0.15200</td>\n      <td>...</td>\n      <td>25.740</td>\n      <td>39.42</td>\n      <td>184.60</td>\n      <td>1821.0</td>\n      <td>0.16500</td>\n      <td>0.86810</td>\n      <td>0.9387</td>\n      <td>0.2650</td>\n      <td>0.4087</td>\n      <td>0.12400</td>\n    </tr>\n    <tr>\n      <th>568</th>\n      <td>92751</td>\n      <td>0</td>\n      <td>7.76</td>\n      <td>24.54</td>\n      <td>47.92</td>\n      <td>181.0</td>\n      <td>0.05263</td>\n      <td>0.04362</td>\n      <td>0.00000</td>\n      <td>0.00000</td>\n      <td>...</td>\n      <td>9.456</td>\n      <td>30.37</td>\n      <td>59.16</td>\n      <td>268.6</td>\n      <td>0.08996</td>\n      <td>0.06444</td>\n      <td>0.0000</td>\n      <td>0.0000</td>\n      <td>0.2871</td>\n      <td>0.07039</td>\n    </tr>\n  </tbody>\n</table>\n<p>3 rows × 32 columns</p>\n</div>",
            "text/plain": "         id  diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n566  926954          1        16.60         28.08          108.30      858.1   \n567  927241          1        20.60         29.33          140.10     1265.0   \n568   92751          0         7.76         24.54           47.92      181.0   \n\n     smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n566          0.08455           0.10230         0.09251              0.05302   \n567          0.11780           0.27700         0.35140              0.15200   \n568          0.05263           0.04362         0.00000              0.00000   \n\n              ...             radius_worst  texture_worst  perimeter_worst  \\\n566           ...                   18.980          34.12           126.70   \n567           ...                   25.740          39.42           184.60   \n568           ...                    9.456          30.37            59.16   \n\n     area_worst  smoothness_worst  compactness_worst  concavity_worst  \\\n566      1124.0           0.11390            0.30940           0.3403   \n567      1821.0           0.16500            0.86810           0.9387   \n568       268.6           0.08996            0.06444           0.0000   \n\n     concave points_worst  symmetry_worst  fractal_dimension_worst  \n566                0.1418          0.2218                  0.07820  \n567                0.2650          0.4087                  0.12400  \n568                0.0000          0.2871                  0.07039  \n\n[3 rows x 32 columns]"
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "y = df.diagnosis.values\nX = df.drop('diagnosis', axis=1)",
      "execution_count": 4,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#split the data into training and test data sets\nfrom sklearn.cross_validation import train_test_split\nX_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)",
      "execution_count": 5,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Gradient Boosting Machine (GBM)"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Build a GBM classification model, create a variable to define the desired parameters to \n#opitmize performance and reduce over fitting\nfrom sklearn import ensemble\nparams = {'n_estimators': 1200, 'max_depth': 5, 'subsample': 0.5,\n         'learning_rate': 0.01, 'min_samples_leaf': 1, 'random_state': 3 }\ngbm1 = ensemble.GradientBoostingClassifier(**params)",
      "execution_count": 6,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "gbm1.fit(X_train, y_train)\nacc = gbm1.score(X_test, y_test)\nprint(\"Accuracy: {:.4f}\".format(acc))",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Accuracy: 0.9720\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Make class predictions for the test set\ny_predict_class_gbm = gbm1.predict(X_test)\n#Make  prediction probabailties for the test set\ny_predict_proba_gbm = gbm1.predict_proba(X_test)[:,1]",
      "execution_count": 8,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Improving performance: Gradient Boosting Machine - Decreased Learning Rate\n\nHaving summarized and examined the model, it was then applied to the test dataset further where a predicted score & confusion table was generated to compare performance against predicted values.\n\nBoosting is implemented to combine weak performer learners, creating a model which should improve accuracy. The parameters are specified (n_estimators': 1200, 'max_depth': 5, 'subsample': 0.5,'learning_rate': 0.01,'min_samples_leaf': 1,'random_state': 3) in such away to improve performance and reduce overfitting thus producing an out of the bag model, where the results were noted as having improved on the initial model.\n\n##### Learning Rate: \n\nGradient boosting Machines esembles in a stage-wise fashion like other boosting methods do, and it generalizes them by allowing optimization of an arbitrary differentiable loss function.\nThe number of weak learners (i.e. decision trees) is controlled by the number of estimators; The size of each tree can be controlled either by max_depth or the learning_rate is a hyper-parameter in the range (0.0, 1.0) that controls overfitting via shrinkage which gradually reduces the impact of predictions of each subsequent tree generated. however increased shrinkage lead to longer run times. In the model created below we set the learning rate to 0.05 which is shown to improve the model performance."
