SDS Seminar Series - Jonathan Huggins, Boston University

The Fall 2025 SDS Seminar Series continues on October 24th from 2:00 p.m. to 3:00 p.m. with Dr.  Jonathan Huggins (Assistant Professor, Department of Mathematics & Statistics, Boston University). This event is in-person in POB 6.304.

Title: Robust Model Selection for Discovery of Latent Mechanistic Processes

Abstract: When learning interpretable latent structures using model-based approaches, even small deviations from modeling assumptions can lead to inferential results that are not mechanistically meaningful. For example, many latent structures consist of K mechanistic processes (with K unknown). When the model is misspecified, likelihood-based model selection methods can substantially overestimate K as the sample size grows, while nonparametric methods can be overly conservative no matter how large the sample size. Hence, there is need for model selection methods that combine the precision of likelihood-based approaches with the robustness of nonparametrics. To address this need in a principled manner, we first formalize the problem of robust model selection in latent variable models designed for mechanistic understanding as requiring an estimator for K to satisfy a robust model selection consistency property. The definition of robust model selection consistency motivates a particular family of model selection procedures, which rely on plug-in estimates of a component-wise discrepancy measure we call the accumulated cutoff discrepancy criterion (ACDC). We provide a method for constructing mechanistically meaningful component-wise discrepancies for a class of latent variable models that includes unsupervised and supervised variants of probabilistic matrix factorization (including factor analysis) and mixture models. We prove that ACDC provides robust model selection consistency for unsupervised matrix factorization and mixture models. Numerical results show that in practice our approach reliably identifies a physically meaningful number of latent processes in four illustrative applications, outperforming widely used model selection methods. An in-depth case study of cell type discovery using single-cell RNA sequencing data demonstrates ACDC outperforms two widely used software packages designed specifically for single-cell data analysis.