How to Calculate Information Gain in Decision Tree?

Answer: To calculate information gain in a decision tree, subtract the weighted average entropy of child nodes from the entropy of the parent node.

To calculate information gain in a decision tree, follow these steps:

1. Calculate the Entropy of the Parent Node:
   • Compute the entropy of the parent node using the formula: Entropy=−∑_i=1 pi ​⋅log_2​(pi​)
   • Where pi​ is the proportion of instances belonging to class i, and c is the number of classes.
2. Split the Data:
   • Split the dataset into subsets based on the values of a selected attribute (feature).
3. Calculate the Entropy of Child Nodes:
   • For each subset (child node), calculate its entropy using the same formula as step 1.
4. Calculate the Weighted Average Entropy of Child Nodes:
   • Calculate the weighted average entropy of the child nodes using the formula: Weighted Average Entropy=
   • Where N_j is the number of instances in the j^th child node, N is the total number of instances, and m is the number of child nodes.
5. Calculate Information Gain:
   • Information Gain is the difference between the entropy of the parent node and the weighted average entropy of the child nodes: Information Gain=Entropy(Parent)−Weighted Average Entropy(Children)Information Gain=Entropy(Parent)−Weighted Average Entropy(Children)
6. Select the Attribute with the Highest Information Gain:
   • Choose the attribute (feature) that yields the highest information gain as the splitting criterion for the current node in the decision tree.

Conclusion:

Information gain quantifies the effectiveness of an attribute in splitting the dataset and is used to select the best attribute for decision tree node splits. By calculating information gain for each attribute, decision trees can efficiently partition the dataset based on the most informative features, leading to effective classification or regression outcomes.