Statistical inference of finite-rank tensors

Hong-Bin Chen, Jean-Christophe Mourrat, Jiaming Xia

Published 2021-04-12Version 1

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.