Department Seminar by Justin Ko

Please Note: This seminar will be given online.

Constrained Low Rank Matrix Estimation and Vector Spin Glasses

In this talk we will introduce a general class of statistical physics models with probability measures that can be written in vector spin form. These measures can be interpreted as the posterior probability measures of a class of high-dimensional inference problems known as constrained low rank matrix estimation. This framework includes a wide range of models in statistical physics and Bayesian inference such as the Sherrington-Kirkpatrick model and stochastic block model. A central quantity is the free energy associated with these models, which is related to the mutual information. We will describe how to prove the replica free energies associated with the inference problems using some of the main mathematical ideas in spin glasses such as interpolation, ultrametricity, and synchronization. This is joint work with Alice Guionnet, Florent Krzakala, and Lenka Zdeborová