Title: Bayesian density trees and forests

Abstract: Density estimation is a fundamental problem in statistics. Once an explicit estimate of the density function is obtained, various kinds of statistical inference can follow, including classification, non-parametric testing, clustering, and data compression. In this talk, I will focus on tree-based methods for density estimation under the Bayesian framework, and introduce two types of priors--the Dirichlet prior and the optional Polya tree (Wong and Ma, 2010). For a class of density functions satisfying a sparsity condition in the spectral domain, we show that Bayesian density trees can achieve fast convergence. The result implies that tree-based methods can adapt to both spatially inhomogeneous and local features of the underlying density function. I will also introduce a novel Bayesian model for density forests and show that for a class of Holder continuous functions, forests can achieve faster convergence than trees. The convergence rate is adaptive in the sense that to achieve such a rate we do not need any prior knowledge of the smoothness level. For both Bayesian density trees and forests, I will provide several numerical results to illustrate their performance in the moderately high-dimensional case.

 

 

 

Dr. Liu, Assistant Professor at the University of Pittsburgh,  holds a Ph.D. in statistics from Stanford University. Her research interests are mainly on Bayesian statistics, density estimation, and nonparametric methods.