Supervised_Learning_Ensembles_of_Decision_Trees.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensembles of Decision Trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Ensembles* are methods that combines multiple machine learning models to create more powerful models. There are several machine learning models that belong to this category, but there are two ensemble models that have proven to be effeictive on a wide range of datasets for classification and regression. Both of them use decision trees as their building blocks: **Random forest** and **Gradient boosted** decision trees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random forests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As mentioned before, a main drawback of decision trees is that they tend to overfit the training data. Random forests are one way to address this problem which is a collection of decision trees where each tree is slightly different from each others. \n",
    "The idea behind random forests is the each tree might do a relatively good job of predicting, but will likely overfit on part of the data. If we build many trees, all of which work well and overfit in different ways, we can reduce the amount of overfitting by averaging their results. \n",
    "Random forests get their name from injecting randomness into the tree building to ensure each tree is different. There are two ways in which the tree in a random forests are randomized: \n",
    "- By selecting the data points used to build a tree \n",
    "- By selecting the features in each split test. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Building random forests:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "For building a random forest model, we need to decide on the number of trees to build (the *n_estimators* parameter of *RandomForestRegressor* or *RandomForestClassifier*). If we want to make 10 trees, these trees will be built compeletly independently from each othe, and the algorithm will make different random choices for each tree to make sure the trees are distinct. To build a tree, we first take what is called a *bootstrap sample* of our data. That is, from our *n_samples* data points, we repeatedly draw an sample randomly with replacement (meaning the same sample can be picked multiple times), *n_samples* times. THis will create a dataset that is as big as the original dataset, but some data points will be missing from it(approximately one third), and some will be repeated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now, I am applying a random forest consisting of five trees to the *two_moons* dataset shown earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import mglearn\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
       "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
       "            min_impurity_split=1e-07, min_samples_leaf=1,\n",
       "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "            n_estimators=5, n_jobs=1, oob_score=False, random_state=2,\n",
       "            verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = make_moons(n_samples=100, noise=0.25, random_state=3)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, stratify=y,\n",
    "                                                   random_state=42)\n",
    "\n",
    "forest = RandomForestClassifier(n_estimators=5, random_state=2)\n",
    "forest.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The trees that are built as part of the random forest are stored in the *estimator_* attribute. Let's visualize the decision boundaries learned by each tree, together with their aggregate prediction as made by the forest. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0bd3daa978>,\n",
       " <matplotlib.lines.Line2D at 0x7f0bd3d336a0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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5Z0REpAbMCSIi8oYZQRTdWMRRocrKLTCm5/jcJj4jFxUVW8PUIyIiUhPmBBERecOMIIpu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\np6p5QKTqebRRj0RHRAB4R1vTbtXVrtHMkVmHM6KnnPjx1/M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iciQ06Yy3bTqbZuXaVpTw5XVVOj8kY+pXMfel15I59SVVOjpj05XFu3rop1F2GxlW/P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\nUNPhejfenPjXq79ST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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0bd7351198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 3, figsize=(20, 10))\n",
    "for i, (ax, tree) in enumerate(zip(axes.ravel(), forest.estimators_)):\n",
    "    ax.set_title('Tree {}'.format(i))\n",
    "    mglearn.plots.plot_tree_partition(X_train, y_train, tree, ax=ax)\n",
    "    \n",
    "mglearn.plots.plot_2d_separator(forest, X_train, fill=True, ax=axes[-1, -1], alpha=0.4)\n",
    "axes[-1, -1].set_title('Random Forest')\n",
    "mglearn.discrete_scatter(X_train[:, 0], X_train[:, 1], y_train)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Figures above show the decision boundaries found by five randomized decision trees and the decision boundary obtained by averaging their predicted probabilities. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Another exampl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's apply a random forest consisting of 100 trees on the Breast Cancer dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.model_selection import train_test_split\n",
