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October 2020 Hamilton–Jacobi equations for finite-rank matrix inference
J.-C. Mourrat
Ann. Appl. Probab. 30(5): 2234-2260 (October 2020). DOI: 10.1214/19-AAP1556

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.

Citation

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J.-C. Mourrat. "Hamilton–Jacobi equations for finite-rank matrix inference." Ann. Appl. Probab. 30 (5) 2234 - 2260, October 2020. https://doi.org/10.1214/19-AAP1556

Information

Received: 1 May 2019; Revised: 1 October 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149527
Digital Object Identifier: 10.1214/19-AAP1556

Subjects:
Primary: 82B44, 82D30

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 5 • October 2020
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