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "from sklearn.ensemble import GradientBoostingClassifier as gbm\nparams_dict = {'n_estimators': 1200, 'random_state': 3}\nplt.figure()\nfor label, color, setting in [('Depth 2, Lr = 0.01', 'turquoise', {'learning_rate': 0.01, 'max_depth': 2}),\n                              ('Depth 4, Lr = 0.01', 'green', {'learning_rate': 0.01, 'max_depth': 4}),\n                              ('Depth 6, Lr = 0.01', 'blue', {'learning_rate':0.01, 'max_depth': 6 }),\n                              ('Depth 2, Lr= 0.05', 'red', {'learning_rate': 0.05, 'max_depth': 2}),\n                              ('Depth 4, Lr = 0.05', 'orange', {'learning_rate': 0.05, 'max_depth': 4}),\n                              ('Depth 6, Lr = 0.05', 'indigo', {'learning_rate':0.05, 'max_depth': 6 })]:\n    params_1 = dict(params_dict)\n    params_1.update(setting)\n    gbm_lr = gbm(**params_1)\n    gbm_lr.fit(X_train, y_train)\n    #calcualte the area under the curce (auc) for the test set\n    test_deviance = np.zeros((params_1['n_estimators'],), dtype=np.float64)\n    for g, y_pred in enumerate(gbm_lr.staged_predict_proba(X_test)):\n        test_deviance[g] =roc_auc_score(y_test, y_pred[:,1])\n    plt.plot((np.arange(test_deviance.shape[0]) + 1), test_deviance, '-', color=color, label=label)\n\nplt.legend(loc='lower left')\npyplot.ylim(0.8, 1.0)\nplt.xlabel('Boosting Iterations')\npyplot.ylabel(\"validation auc\")\nplt.figure(figsize=(12,12))\nplt.show()",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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GtlxCNFXEBJKTsTF85c6x5dPtvxXuQBLEFklZiTnyGR0Tnl1Cx0rM+U0mDpjYwiWJbC+9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\nAAAASUVORK5CYII=\n",
            "text/plain": "<matplotlib.figure.Figure at 0xe80ada0>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<matplotlib.figure.Figure at 0xf2672e8>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Visual examination of improved performance by tuning the hyper-paramters learning rate\n\nThe AUC plot below demonstrates the improved performance and algorithm control of the learning rate over time on the test data. We see as the tree depth increases from 2(turquoise line), 4(green line) & 6(blue line) with learning rate set 0.01 as the tree grows towards the max depth of 6 the learning on the data starts to stagnate as evident from the blue line above.\n\nOn review of the altering the learning rate to 0.05 we see better control and reduced shrinkage as eveident from the red, orange and indigo lines on the graph. Initially learning is slow but we see that improvement over time as the each line begins to gradually incline and straighten. "
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### Gradient Boosting Machine - alter model learning Rate to 0.5"
    },
    {
      "metadata": {
        "collapsed": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "params1 = {'n_estimators': 1200, 'max_depth': 5, 'subsample': 0.5,\n         'learning_rate': 0.05, 'min_samples_leaf': 1, 'random_state': 3 }\ngbm2 = ensemble.GradientBoostingClassifier(**params1)",
      "execution_count": 10,
      "outputs": []
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "gbm2.fit(X_train, y_train)\nacc = gbm2.score(X_test, y_test)\nprint(\"Accuracy: {:.4f}\".format(acc))",
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Accuracy: 0.9790\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": true
      },
      "cell_type": "code",
      "source": "#Make class predictions for the test set\ny_predict_class_gbm2 = gbm2.predict(X_test)\n#Make  prediction probabailties for the test set\ny_predict_proba_gbm2 = gbm2.predict_proba(X_test)[:,1]",
      "execution_count": 12,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### Decision Tree Classifier - Max Depth 4"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Create decision tree classifier with max depth 4 and print out the accuracy.\nfrom sklearn import tree\nparams2 = {'max_depth': 4 , 'min_samples_split': 2, 'min_samples_leaf': 2, 'min_weight_fraction_leaf': 0.5} \ntree1 = tree.DecisionTreeClassifier(**params2)\ntree1 = tree1.fit(X_test, y_test)\nacc2 = tree1.score(X_test, y_test)\nprint(\"Accuracy: {:.4f}\".format(acc2))",
