SDS Seminar Series – Max Goplerud, University of Texas at Austin

The Fall 2025 SDS Seminar Series continues on October 31st from 2:00 p.m. to 3:00 p.m. with Dr. Max Goplerud (Assistant Professor, Department of Government, University of Texas at Austin). This event is in-person in the Avaya Room (POB 2.302).    

Title: Generalized Bilinear Mixed Models and Variational Inference

Abstract: Generalized bilinear mixed models are ubiquitous throughout applied research and include linear mixed models, matrix factorization and item response theory models as special cases. Inference for these models can be challenging for large datasets and models with many random effects. In recent and on-going work, we provide a unified and modular framework for inference for these models using variational inference. I will present work from two projects on this topic: First, focusing on generalized linear mixed models, we show that standard methods based on mean-field variational inference are neither accurate nor scalable for large problems. However, if one uses a more complex variational family based on partial factorizations, and focuses on a stylized-but-realistic example of two crossed random effects, we provide guarantees that this variational approximation is accurate and that it can be obtained using a scalable algorithm. In a much more complex applied example, we find that using a partially factorized variational family performs well in quantifying both the posterior mean and variance. Second, moving to bilinear mixed models, we develop a set of algorithms for estimating item response theory or factor models that are scalable to huge datasets as well as allowing for common extensions in applied work such as ANOVA-style decomposition of the latent positions, smooth trends in the latent positions, and similar.