Machine Learning
Machine Learning
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The Bayesian CART (classification and regression tree) approachproposed by Chipman, George and McCulloch (1998) entails putting aprior distribution on the set of all CART models and then usingstochastic search to select a model. The main thrust of this paper isto propose a new class of hierarchical priors which enhance thepotential of this Bayesian approach. These priors indicate apreference for smooth local mean structure, resulting in tree models whichshrink predictions from adjacent terminal node towards each other.Past methods for tree shrinkage have searched for trees without shrinking,and applied shrinkage to the identified tree only after the search.By using hierarchical priors in the stochastic search, the proposedmethod searches for shrunk trees that fit well and improvesthe tree through shrinkage of predictions.