notebooks/10_EnsembleMethods_Bagging.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10 - Ensemble Methods - Bagging\n",
    "\n",
    "by [Alejandro Correa Bahnsen](albahnsen.com/)\n",
    "\n",
    "version 0.2, May 2016\n",
    "\n",
    "## Part of the class [Machine Learning for Risk Management](https://github.com/albahnsen/ML_RiskManagement)\n",
    "\n",
    "\n",
    "This notebook is licensed under a [Creative Commons Attribution-ShareAlike 3.0 Unported License](http://creativecommons.org/licenses/by-sa/3.0/deed.en_US). Special thanks goes to [Kevin Markham](https://github.com/justmarkham)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why are we learning about ensembling?\n",
    "\n",
    "- Very popular method for improving the predictive performance of machine learning models\n",
    "- Provides a foundation for understanding more sophisticated models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lesson objectives\n",
    "\n",
    "Students will be able to:\n",
    "\n",
    "- Define ensembling and its requirements\n",
    "- Identify the two basic methods of ensembling\n",
    "- Decide whether manual ensembling is a useful approach for a given problem\n",
    "- Explain bagging and how it can be applied to decision trees\n",
    "- Explain how out-of-bag error and feature importances are calculated from bagged trees\n",
    "- Explain the difference between bagged trees and Random Forests\n",
    "- Build and tune a Random Forest model in scikit-learn\n",
    "- Decide whether a decision tree or a Random Forest is a better model for a given problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1: Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensemble learning is a widely studied topic in the machine learning community. The main idea behind \n",
    "the ensemble methodology is to combine several individual base classifiers in   order to have a \n",
    "classifier that outperforms each of them.\n",
    "\n",
    "Nowadays,   ensemble methods are  one \n",
    "of the most popular and well studied machine learning techniques, and it can be \n",
    "noted that since 2009 all the first-place and   second-place winners of the KDD-Cup https://www.sigkdd.org/kddcup/   used  ensemble methods. The core \n",
    "principle in ensemble learning, is to induce random perturbations into  the learning procedure in \n",
    "order to produce several different base classifiers from a single  training set, then combining the \n",
    "base classifiers in order to make the final prediction.  In order to induce the random permutations \n",
    "and therefore create the different base classifiers,   several methods have been proposed, in \n",
    "particular: \n",
    "* bagging\n",
    "* pasting\n",
    "* random forests \n",
    "* random patches  \n",
    "\n",
    "Finally, after  the base   classifiers \n",
    "are trained, they are typically   combined using either:\n",
    "* majority voting\n",
    "* weighted  voting  \n",
    "* stacking\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are three main reasons regarding why ensemble \n",
    "methods perform better than single models: statistical, computational and representational . First, from a statistical point of view, when the learning set is too \n",
    "small, an algorithm can find several good models within the search space, that arise to the same \n",
    "performance on the training set $\\mathcal{S}$. Nevertheless, without a validation set, there is \n",
    "a risk of choosing the wrong model. The second reason is computational; in general, algorithms \n",
    "rely on some local search optimization and may get stuck in a local optima. Then, an ensemble may \n",
    "solve this by focusing different algorithms to different spaces across the training set. The last \n",
    "reason is representational. In most cases, for a learning set of finite size, the  true function \n",
    "$f$ cannot be represented by any of the candidate models. By combining several  models in an \n",
    "ensemble, it may be possible to obtain a model with a larger coverage across the  space of \n",
    "representable functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/ch9_fig1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "Let's pretend that instead of building a single model to solve a binary classification problem, you created **five independent models**, and each model was correct about 70% of the time. If you combined these models into an \"ensemble\" and used their majority vote as a prediction, how often would the ensemble be correct?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1]\n",
      "[1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0]\n",
      "[1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1]\n",
      "[1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0]\n",
      "[0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# set a seed for reproducibility\n",
    "np.random.seed(1234)\n",
    "\n",
    "# generate 1000 random numbers (between 0 and 1) for each model, representing 1000 observations\n",
    "mod1 = np.random.rand(1000)\n",
    "mod2 = np.random.rand(1000)\n",
    "mod3 = np.random.rand(1000)\n",
    "mod4 = np.random.rand(1000)\n",
    "mod5 = np.random.rand(1000)\n",
    "\n",
    "# each model independently predicts 1 (the \"correct response\") if random number was at least 0.3\n",
    "preds1 = np.where(mod1 > 0.3, 1, 0)\n",
    "preds2 = np.where(mod2 > 0.3, 1, 0)\n",
    "preds3 = np.where(mod3 > 0.3, 1, 0)\n",
    "preds4 = np.where(mod4 > 0.3, 1, 0)\n",
    "preds5 = np.where(mod5 > 0.3, 1, 0)\n",
    "\n",
    "# print the first 20 predictions from each model\n",
    "print(preds1[:20])\n",
    "print(preds2[:20])\n",
    "print(preds3[:20])\n",
    "print(preds4[:20])\n",
    "print(preds5[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "# average the predictions and then round to 0 or 1\n",
    "ensemble_preds = np.round((preds1 + preds2 + preds3 + preds4 + preds5)/5.0).astype(int)\n",
    "\n",
    "# print the ensemble's first 20 predictions\n",
    "print(ensemble_preds[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.713\n",
      "0.665\n",
      "0.717\n",
      "0.712\n",
