Mutual information for low-rank even-order symmetric tensor estimation
Information Theory
2020-09-24 v4 Disordered Systems and Neural Networks
Mathematical Physics
math.IT
math.MP
Abstract
We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new nontrivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.
Keywords
Cite
@article{arxiv.1904.04565,
title = {Mutual information for low-rank even-order symmetric tensor estimation},
author = {Clément Luneau and Jean Barbier and Nicolas Macris},
journal= {arXiv preprint arXiv:1904.04565},
year = {2020}
}
Comments
Preprint of an article accepted for publication in Information and Inference: A Journal of the IMA