Seminar by Justin Ko

Estimating Rank-One Matrices with Mismatched Prior and Noise: Universality and Large Deviations

We study a generic class of Bayesian inference models with a mismatch in the prior and noise. We will explain a universality result that reduces the mutual information for inference problems in the mismatched setting to the computation of a modified spin glass free energy. We prove an almost sure large deviations principle for the overlaps between the truth and samples from the posterior. As a consequence, we recover the limit of the mutual information in mismatched inference problems. This is joint work with Alice Guionnet, Florent Krzakala, and Lenka Zdeborova.