      "0.687\n"
     ]
    }
   ],
   "source": [
    "# how accurate was each individual model?\n",
    "print(preds1.mean())\n",
    "print(preds2.mean())\n",
    "print(preds3.mean())\n",
    "print(preds4.mean())\n",
    "print(preds5.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.841\n"
     ]
    }
   ],
   "source": [
    "# how accurate was the ensemble?\n",
    "print(ensemble_preds.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** As you add more models to the voting process, the probability of error decreases, which is known as [Condorcet's Jury Theorem](http://en.wikipedia.org/wiki/Condorcet%27s_jury_theorem)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is ensembling?\n",
    "\n",
    "**Ensemble learning (or \"ensembling\")** is the process of combining several predictive models in order to produce a combined model that is more accurate than any individual model.\n",
    "\n",
    "- **Regression:** take the average of the predictions\n",
    "- **Classification:** take a vote and use the most common prediction, or take the average of the predicted probabilities\n",
    "\n",
    "For ensembling to work well, the models must have the following characteristics:\n",
    "\n",
    "- **Accurate:** they outperform the null model\n",
    "- **Independent:** their predictions are generated using different processes\n",
    "\n",
    "**The big idea:** If you have a collection of individually imperfect (and independent) models, the \"one-off\" mistakes made by each model are probably not going to be made by the rest of the models, and thus the mistakes will be discarded when averaging the models.\n",
    "\n",
    "There are two basic **methods for ensembling:**\n",
    "\n",
    "- Manually ensemble your individual models\n",
    "- Use a model that ensembles for you"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theoretical performance of an ensemble\n",
    "  If we assume that each one of the $T$ base classifiers has a probability $\\rho$ of \n",
    "  being correct, the probability of an ensemble making the correct decision, assuming independence, \n",
    "  denoted by $P_c$, can be calculated using the binomial distribution\n",
    "\n",
    "$$P_c = \\sum_{j>T/2}^{T} {{T}\\choose{j}} \\rho^j(1-\\rho)^{T-j}.$$\n",
    "\n",
    "  Furthermore, as shown, if $T\\ge3$ then:\n",
    "\n",
    "$$\n",
    "  \\lim_{T \\to  \\infty} P_c= \\begin{cases} \n",
    "            1  &\\mbox{if } \\rho>0.5 \\\\ \n",
    "            0  &\\mbox{if } \\rho<0.5 \\\\ \n",
    "            0.5  &\\mbox{if } \\rho=0.5 ,\n",
    "            \\end{cases}\n",
    "$$\n",
    "\tleading to the conclusion that \n",
    "$$\n",
    "  \\rho \\ge 0.5 \\quad \\text{and} \\quad T\\ge3 \\quad \\Rightarrow \\quad P_c\\ge \\rho.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Part 2: Manual ensembling\n",
    "\n",
    "What makes a good manual ensemble?\n",
    "\n",
    "- Different types of **models**\n",
    "- Different combinations of **features**\n",
    "- Different **tuning parameters**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Machine learning flowchart](https://raw.githubusercontent.com/justmarkham/DAT8/master/notebooks/images/crowdflower_ensembling.jpg)\n",
    "\n",
    "*Machine learning flowchart created by the [winner](https://github.com/ChenglongChen/Kaggle_CrowdFlower) of Kaggle's [CrowdFlower competition](https://www.kaggle.com/c/crowdflower-search-relevance)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# read in and prepare the vehicle training data\n",
    "import zipfile\n",
    "import pandas as pd\n",
    "with zipfile.ZipFile('../datasets/vehicles_train.csv.zip', 'r') as z:\n",
    "    f = z.open('vehicles_train.csv')\n",
    "    train = pd.io.parsers.read_table(f, index_col=False, sep=',')\n",
    "with zipfile.ZipFile('../datasets/vehicles_test.csv.zip', 'r') as z:\n",
    "    f = z.open('vehicles_test.csv')\n",
    "    test = pd.io.parsers.read_table(f, index_col=False, sep=',')\n",
    "\n",
    "train['vtype'] = train.vtype.map({'car':0, 'truck':1})\n",
    "# read in and prepare the vehicle testing data\n",
    "test['vtype'] = test.vtype.map({'car':0, 'truck':1})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>price</th>\n",
       "      <th>year</th>\n",
       "      <th>miles</th>\n",
       "      <th>doors</th>\n",
       "      <th>vtype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22000</td>\n",
       "      <td>2012</td>\n",
       "      <td>13000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14000</td>\n",
       "      <td>2010</td>\n",
       "      <td>30000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13000</td>\n",
       "      <td>2010</td>\n",
       "      <td>73500</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9500</td>\n",
       "      <td>2009</td>\n",
       "      <td>78000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9000</td>\n",
       "      <td>2007</td>\n",
       "      <td>47000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price  year  miles  doors  vtype\n",
       "0  22000  2012  13000      2      0\n",
       "1  14000  2010  30000      2      0\n",
       "2  13000  2010  73500      4      0\n",
       "3   9500  2009  78000      4      0\n",
       "4   9000  2007  47000      4      0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train different models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.neighbors import KNeighborsRegressor\n",
    "\n",
    "models = {'lr': LinearRegression(),\n",
    "          'dt': DecisionTreeRegressor(),\n",
    "          'nb': GaussianNB(),\n",
    "          'nn': KNeighborsRegressor()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Train all the models\n",
    "X_train = train.iloc[:, 1:]\n",
    "X_test = test.iloc[:, 1:]\n",
    "y_train = train.price\n",
    "y_test = test.price\n",
    "\n",
    "for model in models.keys():\n",
    "    models[model].fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# predict test for each model\n",
    "y_pred = pd.DataFrame(index=test.index, columns=models.keys())\n",
    "for model in models.keys():\n",
    "    y_pred[model] = models[model].predict(X_test)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt 1414.21356237\n",
