Mathematics Colloquium: Justin Ko

Our third colloquium of 2025 will be held on Friday, January 24 at 2:15 p.m. in Carnegie 122 with guest speaker Justin Ko from the University of Waterloo. We hope to see you there!

Title: Pseudo-Maximum Likelihood Theory for High-Dimension Rank-One Inference

Abstract: We consider the task of estimating a rank-one matrix from noisy observations. Models that fall in this framework include community detection and spiked Wigner models. In this talk, I will discuss pseudo-maximum likelihood theory for such inference problems. We provide a variational formula for the asymptotic maximum pseudo-likelihood and characterize the asymptotic performance of pseudo maximum likelihood estimators. We will also discuss the implications of these findings to least squares estimators. Our approach uses the recent connections between statistical inference, statistical physics and random matrix theory, and in particular the connection between the maximum likelihood and the ground state of a modified spin glass.