Bayesian Covariate-Varying Interaction Analysis for Multivariate Count Data: Application to Microbiome Studies

TL;DR

This paper introduces a Bayesian covariate-varying factor model tailored for high-dimensional microbiome count data, enabling flexible estimation of how microbial interactions change with environmental factors.

Contribution

It develops a novel Bayesian model that jointly estimates covariate-dependent mean and covariance structures, addressing key challenges in microbiome data analysis.

Findings

Model effectively captures covariate-varying microbial interactions.

Demonstrates robustness in high-dimensional, over-dispersed data.

Performs well in simulation and real microbiome datasets.

Abstract

Understanding covariate-varying interdependencies among features is of great interest in various applications. Motivated by microbiome studies where microbial abundances and interactions vary with environmental factors, we develop a Bayesian covariate-varying factor model. This model flexibly estimates heteroscedasticity in the covariance matrix as a function of covariates. Specifically, our approach employs covariance regression through linear regression on a lower-dimensional factor loading matrix. This formulation, combined with joint sparsity induced by the Dirichlet--Horseshoe prior for the factor loadings, provides robust estimation of covariate-varying covariance in high-dimensional settings. The model simultaneously incorporates a regression structure for the mean abundance and jointly addresses the covariate-varying mean and covariance structure. Furthermore, the model tackles key statistical challenges such as discreteness, over-dispersion, compositionality, and high dimensionality, common in microbiome data analysis, using a flexible nonparametric Bayesian framework. We thoroughly investigate the properties of the model and conduct extensive simulation studies to examine its performance. Real microbiome data examples are provided for illustration.