      "lr 2138.35790287\n",
      "nn 1671.32681823\n",
      "nb 5477.22557505\n"
     ]
    }
   ],
   "source": [
    "# Evaluate each model\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "for model in models.keys():\n",
    "    print(model,np.sqrt(mean_squared_error(y_pred[model], y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate the error of the mean of the predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1193.164765760328"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(mean_squared_error(y_pred.mean(axis=1), y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing manual ensembling with a single model approach\n",
    "\n",
    "**Advantages of manual ensembling:**\n",
    "\n",
    "- Increases predictive accuracy\n",
    "- Easy to get started\n",
    "\n",
    "**Disadvantages of manual ensembling:**\n",
    "\n",
    "- Decreases interpretability\n",
    "- Takes longer to train\n",
    "- Takes longer to predict\n",
    "- More complex to automate and maintain\n",
    "- Small gains in accuracy may not be worth the added complexity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 3: Bagging\n",
    "\n",
    "The primary weakness of **decision trees** is that they don't tend to have the best predictive accuracy. This is partially due to **high variance**, meaning that different splits in the training data can lead to very different trees.\n",
    "\n",
    "**Bagging** is a general purpose procedure for reducing the variance of a machine learning method, but is particularly useful for decision trees. Bagging is short for **bootstrap aggregation**, meaning the aggregation of bootstrap samples.\n",
    "\n",
    "What is a **bootstrap sample**? A random sample with replacement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20]\n",
      "[ 6 12 13  9 10 12  6 16  1 17  2 13  8 14  7 19  6 19 12 11]\n"
     ]
    }
   ],
   "source": [
    "# set a seed for reproducibility\n",
    "np.random.seed(1)\n",
    "\n",
    "# create an array of 1 through 20\n",
    "nums = np.arange(1, 21)\n",
    "print(nums)\n",
    "\n",
    "# sample that array 20 times with replacement\n",
    "print(np.random.choice(a=nums, size=20, replace=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How does bagging work (for decision trees)?**\n",
    "\n",
    "1. Grow B trees using B bootstrap samples from the training data.\n",
    "2. Train each tree on its bootstrap sample and make predictions.\n",
    "3. Combine the predictions:\n",
    "    - Average the predictions for **regression trees**\n",
    "    - Take a vote for **classification trees**\n",
    "\n",
    "Notes:\n",
    "\n",
    "- **Each bootstrap sample** should be the same size as the original training set.\n",
    "- **B** should be a large enough value that the error seems to have \"stabilized\".\n",
    "- The trees are **grown deep** so that they have low bias/high variance.\n",
    "\n",
    "Bagging increases predictive accuracy by **reducing the variance**, similar to how cross-validation reduces the variance associated with train/test split (for estimating out-of-sample error) by splitting many times an averaging the results.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([13,  2, 12,  2,  6,  1,  3, 10, 11,  9,  6,  1,  0,  1]),\n",
       " array([ 9,  0,  0,  9,  3, 13,  4,  0,  0,  4,  1,  7,  3,  2]),\n",
       " array([ 4,  7,  2,  4,  8, 13,  0,  7,  9,  3, 12, 12,  4,  6]),\n",
       " array([ 1,  5,  6, 11,  2,  1, 12,  8,  3, 10,  5,  0, 11,  2]),\n",
       " array([10, 10,  6, 13,  2,  4, 11, 11, 13, 12,  4,  6, 13,  3]),\n",
       " array([10,  0,  6,  4,  7, 11,  6,  7,  1, 11, 10,  5,  7,  9]),\n",
       " array([ 2,  4,  8,  1, 12,  2,  1,  1,  3, 12,  5,  9,  0,  8]),\n",
       " array([11,  1,  6,  3,  3, 11,  5,  9,  7,  9,  2,  3, 11,  3]),\n",
       " array([ 3,  8,  6,  9,  7,  6,  3,  9,  6, 12,  6, 11,  6,  1]),\n",
       " array([13, 10,  3,  4,  3,  1, 13,  0,  5,  8, 13,  6, 11,  8])]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set a seed for reproducibility\n",
    "np.random.seed(123)\n",
    "\n",
    "n_samples = train.shape[0]\n",
    "n_B = 10\n",
    "\n",
    "# create ten bootstrap samples (will be used to select rows from the DataFrame)\n",
    "samples = [np.random.choice(a=n_samples, size=n_samples, replace=True) for _ in range(1, n_B +1 )]\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>price</th>\n",
       "      <th>year</th>\n",
       "      <th>miles</th>\n",
       "      <th>doors</th>\n",
       "      <th>vtype</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1300</td>\n",
       "      <td>1997</td>\n",
       "      <td>138000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13000</td>\n",
       "      <td>2010</td>\n",
       "      <td>73500</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1800</td>\n",
       "      <td>1999</td>\n",
       "      <td>163000</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13000</td>\n",
       "      <td>2010</td>\n",
       "      <td>73500</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3000</td>\n",
       "      <td>2004</td>\n",
       "      <td>177000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14000</td>\n",
       "      <td>2010</td>\n",
       "      <td>30000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9500</td>\n",
       "      <td>2009</td>\n",
       "      <td>78000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2500</td>\n",
       "      <td>2003</td>\n",
       "      <td>190000</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5000</td>\n",
       "      <td>2001</td>\n",
       "      <td>62000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1900</td>\n",
       "      <td>2003</td>\n",
       "      <td>160000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3000</td>\n",
       "      <td>2004</td>\n",
       "      <td>177000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14000</td>\n",
       "      <td>2010</td>\n",
       "      <td>30000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>22000</td>\n",
       "      <td>2012</td>\n",
       "      <td>13000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14000</td>\n",
