Title: Scalable computation with skinny Gibbs sampler for high dimensional Bayesian models
Authors: Naveen Naidu Narisetty - University of Illinois at Urbana-Champaign (United States) [presenting]
Abstract: The Bayesian paradigm offers a flexible modeling framework for analyzing data with complex structures, but relative to penalization-based methods, it faces a harsher computational burden due to the posterior computation involved. A particularly challenging problem is to devise scalable Bayesian computational methods for high dimensional data settings that are commonly encountered in many biological applications including gene expression data. We will introduce a new Gibbs sampling algorithm for posterior computation called Skinny Gibbs, which is much more scalable than the standard Gibbs samplers for large datasets. In particular, the complexity of the algorithm is only linear in the number of variables at each iteration. Our Skinny Gibbs algorithm results in the property of strong model selection consistency and is flexible to use in a variety of problems including linear and logistic regressions, and a more challenging problem of censored quantile regression where a non-convex loss function is involved. We will demonstrate the statistical and computational performance of our approach through empirical studies.