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Article Dans Une Revue The Annals of Applied Probability Année : 2020

Hamilton-Jacobi equations for finite-rank matrix inference

Résumé

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.
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hal-02144899 , version 1 (31-05-2019)

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Jean-Christophe Mourrat. Hamilton-Jacobi equations for finite-rank matrix inference. The Annals of Applied Probability, 2020, ⟨10.1214/19-AAP1556⟩. ⟨hal-02144899⟩
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