       "      <td>2010</td>\n",
       "      <td>30000</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    price  year   miles  doors  vtype\n",
       "13   1300  1997  138000      4      0\n",
       "2   13000  2010   73500      4      0\n",
       "12   1800  1999  163000      2      1\n",
       "2   13000  2010   73500      4      0\n",
       "6    3000  2004  177000      4      0\n",
       "1   14000  2010   30000      2      0\n",
       "3    9500  2009   78000      4      0\n",
       "10   2500  2003  190000      2      1\n",
       "11   5000  2001   62000      4      0\n",
       "9    1900  2003  160000      4      0\n",
       "6    3000  2004  177000      4      0\n",
       "1   14000  2010   30000      2      0\n",
       "0   22000  2012   13000      2      0\n",
       "1   14000  2010   30000      2      0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the rows for the first decision tree\n",
    "train.iloc[samples[0], :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Build one tree for each sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "# grow each tree deep\n",
    "treereg = DecisionTreeRegressor(max_depth=None, random_state=123)\n",
    "\n",
    "# DataFrame for storing predicted price from each tree\n",
    "y_pred = pd.DataFrame(index=test.index, columns=[list(range(n_B))])\n",
    "\n",
    "# grow one tree for each bootstrap sample and make predictions on testing data\n",
    "for i, sample in enumerate(samples):\n",
    "    X_train = train.iloc[sample, 1:]\n",
    "    y_train = train.iloc[sample, 0]\n",
    "    treereg.fit(X_train, y_train)\n",
    "    y_pred[i] = treereg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1300.0</td>\n",
       "      <td>1300.0</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>1300.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>4000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5000.0</td>\n",
       "      <td>1300.0</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>4000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>5000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>14000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>13000.0</td>\n",
       "      <td>9500.0</td>\n",
       "      <td>9000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0        1        2        3        4        5        6        7  \\\n",
       "0   1300.0   1300.0   3000.0   4000.0   1300.0   4000.0   4000.0   4000.0   \n",
       "1   5000.0   1300.0   3000.0   5000.0   5000.0   5000.0   4000.0   5000.0   \n",
       "2  14000.0  13000.0  13000.0  13000.0  13000.0  14000.0  13000.0  13000.0   \n",
       "\n",
       "        8       9  \n",
       "0  3000.0  4000.0  \n",
       "1  5000.0  5000.0  \n",
       "2  9500.0  9000.0  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results of each tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1621.72747402\n",
      "1 2942.78779391\n",
      "2 1825.74185835\n",
      "3 1000.0\n",
      "4 1276.71453348\n",
      "5 1414.21356237\n",
      "6 1414.21356237\n",
      "7 1000.0\n",
      "8 1554.56317551\n",
      "9 1914.85421551\n"
     ]
    }
   ],
   "source": [
    "for i in range(n_B):\n",
    "    print(i, np.sqrt(mean_squared_error(y_pred[i], y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results of the ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     2990.0\n",
       "1     4330.0\n",
       "2    12450.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "998.58232843700307"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(mean_squared_error(y_test, y_pred.mean(axis=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bagged decision trees in scikit-learn (with B=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define the training and testing sets\n",
    "X_train = train.iloc[:, 1:]\n",
    "y_train = train.iloc[:, 0]\n",
    "X_test = test.iloc[:, 1:]\n",
    "y_test = test.iloc[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# instruct BaggingRegressor to use DecisionTreeRegressor as the \"base estimator\"\n",
    "from sklearn.ensemble import BaggingRegressor\n",
    "bagreg = BaggingRegressor(DecisionTreeRegressor(), n_estimators=500, \n",
    "                          bootstrap=True, oob_score=True, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  3344.2,   5395. ,  12902. ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit and predict\n",
    "bagreg.fit(X_train, y_train)\n",
    "y_pred = bagreg.predict(X_test)\n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "657.80003040437748"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate RMSE\n",
    "np.sqrt(mean_squared_error(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating out-of-sample error\n",
    "\n",
    "For bagged models, out-of-sample error can be estimated without using **train/test split** or **cross-validation**!\n",
    "\n",
    "On average, each bagged tree uses about **two-thirds** of the observations. For each tree, the **remaining observations** are called \"out-of-bag\" observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13,  2, 12,  2,  6,  1,  3, 10, 11,  9,  6,  1,  0,  1])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the first bootstrap sample\n",
    "samples[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 6, 9, 10, 11, 12, 13}\n",
      "{0, 1, 2, 3, 4, 7, 9, 13}\n",
      "{0, 2, 3, 4, 6, 7, 8, 9, 12, 13}\n",
      "{0, 1, 2, 3, 5, 6, 8, 10, 11, 12}\n",
      "{2, 3, 4, 6, 10, 11, 12, 13}\n",
      "{0, 1, 4, 5, 6, 7, 9, 10, 11}\n",
      "{0, 1, 2, 3, 4, 5, 8, 9, 12}\n",
      "{1, 2, 3, 5, 6, 7, 9, 11}\n",
      "{1, 3, 6, 7, 8, 9, 11, 12}\n",
      "{0, 1, 3, 4, 5, 6, 8, 10, 11, 13}\n"
     ]
    }
   ],
   "source": [
    "# show the \"in-bag\" observations for each sample\n",
    "for sample in samples:\n",
    "    print(set(sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 5, 7, 8]\n",
      "[5, 6, 8, 10, 11, 12]\n",
      "[1, 5, 10, 11]\n",
      "[4, 7, 9, 13]\n",
      "[0, 1, 5, 7, 8, 9]\n",
      "[2, 3, 8, 12, 13]\n",
      "[6, 7, 10, 11, 13]\n",
      "[0, 4, 8, 10, 12, 13]\n",
      "[0, 2, 4, 5, 10, 13]\n",
      "[2, 7, 9, 12]\n"
     ]
