A0313
Title: Scalable Bayesian multivariate regression analysis for selecting targeted regressors in microbiome analysis
Authors: Sounak Chakraborty - University of Missouri, Columbia (United States) [presenting]
Priyam Das - Virginia Commonwealth University (United States)
Tanujit Dey - Harvard Medical School (United States)
Christine Peterson - The University of Texas MD Anderson Cancer Center (United States)
Abstract: B-MASTER (Bayesian multivariate regression analysis for selecting targeted essential regressors) is introduced, a fully Bayesian framework for scalable multivariate regression in high dimensions. B-MASTER is designed to identify master predictors covariates exerting widespread influence across many outcomes via a hybrid penalty: An $\ell_1$ penalty induces elementwise sparsity, while an $\ell_2$ penalty enforces groupwise shrinkage across rows of the coefficient matrix. This structure selects a parsimonious set of key covariates, enhancing interpretability. A tailored Gibbs sampler achieves scalability, with runtime growing linearly in parameter dimension and remaining stable across sample sizes; full posterior inference is feasible for models with up to four million parameters. Posterior consistency and contraction rate results are established, showing that B-MASTER concentrates around the truth at the minimax-optimal rate under sparsity. These theoretical guarantees are supported by strong empirical performance: In simulations, B-MASTER outperforms competing methods in estimation and signal recovery. Applied to microbiome metabolomics data from colorectal cancer patients, B-MASTER reveals microbial genera that shape broad metabolite profiles, uncovering relationships missed by other methods. The proposed approach is principled, interpretable, and scalable for discovering systemic patterns in ultra-high-dimensional biomedical data.
