Hamilton-Jacobi equations for finite-rank matrix inference
Probability
2019-04-11 v1 Disordered Systems and Neural Networks
Abstract
We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in arXiv:1811.01432 which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of arXiv:1811.01432 using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the non-linearity in the equation is convex.
Cite
@article{arxiv.1904.05294,
title = {Hamilton-Jacobi equations for finite-rank matrix inference},
author = {Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:1904.05294},
year = {2019}
}
Comments
26 pages