HAMILTON-JACOBI EQUATIONS FOR FINITE-RANK MATRIX INFERENCE

• 成果类型: Article
• 署名作者: Mourrat, J-C
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1556
• 发表日期: 2020
• 页码: 2234-2260
• 关键词: free-energy

摘要

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.