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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