Hamilton-jacobi equations for finite-rank matrix inference

J. C. MOURRAT

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)2234-2260
Number of pages27
JournalAnnals of Applied Probability
Volume30
Issue number5
DOIs
StatePublished - 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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