(Solution) - In the recursive construction of decision trees it sometimes ha -(2025 Original AI-Free Solution)

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In the recursive construction of decision trees, it sometimes happens that a mixed set of positive and negative examples remains at a leaf node, even after all the attributes have been used. Suppose that we have p positive examples and r negative examples.
a. Show that the solution used by DECISION-TREE-LEARNING, which picks the majority classification, minimizes the absolute error over the set of examples at the leaf.
b. Show that the class probability p/ (p + n) minimizes the sum of squared errors.