    }
   ],
   "source": [
    "# show the \"out-of-bag\" observations for each sample\n",
    "for sample in samples:\n",
    "    print(sorted(set(range(n_samples)) - set(sample)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to calculate **\"out-of-bag error\":**\n",
    "\n",
    "1. For every observation in the training data, predict its response value using **only** the trees in which that observation was out-of-bag. Average those predictions (for regression) or take a vote (for classification).\n",
    "2. Compare all predictions to the actual response values in order to compute the out-of-bag error.\n",
    "\n",
    "When B is sufficiently large, the **out-of-bag error** is an accurate estimate of **out-of-sample error**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76698184959239768"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the out-of-bag R-squared score (not MSE, unfortunately!) for B=500\n",
    "bagreg.oob_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating feature importance\n",
    "\n",
    "Bagging increases **predictive accuracy**, but decreases **model interpretability** because it's no longer possible to visualize the tree to understand the importance of each feature.\n",
    "\n",
    "However, we can still obtain an overall summary of **feature importance** from bagged models:\n",
    "\n",
    "- **Bagged regression trees:** calculate the total amount that **MSE** is decreased due to splits over a given feature, averaged over all trees\n",
    "- **Bagged classification trees:** calculate the total amount that **Gini index** is decreased due to splits over a given feature, averaged over all trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 4: Random Forests\n",
    "\n",
    "Random Forests is a **slight variation of bagged trees** that has even better performance:\n",
    "\n",
    "- Exactly like bagging, we create an ensemble of decision trees using bootstrapped samples of the training set.\n",
    "- However, when building each tree, each time a split is considered, a **random sample of m features** is chosen as split candidates from the **full set of p features**. The split is only allowed to use **one of those m features**.\n",
    "    - A new random sample of features is chosen for **every single tree at every single split**.\n",
    "    - For **classification**, m is typically chosen to be the square root of p.\n",
    "    - For **regression**, m is typically chosen to be somewhere between p/3 and p.\n",
    "\n",
    "What's the point?\n",
    "\n",
    "- Suppose there is **one very strong feature** in the data set. When using bagged trees, most of the trees will use that feature as the top split, resulting in an ensemble of similar trees that are **highly correlated**.\n",
    "- Averaging highly correlated quantities does not significantly reduce variance (which is the entire goal of bagging).\n",
    "- By randomly leaving out candidate features from each split, **Random Forests \"decorrelates\" the trees**, such that the averaging process can reduce the variance of the resulting model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 5: Building and tuning decision trees and Random Forests\n",
    "\n",
    "- Major League Baseball player data from 1986-87: [data](https://github.com/justmarkham/DAT8/blob/master/data/hitters.csv), [data dictionary](https://cran.r-project.org/web/packages/ISLR/ISLR.pdf) (page 7)\n",
    "- Each observation represents a player\n",
    "- **Goal:** Predict player salary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>N</td>\n",
       "      <td>W</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>475.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>480.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>500.0</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>N</td>\n",
       "      <td>E</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>91.5</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>A</td>\n",
       "      <td>W</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>750.0</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  CHmRun  CRuns  \\\n",
       "1    315    81      7    24   38     39     14    3449    835      69    321   \n",
       "2    479   130     18    66   72     76      3    1624    457      63    224   \n",
       "3    496   141     20    65   78     37     11    5628   1575     225    828   \n",
       "4    321    87     10    39   42     30      2     396    101      12     48   \n",
       "5    594   169      4    74   51     35     11    4408   1133      19    501   \n",
       "\n",
       "   CRBI  CWalks League Division  PutOuts  Assists  Errors  Salary NewLeague  \n",
       "1   414     375      N        W      632       43      10   475.0         N  \n",
       "2   266     263      A        W      880       82      14   480.0         A  \n",
       "3   838     354      N        E      200       11       3   500.0         N  \n",
       "4    46      33      N        E      805       40       4    91.5         N  \n",
       "5   336     194      A        W      282      421      25   750.0         A  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read in the data\n",
    "with zipfile.ZipFile('../datasets/hitters.csv.zip', 'r') as z:\n",
    "    f = z.open('hitters.csv')\n",
    "    hitters = pd.read_csv(f, sep=',', index_col=False)\n",
    "\n",
    "# remove rows with missing values\n",
    "hitters.dropna(inplace=True)\n",
    "hitters.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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>AtBat</th>\n",
       "      <th>Hits</th>\n",
       "      <th>HmRun</th>\n",
       "      <th>Runs</th>\n",
       "      <th>RBI</th>\n",
       "      <th>Walks</th>\n",
       "      <th>Years</th>\n",
       "      <th>CAtBat</th>\n",
       "      <th>CHits</th>\n",
       "      <th>CHmRun</th>\n",
       "      <th>CRuns</th>\n",
       "      <th>CRBI</th>\n",
       "      <th>CWalks</th>\n",
       "      <th>League</th>\n",
       "      <th>Division</th>\n",
       "      <th>PutOuts</th>\n",
       "      <th>Assists</th>\n",
       "      <th>Errors</th>\n",
       "      <th>Salary</th>\n",
