A0756
Title: A generalized Bayesian tree ensemble approach to density learning
Authors: Linxi Liu - University of Pittsburgh (United States) [presenting]
Li Ma - Duke University (United States)
Abstract: Tree-based methods cover a broad class of effective and computationally efficient nonparametric learning algorithms. In supervised learning, tree ensembles, such as forests, boosting, and BART, are among the most successful and widely adopted algorithms, even when facing the competition of deep learning methods. In unsupervised learning, tree-based methods have been proven effective in a range of statistical inference tasks, such as density estimation, clustering, multi-resolution sketching of distributional variations, and data compression. Density learning, which includes both density estimation and generative modeling, is a fundamental problem in unsupervised learning. A novel generalized Bayesian tree ensemble approach is introduced to density learning, called Gibbs density forests. Instead of making likelihood-based inference under the classical Bayesian framework, the method employs an empirical risk function for each forest topology and makes risk-based generalized Bayesian inference. A carefully designed risk function is central to this framework. Such a risk function is proposed, and its effectiveness is demonstrated in quantifying the goodness of each forest. In addition, an efficient computational algorithm is proposed based on sequential Monte Carlo for computing the density estimates, and the practical performance of the proposed method is illustrated through simulations in both low-dimensional and moderately high-dimensional settings.
