A0846
Title: A partial likelihood approach to tree-based density modeling and its application in Bayesian inference
Authors: Li Ma - Duke University (United States)
Benedetta Bruni - Duke University (United States) [presenting]
Abstract: Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density over the entire sample space, 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 make inference prone to overfitting, especially in regions with little probability mass. Thus, existing models rely on relatively shallow trees, limiting their ability to characterize local features and reducing statistical efficiency. This compromise can be inevitable to ensure coherent likelihood-based reasoning in Bayesian inference, as a data-dependent partition system allowing deeper expansion only in regions with more observations would induce double dipping of the data. The proposal is to restore coherency while allowing candidate partitions to be data-dependent using Cox's partial likelihood. The approach applies to existing likelihood-based methods, particularly to Bayesian inference on tree-based models. Density estimation examples are given, where the partial likelihood is endowed with existing priors on tree-based models and is compared with the standard, full-likelihood approach. The results show substantial gains in estimation accuracy and computational efficiency from adopting the partial likelihood.