    "cancer = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, random_state=0)\n",
    "forest = RandomForestClassifier(n_estimators=100, random_state=0)\n",
    "forest.fit(X_train, y_train)\n",
    "\n",
    "print('Accuracy on training set is: {:.3F}'.format(forest.score(X_train, y_train)))\n",
    "print('Accuracy on test set is: {:.3F}'.format(forest.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 0.960\n",
      "Accuracy on test set is: 0.881\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.951\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n"
     ]
    }
   ],
   "source": [
    "for n in [1, 10, 100, 1000]:\n",
    "    forest = RandomForestClassifier(n_estimators=n, random_state=0)\n",
    "    forest.fit(X_train, y_train)\n",
    "    print('Accuracy on training set is: {:.3F}'.format(forest.score(X_train, y_train)))\n",
    "    print('Accuracy on test set is: {:.3F}'.format(forest.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.958\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n"
     ]
    }
   ],
   "source": [
    "for max_feature in [1, 10]:\n",
    "    forest = RandomForestClassifier(n_estimators=100, max_features=max_feature, random_state=0)\n",
    "    forest.fit(X_train, y_train)\n",
    "    print('Accuracy on training set is: {:.3F}'.format(forest.score(X_train, y_train)))\n",
    "    print('Accuracy on test set is: {:.3F}'.format(forest.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, random_state=0)\n",
    "forest = RandomForestClassifier(n_estimators=100, random_state=0)\n",
    "forest.fit(X_train, y_train)\n",
    "\n",
    "print('Accuracy on training set is: {:.3F}'.format(forest.score(X_train, y_train)))\n",
    "print('Accuracy on test set is: {:.3F}'.format(forest.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 30)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cancer.data.shape # number of rows and feature in the cancer dataset "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How to deal with feature importance in Random Forest?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def plot_feature_importances_cancer(model):\n",
    "    \n",
    "    \"\"\"Plot horizental bars for feature importance \n",
    "       for the selected model\"\"\"\n",
    "    Fig = plt.figure(figsize=(13,10))\n",
    "    n_features = cancer.data.shape[1]\n",
    "    plt.barh(range(n_features), model.feature_importances_, align='center')\n",
    "    plt.yticks(np.arange(n_features), cancer.feature_names)\n",
    "    plt.xlabel('Feature importance')\n",
    "    plt.ylabel('Feature')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YniXpbcAZwGpJE2z/d7sx1wPXAwwdOaa3MURERERExB4YTBU5qCpvlwPLSnsWsNa2gVXA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0bd1d535f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_feature_importances_cancer(forest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The important parameters to adjust are *n_estimators, max_features* and possibly pre-pruning options like *max_depth*. for *n_estimators*, larger is always better. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient boosted regression trees (gradient boosting machines)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast to the random forest approach, gradient boosting works by building trees in a serial manner, where each tree tries to correct the mistakes of the previous one. By default, there is no randomization in gradient boosted regression trees. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.958\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, random_state=0)\n",
    "gbrt = GradientBoostingClassifier(random_state=0)\n",
    "gbrt.fit(X_train, y_train)\n",
    "\n",
    "print('Accuracy on training set is: {:.3F}'.format(gbrt.score(X_train, y_train)))\n",
    "print('Accuracy on test set is: {:.3F}'.format(gbrt.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main idea behind gradient boosting is to combine many simple models (in this\n",
    "context known as weak learners), like shallow trees. Each tree can only provide good\n",
    "predictions on part of the data, and so more and more trees are added to iteratively\n",
    "improve performance.\n",
    "Gradient boosted trees are frequently the winning entries in machine learning com‐\n",
    "petitions, and are widely used in industry. They are generally a bit more sensitive to\n",
    "parameter settings than random forests, but can provide better accuracy if the param‐\n",
    "eters are set correctly.\n",
    "Apart from the pre-pruning and the number of trees in the ensemble, another impor‐\n",
    "tant parameter of gradient boosting is the learning_rate , which controls how\n",
    "strongly each tree tries to correct the mistakes of the previous trees. A higher learning\n",
    "rate means each tree can make stronger corrections, allowing for more complex mod‐\n",
    "els. Adding more trees to the ensemble, which can be accomplished by increasing\n",
    "n_estimators , also increases the model complexity, as the model has more chances\n",
    "to correct mistakes on the training set.\n",
    "Here is an example of using GradientBoostingClassifier on the Breast Cancer\n",