       "      <th>NewLeague</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>315</td>\n",
       "      <td>81</td>\n",
       "      <td>7</td>\n",
       "      <td>24</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>14</td>\n",
       "      <td>3449</td>\n",
       "      <td>835</td>\n",
       "      <td>69</td>\n",
       "      <td>321</td>\n",
       "      <td>414</td>\n",
       "      <td>375</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>632</td>\n",
       "      <td>43</td>\n",
       "      <td>10</td>\n",
       "      <td>475.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>479</td>\n",
       "      <td>130</td>\n",
       "      <td>18</td>\n",
       "      <td>66</td>\n",
       "      <td>72</td>\n",
       "      <td>76</td>\n",
       "      <td>3</td>\n",
       "      <td>1624</td>\n",
       "      <td>457</td>\n",
       "      <td>63</td>\n",
       "      <td>224</td>\n",
       "      <td>266</td>\n",
       "      <td>263</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>880</td>\n",
       "      <td>82</td>\n",
       "      <td>14</td>\n",
       "      <td>480.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>496</td>\n",
       "      <td>141</td>\n",
       "      <td>20</td>\n",
       "      <td>65</td>\n",
       "      <td>78</td>\n",
       "      <td>37</td>\n",
       "      <td>11</td>\n",
       "      <td>5628</td>\n",
       "      <td>1575</td>\n",
       "      <td>225</td>\n",
       "      <td>828</td>\n",
       "      <td>838</td>\n",
       "      <td>354</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>200</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>500.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>321</td>\n",
       "      <td>87</td>\n",
       "      <td>10</td>\n",
       "      <td>39</td>\n",
       "      <td>42</td>\n",
       "      <td>30</td>\n",
       "      <td>2</td>\n",
       "      <td>396</td>\n",
       "      <td>101</td>\n",
       "      <td>12</td>\n",
       "      <td>48</td>\n",
       "      <td>46</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>805</td>\n",
       "      <td>40</td>\n",
       "      <td>4</td>\n",
       "      <td>91.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>594</td>\n",
       "      <td>169</td>\n",
       "      <td>4</td>\n",
       "      <td>74</td>\n",
       "      <td>51</td>\n",
       "      <td>35</td>\n",
       "      <td>11</td>\n",
       "      <td>4408</td>\n",
       "      <td>1133</td>\n",
       "      <td>19</td>\n",
       "      <td>501</td>\n",
       "      <td>336</td>\n",
       "      <td>194</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>282</td>\n",
       "      <td>421</td>\n",
       "      <td>25</td>\n",
       "      <td>750.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  CHmRun  CRuns  \\\n",
       "1    315    81      7    24   38     39     14    3449    835      69    321   \n",
       "2    479   130     18    66   72     76      3    1624    457      63    224   \n",
       "3    496   141     20    65   78     37     11    5628   1575     225    828   \n",
       "4    321    87     10    39   42     30      2     396    101      12     48   \n",
       "5    594   169      4    74   51     35     11    4408   1133      19    501   \n",
       "\n",
       "   CRBI  CWalks  League  Division  PutOuts  Assists  Errors  Salary  NewLeague  \n",
       "1   414     375       0         0      632       43      10   475.0          0  \n",
       "2   266     263       1         0      880       82      14   480.0          1  \n",
       "3   838     354       0         1      200       11       3   500.0          0  \n",
       "4    46      33       0         1      805       40       4    91.5          0  \n",
       "5   336     194       1         0      282      421      25   750.0          1  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# encode categorical variables as integers\n",
    "hitters['League'] = pd.factorize(hitters.League)[0]\n",
    "hitters['Division'] = pd.factorize(hitters.Division)[0]\n",
    "hitters['NewLeague'] = pd.factorize(hitters.NewLeague)[0]\n",
    "hitters.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# allow plots to appear in the notebook\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f3a5e247208>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HxcWB55ItkGz8pDtMUQctxZIjYFohuGS3mwNvv+17nLdpE04RNIWGopY1zczMTF/A7NCh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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3a5e237780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# scatter plot of Years versus Hits colored by Salary\n",
    "hitters.plot(kind='scatter', x='Years', y='Hits', c='Salary', colormap='jet', xlim=(0, 25), ylim=(0, 250))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['AtBat', 'Hits', 'HmRun', 'Runs', 'RBI', 'Walks', 'Years', 'League',\n",
       "       'Division', 'PutOuts', 'Assists', 'Errors', 'NewLeague'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define features: exclude career statistics (which start with \"C\") and the response (Salary)\n",
    "feature_cols = hitters.columns[hitters.columns.str.startswith('C') == False].drop('Salary')\n",
    "feature_cols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define X and y\n",
    "X = hitters[feature_cols]\n",
    "y = hitters.Salary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predicting salary with a decision tree\n",
    "\n",
    "Find the best **max_depth** for a decision tree using cross-validation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# list of values to try for max_depth\n",
    "max_depth_range = range(1, 21)\n",
    "\n",
    "# list to store the average RMSE for each value of max_depth\n",
    "RMSE_scores = []\n",
    "\n",
    "# use 10-fold cross-validation with each value of max_depth\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "for depth in max_depth_range:\n",
    "    treereg = DecisionTreeRegressor(max_depth=depth, random_state=1)\n",
    "    MSE_scores = cross_val_score(treereg, X, y, cv=10, scoring='mean_squared_error')\n",
