Graph-Adaptive Shrinkage for Compositional Regression

Thomas M. Menino Convention & Exhibition Center 

Compositional predictors, such as microbiome abundances, pose unique challenges in variable selection due to their unit-sum constraint and inherent dependencies. Existing approaches often rely on fixed association graphs derived from phylogenetic or ecological distances, which may not reflect outcome-relevant relationships. We propose GRACE (GRaph-Adaptive horseshoe for Compositional rEgression), a fully Bayesian framework that enforces compositional constraints, performs variable selection, and adaptively learns an outcome-driven feature graph. GRACE achieves compositionality through a novel linear reparameterization of regression coefficients, while a structured horseshoe prior induces sparsity and smooths coefficients along the learned graph. Through extensive simulations, GRACE demonstrates competitive predictive accuracy and improved graph recovery compared with existing methods, particularly under graph misspecification. Application to oral microbiome data from the ORIGINS study identifies taxa associated with insulin resistance and reveals an outcome-driven microbial network that differs substantially from phylogenetic or co-occurrence networks.

Compositional regression

Bayesian variable selection

Shrinkage priors

Microbiome data analysis. 

Section on Bayesian Statistical Science