Statistical inference of finite-rank tensors
Probability
2022-03-29 v2 Disordered Systems and Neural Networks
Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.2104.05360,
title = {Statistical inference of finite-rank tensors},
author = {Hong-Bin Chen and Jean-Christophe Mourrat and Jiaming Xia},
journal= {arXiv preprint arXiv:2104.05360},
year = {2022}
}
Comments
24 pages, final version