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arXiv · 1904.05294

Hamilton-Jacobi equations for finite-rank matrix inference

Jean-Christophe Mourrat
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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 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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Jean-Christophe Mourrat. 2019-04-10. Hamilton-Jacobi equations for finite-rank matrix inference. https://arxiv.org/abs/1904.05294

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