Jonathan Huggins: Robust Model Selection for Discovery of Latent Mechanistic Processes

Speaker: Jonathan Huggins

Institution: Boston University's Department of Mathematics & Statistics and Faculty of Computing & Data Sciences 

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. In this work, we consider latent structures that consist of K mechanistic processes, where K is unknown. When the model is misspecified, likelihood-based model selection methods can substantially overestimate K while more robust nonparametric methods can be overly conservative. Hence, there is a need for approaches that combine the sensitivity of likelihood-based methods with the robustness of nonparametric ones. We formalize this objective in terms of a robust model selection consistency property, which is based on a component-level discrepancy measure that captures the mechanistic structure of the model. We then propose the accumulated cutoff discrepancy criterion (ACDC), which leverages plug-in estimates of component-level discrepancies. To apply ACDC, we develop mechanistically meaningful component-level discrepancies for a general class of latent variable models that includes unsupervised and supervised variants of probabilistic matrix factorization and mixture modeling. We show that ACDC is robustly consistent when applied to unsupervised matrix factorization and mixture models. Numerical results demonstrate that in practice our approach reliably identifies a mechanistically meaningful number of latent processes in numerous illustrative applications, outperforming existing methods.

Biography: Dr. Jonathan Huggins is an Assistant Professor of Mathematics & Statistics and of Computing & Data Sciences at Boston University. His group’s research focuses on the development of trustworthy, scalable methods for inference and uncertainty quantification that balance the need for computational efficiency and the desire for statistical optimality with the inherent imperfections that come from real-world problems, large datasets, and complex models. Their current applied work is focused on developing software tools and computational methods for (1) accelerating and improving large-scale forecasting of ecological systems and (2) enabling more effective scientific discovery from high-throughput and multi-modal genomic data.