Sparse Bayesian Group Factor Model for Feature Interactions in Multiple Count Tables Data

Shuangjie Zhang, Yuning Shen, Irene A. Chen and Juhee Lee

Journal of the American Statistical Association, 2025, vol. 120, issue 550, 723-736

Abstract: Group factor models have been developed to infer relationships between multiple co-occurring multivariate continuous responses. Motivated by complex count data from multi-domain microbiome studies using next-generation sequencing, we develop a sparse Bayesian group factor model (Sp-BGFM) for multiple count table data that captures the interaction between microorganisms in different domains. Sp-BGFM uses a rounded kernel mixture model using a Dirichlet process (DP) prior with log-normal mixture kernels for count vectors. A group factor model is used to model the covariance matrix of the mixing kernel that describes microorganism interaction. We construct a Dirichlet-Horseshoe (Dir-HS) shrinkage prior and use it as a joint prior for factor loading vectors. Joint sparsity induced by a Dir-HS prior greatly improves the performance in high-dimensional applications. We further model the effects of covariates on microbial abundances using regression. The semiparametric model flexibly accommodates large variability in observed counts and excess zero counts and provides a basis for robust estimation of the interaction and covariate effects. We evaluate Sp-BGFM using simulation studies and real data analysis, comparing it to popular alternatives. Our results highlight the necessity of joint sparsity induced by the Dir-HS prior, and the benefits of a flexible DP model for baseline abundances. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Date: 2025
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DOI: 10.1080/01621459.2025.2449721

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