B-MASTER: Scalable Bayesian Multivariate Regression Analysis for Selecting Targeted Essential Regressors to Identify the Key Genera in Microbiome-Metabolite Relation Dynamics (2412.05998v2)

Abstract: We introduce B-MASTER (Bayesian Multivariate regression Analysis for Selecting Targeted Essential Regressors), a fully Bayesian framework for scalable multivariate regression in high dimensions. B-MASTER is designed to identify master predictors, i.e., covariates exerting widespread influence across many outcomes, via a hybrid penalty: an L1 penalty induces elementwise sparsity, while an L2 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. We establish posterior consistency and contraction rate results, 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.