Module-03e-Model-RandomForest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Forest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "In random forests, each tree in the ensemble is built from a **sample drawn with replacement** (i.e., a bootstrap sample) from the training set. In addition, when splitting a node during the construction of the tree, the split that is chosen is no longer the best split among all features. Instead, the split that is picked is the best split among a **random subset of the features**. \n",
    "\n",
    "As a result of this randomness, the bias of the forest usually slightly increases (with respect to the bias of a single non-random tree) but, due to averaging, its variance also decreases, usually more than compensating for the increase in bias, hence yielding an overall better model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"data/historical_loan.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# refine the data\n",
    "df.years = df.years.fillna(np.mean(df.years))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Load the preprocessing module\n",
    "from sklearn import preprocessing\n",
    "categorical_variables = df.dtypes[df.dtypes==\"object\"].index.tolist()\n",
    "for i in categorical_variables:\n",
    "    lbl = preprocessing.LabelEncoder()\n",
    "    lbl.fit(list(df[i]))\n",
    "    df[i] = lbl.transform(df[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "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>default</th>\n",
       "      <th>amount</th>\n",
       "      <th>grade</th>\n",
       "      <th>years</th>\n",
       "      <th>ownership</th>\n",
       "      <th>income</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1000</td>\n",
       "      <td>1</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>19200.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>6500</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0</td>\n",
       "      <td>66000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2400</td>\n",
       "      <td>0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>60000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>10000</td>\n",
       "      <td>2</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3</td>\n",
       "      <td>62000.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>4000</td>\n",
       "      <td>2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3</td>\n",
       "      <td>20000.0</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   default  amount  grade  years  ownership   income  age\n",
       "0        0    1000      1    2.0          3  19200.0   24\n",
       "1        1    6500      0    2.0          0  66000.0   28\n",
       "2        0    2400      0    2.0          3  60000.0   36\n",
       "3        0   10000      2    3.0          3  62000.0   24\n",
       "4        1    4000      2    2.0          3  20000.0   28"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df.iloc[:,1:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df.iloc[:,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = RandomForestClassifier(class_weight=\"balanced\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight='balanced',\n",
       "            criterion='gini', max_depth=None, max_features='auto',\n",
       "            max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "            min_impurity_split=None, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            n_estimators=10, n_jobs=1, oob_score=False, random_state=None,\n",
       "            verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Key input parameters (in addition to decision trees)\n",
    "- **bootstrap**: Whether bootstrap samples are used when building trees\n",
    "- **max_features**: The number of features to consider when looking for the best split (auto = sqrt) \n",
    "- **n_estimators**: The number of trees in the forest\n",
    "- **oob_score**: Whether to use out-of-bag samples to estimate the generalization accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Key output parameters \n",
    "\n",
    "- **Feature Importance**: The higher, the more important the feature\n",
    "- **Out-of-Bag Score**: Validation score of the training dataset obtained using an out-of-bag estimate.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Importance\n",
    "\n",
    "There are several ways to get feature \"importances\" with no strict consensus on what it means.\n",
    "\n",
    "#### Mean Decrease Impurity \n",
    "\n",
    "The relative rank (i.e. depth) of a feature used as a decision node in a tree can be used to assess the relative importance of that feature with respect to the predictability of the target variable. Features used at the top of the tree contribute to the final prediction decision of a larger fraction of the input samples. The **expected fraction of the samples they contribute to** can thus be used as an estimate of the relative importance of the features.\n",
    "\n",
    "In scikit-learn, it is implemented by using  \"gini importance\" or \"mean decrease impurity\" and is defined as the total decrease in node impurity (weighted by the probability of reaching that node (which is approximated by the proportion of samples reaching that node)) averaged over all trees of the ensemble.\n",
    "\n",
    "\n",
    "#### Mean Decrease Accuracy\n",
    "\n",
    "In the literature or in some other packages, you can also find feature importances implemented as the \"mean decrease accuracy\". Basically, the idea is to measure the decrease in accuracy on OOB data when you randomly permute the values for that feature. If the decrease is low, then the feature is not important, and vice-versa.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "By averaging those expected activity rates over random trees one can reduce the variance of such an estimate and use it for feature selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "importances = clf.feature_importances_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.22541327,  0.11081867,  0.1679413 ,  0.03932398,  0.2825136 ,\n",
       "        0.17398918])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importance of the features in the forest\n",
    "importances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calculate the standard deviation of variable importance\n",
    "std = np.std([tree.feature_importances_ for tree in clf.estimators_], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.01667274,  0.00867487,  0.00816368,  0.00753017,  0.01572384,\n",
       "        0.01548575])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 0, 5, 2, 1, 3])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = np.argsort(importances)[::-1]\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "length = X.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "labels = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(length):\n",
    "    labels.append(X.columns[indices[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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lKLipw2eXOKYwceNBgo74sLA4nG4Mn0amS3Cgb3ghCSrI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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11118be10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the feature importances of the forest\n",
    "plt.figure(figsize=(16, 6))\n",
    "plt.title(\"Feature importances\")\n",
    "plt.bar(range(length), importances[indices], yerr=std[indices], align=\"center\")\n",
    "plt.xticks(range(length), labels)\n",
    "plt.xlim([-1, length])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "Calculate the Feature Importance plot for max_depth = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Out-of-Bag Error\n",
    "The out-of-bag (OOB) error is the average error for each training observation calculated using predictions from the trees that do not contain it in their respective bootstrap sample. This allows the RandomForest to be fit and validated whilst being trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "clf2 = RandomForestClassifier(warm_start=True, class_weight=\"balanced\", \n",
    "                              oob_score=True, max_features=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight='balanced',\n",
       "            criterion='gini', max_depth=None, max_features=None,\n",
       "            max_leaf_nodes=None, min_impurity_decrease=0.0,\n",
       "            min_impurity_split=None, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            n_estimators=10, n_jobs=1, oob_score=True, random_state=None,\n",
       "            verbose=0, warm_start=True)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf2.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.62495146887537212"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf2.oob_score_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "min_estimators = 10\n",
    "max_estimators = 50\n",
    "error_rate = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(min_estimators, max_estimators + 1):\n",
    "    clf2.set_params(n_estimators=i)\n",
    "    clf2.fit(X, y)\n",
    "    oob_error = 1 - clf2.oob_score_\n",
    "    error_rate.append(oob_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "error_rate_indice = [x for x in range(min_estimators, max_estimators + 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114154b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8+LAuuugizZkzR4Zh6OOPP9YjjzyiCy64QCaTSZMnT67Xw++44w7Nnz9fb775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\nERERERFxG/8DJXuySNTc3VMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1141549e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.figure(figsize=(16, 6))\n",
    "plt.plot(error_rate_indice, error_rate)\n",
    "plt.xlim(min_estimators, max_estimators)\n",
    "plt.xlabel(\"n_estimators\")\n",
    "plt.ylabel(\"OOB error rate\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "Calculate the OOB error rate plot with max_feature = sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "Calculate the OOB error rate plot with max_depth = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercise 4\n",
    "Plot the change of AUC score for change in max-depth and no of estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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