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

Series
Stochastics Seminar
Time
Thursday, September 19, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Justin Ko – University of Waterloo
Organizer
Cheng Mao

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 and statistical physics, and in particular the connection between the maximum likelihood and the ground state of a modified spin glass.

Based on joint work with Curtis Grant and Aukosh Jagannath.