    "    RMSE_scores.append(np.mean(np.sqrt(-MSE_scores)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3a5dc99eb8>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oBlDz/04X8/9OFxPqqWTAfW4MaONG1wCXe9ouadXpYi5V6ip9vocPXi7S8SGE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\np/n80QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3a5e237da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot max_depth (x-axis) versus RMSE (y-axis)\n",
    "plt.plot(max_depth_range, RMSE_scores)\n",
    "plt.xlabel('max_depth')\n",
    "plt.ylabel('RMSE (lower is better)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(340.03416870475201, 2)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the best RMSE and the corresponding max_depth\n",
    "sorted(zip(RMSE_scores, max_depth_range))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(criterion='mse', max_depth=2, max_features=None,\n",
       "           max_leaf_nodes=None, min_samples_leaf=1, min_samples_split=2,\n",
       "           min_weight_fraction_leaf=0.0, presort=False, random_state=1,\n",
       "           splitter='best')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# max_depth=2 was best, so fit a tree using that parameter\n",
    "treereg = DecisionTreeRegressor(max_depth=2, random_state=1)\n",
    "treereg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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>feature</th>\n",
       "      <th>importance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AtBat</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HmRun</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Runs</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>RBI</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Walks</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>League</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Division</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PutOuts</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Assists</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Errors</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NewLeague</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Years</td>\n",
       "      <td>0.488391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Hits</td>\n",
       "      <td>0.511609</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      feature  importance\n",
       "0       AtBat    0.000000\n",
       "2       HmRun    0.000000\n",
       "3        Runs    0.000000\n",
       "4         RBI    0.000000\n",
       "5       Walks    0.000000\n",
       "7      League    0.000000\n",
       "8    Division    0.000000\n",
       "9     PutOuts    0.000000\n",
       "10    Assists    0.000000\n",
       "11     Errors    0.000000\n",
       "12  NewLeague    0.000000\n",
       "6       Years    0.488391\n",
       "1        Hits    0.511609"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute feature importances\n",
    "pd.DataFrame({'feature':feature_cols, 'importance':treereg.feature_importances_}).sort_values('importance')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predicting salary with a Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,\n",
       "           max_features='auto', max_leaf_nodes=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": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "rfreg = RandomForestRegressor()\n",
    "rfreg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tuning n_estimators\n",
    "\n",
    "One important tuning parameter is **n_estimators**, which is the number of trees that should be grown. It should be a large enough value that the error seems to have \"stabilized\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# list of values to try for n_estimators\n",
    "estimator_range = range(10, 310, 10)\n",
    "\n",
    "# list to store the average RMSE for each value of n_estimators\n",
    "RMSE_scores = []\n",
    "\n",
    "# use 5-fold cross-validation with each value of n_estimators (WARNING: SLOW!)\n",
    "for estimator in estimator_range:\n",
    "    rfreg = RandomForestRegressor(n_estimators=estimator, random_state=1, n_jobs=-1)\n",
    "    MSE_scores = cross_val_score(rfreg, X, y, cv=5, scoring='mean_squared_error')\n",
    "    RMSE_scores.append(np.mean(np.sqrt(-MSE_scores)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3a5dc062b0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qa66flZSUkJKSwurVqxk1ahQAa9asIS4ujs8//5wxY8a0OLbmkp6kEEI4H5tv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\nIAGeO1KKRlFI6uG6ReGNZjNHztfwWZ6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zmynihmdInnl5eZiYmGBlZVWjT25ubpPF2hhG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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3a5dcd8198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot n_estimators (x-axis) versus RMSE (y-axis)\n",
    "plt.plot(estimator_range, RMSE_scores)\n",
    "plt.xlabel('n_estimators')\n",
    "plt.ylabel('RMSE (lower is better)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tuning max_features\n",
    "\n",
    "The other important tuning parameter is **max_features**, which is the number of features that should be considered at each split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# list of values to try for max_features\n",
    "feature_range = range(1, len(feature_cols)+1)\n",
    "\n",
    "# list to store the average RMSE for each value of max_features\n",
    "RMSE_scores = []\n",
    "\n",
    "# use 10-fold cross-validation with each value of max_features (WARNING: SLOW!)\n",
    "for feature in feature_range:\n",
    "    rfreg = RandomForestRegressor(n_estimators=150, max_features=feature, random_state=1, n_jobs=-1)\n",
    "    MSE_scores = cross_val_score(rfreg, X, y, cv=10, scoring='mean_squared_error')\n",
    "    RMSE_scores.append(np.mean(np.sqrt(-MSE_scores)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f3a5dc06e48>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dTkdUVBSLFi1qcDzgzcjNzWXhwoXk5eXh6enJ4MGDSU5OZvz48QB88cUXPPbY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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3a5dcd8ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot max_features (x-axis) versus RMSE (y-axis)\n",
