BIRS Workshop Lecture Videos
Rank-one matrix estimation and Hamilton-Jacobi equations - 1 Mourrat, Jean Christophe
We consider the problem of estimating a large rank-one matrix, given noisy observations. This inference problem is known to have a phase transition, in the sense that the 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 to obtain better rates of convergence, and also seems more amenable to extensions to other models such as spin glasses.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International