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

2026-03-12

AI Summary

This study addresses the challenge of modeling covariate-dependent mean and covariance structures in high-dimensional count data, such as microbiome datasets. The authors propose a Bayesian covariate-dependent factor model that incorporates linear regression on low-dimensional factor loadings to enable covariance regression. By employing a Dirichlet–Horseshoe prior, the method induces joint sparsity while effectively accommodating key data characteristics—including discreteness, overdispersion, compositionality, and high dimensionality. Within a nonparametric Bayesian framework, the model provides a unified approach to simultaneously handle these statistical complexities, yielding robust estimation of covariate-dependent interaction structures. Extensive simulations and analyses of real microbiome data demonstrate that the proposed method substantially outperforms existing approaches in both estimation accuracy and robustness.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• covariate-varying interaction
• multivariate count data
• microbiome studies
• high dimensionality
• compositionality

Innovation

• Bayesian covariance regression
• covariate-varying interactions
• Dirichlet–Horseshoe prior
• factor model
• microbiome count data