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": "Accuracy: 0.9930\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "#Make class predictions for the test set\ny_predict_class_tree1 = tree1.predict(X_test)\n#Make  prediction probabailties for the test set\ny_predict_proba_tree1 = tree1.predict_proba(X_test)[:,1]",
      "execution_count": 14,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### Area Under AUC Curve\n\nThe ROC curve helps to select a threshold value that balances sensitivity and specificity in a way that makes sense.\n\nAUC is a popular metric. I believe it is a good metric given the unbalaced classes seen above. It is used to judge predictions in binary response (0/1) problem. It is only sensitive to the order determined by the predictions and not their magnitudes.\n\nFor other evaluation methods, a user has to choose a cut-off point above which the target variable is part of the positive class (e.g. a logistic regression model returns any real number between 0 and 1 - the modeler might decide that predictions greater than 0.5 mean a positive class prediction while a prediction of less than 0.5 mean a negative class prediction). AUC evaluates entries at all cut-off points, giving better insight into how well the classifier is able to separate the two classes.\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### ROC Curve for Cancer Prediction - Gradient Boosting Machine - learning rate 0.01"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_predict_proba_gbm)\nplt.plot(fpr, tpr)\nplt.xlim([0.0,1.0])\nplt.ylim([0.0,1.0])\nplt.title('ROC Curve for Cancer Prediction Gradient Boosting Machine - learning rate 0.01')\nplt.xlabel('False Positive Rate(1 - specificity)')\nplt.ylabel('True Positive Rate(sensitivity)')\nplt.grid(True)",
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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trc0alGm5SNfwxue8TwK2yUGtu3raGdgs/1YfIHUpn0+6rvgY8FhEPES6pndMg3IUy9fV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\nmVkZymzhjZI0Fhg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            "text/plain": "<matplotlib.figure.Figure at 0x10c1f518>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### ROC Curve for Cancer Prediction - Gradient Boosting Machine - learning rate 0.05"
    },
    {
      "metadata": {
        "collapsed": false,
        "trusted": true
      },
      "cell_type": "code",
      "source": "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_predict_proba_gbm2)\nplt.plot(fpr, tpr)\nplt.xlim([0.0,1.0])\nplt.ylim([0.0,1.0])\nplt.title('ROC Curve for Cancer Prediction Gradient Boosting Machine - learning rate 0.05')\nplt.xlabel('False Positive Rate(1 - specificity)')\nplt.ylabel('True Positive Rate(sensitivity)')\nplt.grid(True)",
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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0bbRoClDsGj2P9ILac+rW+yTpjd1mLXHAs/5qdhv4UcCEiPgz6XrO\nU6QDUs01wFsR8QjpZoPLJD1Cun6zRkQ8BFxMuoX/jVYLI2kiqfvyjoh4lPRW5iNIt8O/2SC/Yvmv\nAh7KrYzi/AuAlfL/te663YBLczlXJnXh1vtA3Uh6N5fl+6QD80MRIdKNNa/TE8BuAg7PXZ77N6mP\n8XywO296NKsbgDnzd3g1PTfmHE3q0pyYy3qIpKdI3b5v5rLeAOwn6T919dBof/kqcFTuot6WdENL\n0U3AYbk+IN2gMgfw/qusImIeYKSkh6etCqwd+fVAZjOJiBgHHFkITmWnfw5w64z0MtzcS7A3sIyk\nbxXmfxN4T5Lv0rSW+Rqe2czjIFJra9eK0p8Rz34vJ3WffrY2I9+1uhGw1WAVymZObuGZmVlb8DU8\nMzNrCw54ZmbWFhzwzMysLTjgmZlZW3DAMzOztuCAZ2ZmbeH/AdWeeZec6sGpAAAAAElFTkSuQmCC\n",
            "text/plain": "<matplotlib.figure.Figure at 0x10c85748>"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "#### ROC Curve for Cancer Prediction - Decison Tree - Max Depth 4"
    },
    {
      "metadata": {
        "trusted": true,
        "collapsed": false
      },
      "cell_type": "code",
      "source": "fpr, tpr, thresholds = metrics.roc_curve(y_test, y_predict_proba_tree1)\nplt.plot(fpr, tpr)\nplt.xlim([0.0,1.0])\nplt.ylim([0.0,1.0])\nplt.title('ROC Curve for Cancer Prediction - Decision Tree - Max Depth 4')\nplt.xlabel('False Positive Rate(1 - specificity)')\nplt.ylabel('True Positive Rate(sensitivity)')\nplt.grid(True)",
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": "<matplotlib.figure.Figure at 0xed29d30>"
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      "name": "python2",
      "display_name": "Python 2",
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    "language_info": {
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      "data": {
        "description": "Gradient Boosting Machines Out of Bag - Sklearn.ipynb",
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}