    "dataset. By default, 100 trees of maximum depth 3 and a learning rate of 0.1 are used:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above example, the training set accuracy is 100% which is likely to be overfitting. To reduce overfitting, we could either apply stronger pre-prunning by limiting the maximum depth or lower the learning rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 0.991\n",
      "Accuracy on test set is: 0.972\n"
     ]
    }
   ],
   "source": [
    "gbrt = GradientBoostingClassifier(random_state=0, max_depth=1)\n",
    "gbrt.fit(X_train, y_train)\n",
    "\n",
    "print('Accuracy on training set is: {:.3F}'.format(gbrt.score(X_train, y_train)))\n",
    "print('Accuracy on test set is: {:.3F}'.format(gbrt.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max depth is: 1\n",
      "Accuracy on training set is: 0.991\n",
      "Accuracy on test set is: 0.972\n",
      "Max depth is: 2\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.972\n",
      "Max depth is: 3\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.958\n",
      "Max depth is: 4\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.958\n",
      "Max depth is: 5\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.902\n",
      "Max depth is: 6\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.944\n",
      "Max depth is: 7\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.888\n",
      "Max depth is: 8\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.888\n",
      "Max depth is: 9\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.888\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 10):\n",
    "    gbrt = GradientBoostingClassifier(random_state=0, max_depth=i)\n",
    "    gbrt.fit(X_train, y_train)\n",
    "    print('Max depth is: {}'.format(i))\n",
    "    print('Accuracy on training set is: {:.3F}'.format(gbrt.score(X_train, y_train)))\n",
    "    print('Accuracy on test set is: {:.3F}'.format(gbrt.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Checking the effect of **learning rate**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set is: 0.988\n",
      "Accuracy on test set is: 0.965\n"
     ]
    }
   ],
   "source": [
    "gbrt = GradientBoostingClassifier(random_state=0, learning_rate=0.01)\n",
    "gbrt.fit(X_train, y_train)\n",
    "\n",
    "print('Accuracy on training set is: {:.3f}'.format(gbrt.score(X_train, y_train)))\n",
    "print('Accuracy on test set is: {:.3f}'.format(gbrt.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Learning rate is: 0.0001\n",
      "Accuracy on training set is: 0.627\n",
      "Accuracy on test set is: 0.629\n",
      "Learning rate is: 0.001\n",
      "Accuracy on training set is: 0.627\n",
      "Accuracy on test set is: 0.629\n",
      "Learning rate is: 0.01\n",
      "Accuracy on training set is: 0.988\n",
      "Accuracy on test set is: 0.965\n",
      "Learning rate is: 0.1\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.958\n",
      "Learning rate is: 1\n",
      "Accuracy on training set is: 1.000\n",
      "Accuracy on test set is: 0.986\n",
      "Learning rate is: 10\n",
      "Accuracy on training set is: 0.293\n",
      "Accuracy on test set is: 0.308\n"
     ]
    }
   ],
   "source": [
    "for i in [0.0001, 0.001, 0.01, 0.1, 1, 10]:\n",
    "    gbrt = GradientBoostingClassifier(random_state=0, learning_rate=i)\n",
    "    gbrt.fit(X_train, y_train)\n",
    "    print('Learning rate is: {}'.format(i))\n",
    "    print('Accuracy on training set is: {:.3F}'.format(gbrt.score(X_train, y_train)))\n",
    "    print('Accuracy on test set is: {:.3F}'.format(gbrt.score(X_test, y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both methods of decreasing the model complexity reduced the training set accuracy,\n",
    "as expected. In this case, lowering the maximum depth of the trees provided a signifi‐\n",
    "cant improvement of the model, while lowering the learning rate only increased the\n",
    "generalization performance slightly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Feature importance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ge46ktwCnAmskTbL9323GXANcAzB09LiexhAREREREXthIFXkoKq8XQIsL+05wFrbBlYD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\nVwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0bd1bd1ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gbrt = GradientBoostingClassifier(random_state=0, max_depth=1)\n",
    "gbrt.fit(X_train, y_train)\n",
    "\n",
    "plot_feature_importances_cancer(gbrt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the feature importances of the gradient boosted trees are somewhat\n",
    "similar to the feature importances of the random forests, though the gradient boost‐\n",
    "ing completely ignored some of the features.\n",
    "As both gradient boosting and random forests perform well on similar kinds of data,\n",
    "a common approach is to first try random forests, which work quite robustly. If ran‐\n",
    "dom forests work well but prediction time is at a premium, or it is important to\n",
    "squeeze out the last percentage of accuracy from the machine learning model, mov‐\n",
    "ing to gradient boosting often helps.\n",
    "If you want to apply gradient boosting to a large-scale problem, it might be worth\n",
    "looking into the xgboost package and its Python interface, which at the time of writ‐\n",
    "ing is faster (and sometimes easier to tune) than the scikit-learn implementation of\n",
    "gradient boosting on many datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}