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204.3.5 Information Gain in Decision Tree Split

Calculating information gain after a split in Decision Tree algorithm.

Link to the previous post : https://statinfer.com/204-3-4-how-to-calculate-entropy-for-decision-tree-split/


In the previous post of this series we calculated the entropy for each split. In this post we will calculate the information gain or decrease in entropy after split.

Information Gain

  • Information Gain= entropyBeforeSplit – entropyAfterSplit.
  • Easy way to understand Information gain= (overall entropy at parent node) – (sum of weighted entropy at each child node).
  • Attribute with maximum information is best split attribute.

Information Gain- Calculation

  • Entropy Ovearll = 100% (Impurity)
  • Entropy Young Segment = 99%
  • Entropy Old Sgment = 99%
  • Information Gain for Age =100-(0.699+0.499)=1
  • Entropy Ovearll = 100% (Impurity)
  • Entropy Male Segment = 72%
  • Entropy Female Sgment = 29%
  • Information Gain for Age =100-(0.672+0.429)=45.2

Practice : Information Gain

Calculate the information gain this example base on the variable split

Output-Information Gain

Split With Respect to ‘Owning a car’

  • Entropy([28+,39-]) Ovearll = -28/67 log2 28/67 – 39/67 log2 39/67 = 98% (Impurity)
  • Entropy([25+,4-]) Owing a car = 57%
  • Entropy([3+,35-]) No car = 40%
  • Information Gain for Owing a car =98-((29/67)57+(38/67)40)=50.6

Split With Respect to ‘Gender’

  • Entropy([19+,21-]) Male= 99%
  • Entropy([9+,18-]) Female = 91%
  • Information Gain for Gender=98-((40/67)99+(27/67)91) =2.2

Other Purity (Diversity) Measures

  • Chi-square measure of association
  • Gini Index : Gini(T) = 1p2j
  • Information Gain Ratio
  • Misclassification error

The next post is about the decision tree algorithm.

Link to the next post : https://statinfer.com/204-3-6-the-decision-tree-algorithm/

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