BIRS Workshop Lecture Videos
Rank-one matrix estimation and Hamilton-Jacobi equations - 2 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.
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