A1526
Title: A partial-likelihood approach to tree-based density modeling and its applications to Bayesian inference
Authors: Li Ma - University of Chicago (United States)
Benedetta Bruni - Duke University (United States) [presenting]
Abstract: Tree based priors for probability distributions are specified using a predetermined, data independent collection of candidate recursive partitions of the sample space. To characterize a target density in detail, candidate partitions must expand deeply into all areas of the sample space with potential non zero sampling probability. Such a system of partitions can incur prohibitive computational costs and cause overfitting, especially in regions with little probability mass. Existing models typically rely on relatively shallow trees. This hampers one of the most desirable features of trees, their ability to characterize local features, and reduces statistical efficiency. Traditional wisdom holds that this compromise is necessary for coherent likelihood based Bayesian inference, as a data dependent partition system that allows deeper expansion only in regions with more observations would induce double dipping of the data. We propose to restore coherency while allowing the candidate partitions to be data dependent, using Coxs partial likelihood. Our partial likelihood approach is applicable to existing likelihood based methods and to Bayesian inference on tree based models. We give examples in density estimation where the partial likelihood is endowed with existing priors on tree based models and compare with the standard, full likelihood approach. The results show substantial gains in estimation accuracy and computational efficiency from adopting the partial likelihood.
