Hamilton-jacobi equations for finite-rank matrix inference

J. C. MOURRAT

doi:10.1214/19-AAP1556

Hamilton-jacobi equations for finite-rank matrix inference

J. C. MOURRAT

Mathematics

Research output: Contribution to journal › Article › peer-review

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 Mourrat (2018) which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of Mourrat (2018) using a notion of weak solution of the Hamilton- Jacobi equation which is more convenient to work with and is applicable whenever the nonlinearity in the equation is convex.

Original language	English (US)
Pages (from-to)	2234-2260
Number of pages	27
Journal	Annals of Applied Probability
Volume	30
Issue number	5
DOIs	https://doi.org/10.1214/19-AAP1556
State	Published - Oct 2020

Keywords

Hamilton-Jacobi equation
Spin glass
Statistical inference

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/19-AAP1556

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Hamilton-jacobi equations for finite-rank matrix inference

Abstract

Keywords

ASJC Scopus subject areas

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