{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Nonlinear Classification and Regression with Decision Trees \n", "\n", "#### Decision trees \n", "\n", "Decision trees are commonly learned by recursively splitting the set of training\n", "instances into subsets based on the instances' values for the explanatory variables. \n", "\n", "In classification tasks, the leaf nodes\n", "of the decision tree represent classes. In regression tasks, the values of the response\n", "variable for the instances contained in a leaf node may be averaged to produce the\n", "estimate for the response variable. After the decision tree has been constructed,\n", "making a prediction for a test instance requires only following the edges until a\n", "leaf node is reached. \n", "\n", "Let's create a decision tree using an algorithm called Iterative Dichotomiser 3 (ID3).\n", "Invented by Ross Quinlan, ID3 was one of the first algorithms used to train decision\n", "trees. \n", "\n", "But how to choose the first variable on which we have to divide the data so that we can have smaller tree. \n", "\n", "Measured in bits, entropy quantifies the amount of uncertainty in a variable. Entropy\n", "is given by the following equation, where n is the number of outcomes and ( ) i P x is\n", "the probability of the outcome i. Common values for b are 2, e, and 10. Because the\n", "log of a number less than one will be negative, the entire sum is negated to return a\n", "positive value. \n", "\n", "**entropy** $$ H(X) = -\\sum_{i=1}^{n} P(x_i)log_b P(x_i) $$ \n", "\n", "\n", "#### Information gain \n", "Selecting the test that produces the subsets with the lowest average entropy can produce a suboptimal tree. \n", "we will measure the reduction in entropy using a metric called information gain. \n", "Calculated with the following equation, information gain is the difference between the entropy of the parent\n", "node, H (T ), and the weighted average of the children nodes' entropies. \n", "\n", "![](data/information_gain.png) \n", "\n", "\n", "For creating Decision Tree, Algo **ID3** is the one mostly used. **C4.5** is a modified version of ID3\n", "that can be used with continuous explanatory variables and can accommodate\n", "missing values for features. C4.5 also can prune trees. \n", "Pruning reduces the size of a tree by replacing branches that classify few instances with leaf nodes. Used by\n", "scikit-learn's implementation of decision trees, **CART** is another learning algorithm\n", "that supports pruning." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Gini impurity \n", "Gini impurity measures the proportions of classes in a set. Gini impurity\n", "is given by the following equation, where j is the number of classes, t is the subset\n", "of instances for the node, and P(i|t) is the probability of selecting an element of\n", "class i from the node's subset: \n", "\n", "$$ Gini (t) = 1 - \\sum_{i=1}^{j} P(i|t)^2 $$ \n", "\n", "Intuitively, Gini impurity is zero when all of the elements of the set are the same\n", "class, as the probability of selecting an element of that class is equal to one. Like\n", "entropy, Gini impurity is greatest when each class has an equal probability of being\n", "selected. The maximum value of Gini impurity depends on the number of possible\n", "classes, and it is given by the following equation: \n", "\n", "$$ Gini_{max} = 1 - \\frac{1}{n} $$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# import\n", "import pandas as pd\n", "\n", "from sklearn.tree import DecisionTreeClassifier\n", "from sklearn.grid_search import GridSearchCV\n", "from sklearn.metrics import classification_report\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.ensemble import RandomForestClassifier" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Anaconda3\\lib\\site-packages\\IPython\\core\\interactiveshell.py:2723: DtypeWarning: Columns (3) have mixed types. Specify dtype option on import or set low_memory=False.\n", " interactivity=interactivity, compiler=compiler, result=result)\n" ] } ], "source": [ "df = pd.read_csv(\"data/ad.data\", header=None)\n", "\n", "explanatory_variable_columns = set(df.columns.values)\n", "response_variable_column = df[len(df.columns.values)-1]\n", "# The last column describes the targets\n", "explanatory_variable_columns.remove(len(df.columns.values)-1)\n", "y = [1 if e == 'ad.' else 0 for e in response_variable_column]\n", "X = df[list(explanatory_variable_columns)]\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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3279 rows × 1558 columns
\n", "