Conditional Probability Tensor Decompositions for Multivariate Categorical Response Regression

• 成果类型: Article
• 署名作者: Molstad, Aaron J.; Zhang, Xin
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; Florida State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2567045
• 发表日期: 2026-04-03
• 页码: 1310-1323
• 关键词: dimension reduction; Generalized Linear Model; latent variable model; Mixture regression; tensor decomposition; BINARY RELEVANCE; em algorithm; models; factorizations; mixtures

摘要

In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a probability mass function in settings where the number of response variables, the number of categories per response, and the dimension of the predictor are large. Our method relies on a functional probability tensor decomposition: a decomposition of a tensor-valued function such that its range is a restricted set of low-rank probability tensors. This decomposition is motivated by the connection between the conditional independence of responses, or lack thereof, and their probability tensor rank. We show that the model implied by such a low-rank functional probability tensor decomposition can be interpreted in terms of a mixture of regressions and can thus be fit using maximum likelihood. We derive an efficient and scalable penalized expectation maximization algorithm to fit this model and examine its statistical properties. We demonstrate the encouraging performance of our method through both simulation studies and an application to modeling the functional classes of genes. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.