Statistical inference of finite-rank tensors

Hongbin Chen , Jean-Christophe Mourrat (1) , Jiaming Xia

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Domaines: Probabilités [math.PR]

Hongbin Chen, Jean-Christophe Mourrat, Jiaming Xia. Statistical inference of finite-rank tensors. Annales Henri Lebesgue, 2022, 5, pp.1161-1189. ⟨10.5802/ahl.146⟩. ⟨hal-03581463⟩