Date: 2026-11-20

Time: 15:30-16:30 (Montreal time)

Location: Online via Zoom

https://mcgill.zoom.us/j/83483745684

Meeting ID: 834 8374 5684

Abstract:

An age-old question in principal components analysis (PCA) is how many principal directions should be retained? Model-based approaches, like probabilistic PCA, provide one way of addressing this question. Information criteria can be used to treat the choice of the number of PCs as a model selection problem. However, there is a subtlety that is often overlooked: the PPCA model, as well as the related factor analysis model, both have singularities, which alter convergence rates that motivate information criteria like the BIC. In this talk, I will provide an overview of singular learning theory, an area that involves using ideas from algebraic geometry to tame the asymptotics of models with singularities. I will also introduce the singular BIC (sBIC) as an information criteria that is able to incorporate asymptotic information at singularities and can be used for model selection. The efficacy of the sBIC as compared to the BIC is demonstrated empirically and theoretically, where it is shown that in high-dimensional settings the sBIC requires a smaller eigengap in order to detect principal component directions.

This project is joint work with Mathias Drton and Daniel Windisch.

Speaker

Andy McCormack is an assistant professor at the University of Alberta. He received his PhD from Duke University in 2023 under the supervision of Peter Hoff and subsequently did a postdoc under Mathias Drton at the Technical University of Munich. He is interested in any problem where algebra, geometry, and statistics come together to provide practical insights. In particular, he is interested in the areas of non-Euclidean data analysis, algebraic statistics, information geometry, and the analysis of tensor-valued data.