Statistical inference of finite-rank tensors
Annales Henri Lebesgue, Volume 5 (2022), pp. 1161-1189.

Keywords inference problem, Hamilton–Jacobi equation, tensor

Abstract

We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach consists of showing first that the limit free energy must be the viscosity solution to a certain Hamilton–Jacobi equation.

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