UBC Probability Seminar: Jean-Christoph Mourrat (Online)

We consider the problem of estimating large rank-one matrix, given noisy observations. This inference problem is known to have a phase transition, in the sense that partial recovery of the original matrix is only possible if the signal-to-noise ratio exceeds a (non-zero) value. We will present a new proof of this fact based on the study of a Hamilton-Jacobi equation. This alternative argument allows one to obtain better rates of convergence, and also seems more amenable to extensions to other models such as spin glasses.