Fast Bayesian Sparse Learning via Thresholding Priors

• Activity Number: 536 - Contributed Poster Presentations: Section on Statistics in Imaging
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Andrew Whiteman* and Jian Kang
• Companies: University of Michigan and University of Michigan
• Keywords: sparsity; Bayesian modeling; regularization; brain imaging; high-dimensional

Abstract

Motivated by the needs of analyzing large scale complex biomedical data, we propose a general framework for imposing sparsity on any given Bayesian model with a large parameter space by constructing thresholding priors. Our approach is a compelling alternative to existing frequentist regularization methods since it can provide uncertainty measures for sparse learning on complex statistical models. We develop several efficient posterior computation algorithms that are scalable to ultrahigh-dimensional parameter space. For variable selection in the linear or generalized linear model, we show that the proposed approach outperforms various existing methods in terms of both accuracy and computing time even when the number of predictors is on the exponential order of sample size. We illustrate the proposed method on an analysis of resting-state functional magnetic resonance imaging data in the the Autism Brain Imaging Data Exchange (ABIDE) study.