You use your favorite decision tree algorithm to learn a decision tree for binary classification. Your tree has J leaves indexed j = 1, . . . , J. Leaf j contains nj training examples, mj of which are positive. However, instead of predicting a label, you would like to use this tree to predict the probability P(Y = 1 | X) (where Y is the binary class and X are the input attributes). Therefore, you decide to have each leaf predict a real value pj ∈ [0, 1]. -What are the values pj that yield the largest log likelihood? Show your work.

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Decision Tree

A decision tree is a unique kind of probability tree. A popular and powerful tool used for prediction and classification. The decision tree structure is the same as a flowchart with a tree structure. The internal node refers to the attribute test, the branch refers to the outcome of the test, and the leaf node(terminal) contains the class label.