    "plt.plot(feature_range, RMSE_scores)\n",
    "plt.xlabel('max_features')\n",
    "plt.ylabel('RMSE (lower is better)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(290.00785113284348, 10)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# show the best RMSE and the corresponding max_features\n",
    "sorted(zip(RMSE_scores, feature_range))[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a Random Forest with the best parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=None,\n",
       "           max_features=8, max_leaf_nodes=None, min_samples_leaf=1,\n",
       "           min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "           n_estimators=150, n_jobs=1, oob_score=True, random_state=1,\n",
       "           verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# max_features=8 is best and n_estimators=150 is sufficiently large\n",
    "rfreg = RandomForestRegressor(n_estimators=150, max_features=8, oob_score=True, random_state=1)\n",
    "rfreg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "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>feature</th>\n",
       "      <th>importance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>League</td>\n",
       "      <td>0.003603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>NewLeague</td>\n",
       "      <td>0.004290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Division</td>\n",
       "      <td>0.005477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Assists</td>\n",
       "      <td>0.023842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Errors</td>\n",
       "      <td>0.028618</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>HmRun</td>\n",
       "      <td>0.044607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>PutOuts</td>\n",
       "      <td>0.060063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Runs</td>\n",
       "      <td>0.071800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AtBat</td>\n",
       "      <td>0.094592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>RBI</td>\n",
       "      <td>0.130965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Walks</td>\n",
       "      <td>0.139899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Hits</td>\n",
       "      <td>0.145264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Years</td>\n",
       "      <td>0.246980</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      feature  importance\n",
       "7      League    0.003603\n",
       "12  NewLeague    0.004290\n",
       "8    Division    0.005477\n",
       "10    Assists    0.023842\n",
       "11     Errors    0.028618\n",
       "2       HmRun    0.044607\n",
       "9     PutOuts    0.060063\n",
       "3        Runs    0.071800\n",
       "0       AtBat    0.094592\n",
       "4         RBI    0.130965\n",
       "5       Walks    0.139899\n",
       "1        Hits    0.145264\n",
       "6       Years    0.246980"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute feature importances\n",
    "pd.DataFrame({'feature':feature_cols, 'importance':rfreg.feature_importances_}).sort_values('importance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.52741870027692672"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the out-of-bag R-squared score\n",
    "rfreg.oob_score_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reducing X to its most important features\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(263, 13)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the shape of X\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(263, 4)\n",
      "(263, 5)\n",
      "(263, 7)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/al/anaconda3/lib/python3.5/site-packages/sklearn/utils/__init__.py:93: DeprecationWarning: Function transform is deprecated; Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/home/al/anaconda3/lib/python3.5/site-packages/sklearn/utils/__init__.py:93: DeprecationWarning: Function transform is deprecated; Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/home/al/anaconda3/lib/python3.5/site-packages/sklearn/utils/__init__.py:93: DeprecationWarning: Function transform is deprecated; Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "# set a threshold for which features to include\n",
    "print(rfreg.transform(X, threshold=0.1).shape)\n",
    "print(rfreg.transform(X, threshold='mean').shape)\n",
    "print(rfreg.transform(X, threshold='median').shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/al/anaconda3/lib/python3.5/site-packages/sklearn/utils/__init__.py:93: DeprecationWarning: Function transform is deprecated; Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "# create a new feature matrix that only includes important features\n",
    "X_important = rfreg.transform(X, threshold='mean')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "284.35550515135395"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the RMSE for a Random Forest that only includes important features\n",
    "rfreg = RandomForestRegressor(n_estimators=150, max_features=3, random_state=1)\n",
    "scores = cross_val_score(rfreg, X_important, y, cv=10, scoring='mean_squared_error')\n",
    "np.mean(np.sqrt(-scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Random Forests with decision trees\n",
    "\n",
    "**Advantages of Random Forests:**\n",
    "\n",
    "- Performance is competitive with the best supervised learning methods\n",
    "- Provides a more reliable estimate of feature importance\n",
    "- Allows you to estimate out-of-sample error without using train/test split or cross-validation\n",
    "\n",
    "**Disadvantages of Random Forests:**\n",
    "\n",
    "- Less interpretable\n",
    "- Slower to train\n",
    "- Slower to predict"
   ]
  },
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    "![Machine learning flowchart](images/driver_ensembling.png)\n",
    "\n",
    "*Machine learning flowchart created by the [second place finisher](http://blog.kaggle.com/2015/04/20/axa-winners-interview-learning-telematic-fingerprints-from-gps-data/) of Kaggle's [Driver Telematics competition](https://www.kaggle.com/c/axa-driver-telematics-analysis)*"
   ]
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