The Layered Structure of Tensor Estimation and its Mutual Information
Abstract
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using a new type of interpolation method developed in [1]. We then show how to harness the structure in "layers" of tensor estimation in order to obtain a formula for the mutual information for the order 3 problem from the knowledge of the formula for the order 2 problem, still using the same kind of interpolation. Our proof technique straightforwardly generalizes and allows to rigorously obtain the mutual information at any order in a recursive way.
Cite
@article{arxiv.1709.10368,
title = {The Layered Structure of Tensor Estimation and its Mutual Information},
author = {Jean Barbier and Nicolas Macris and Léo Miolane},
journal= {arXiv preprint arXiv:1709.10368},
year = {2018}
}
Comments
55th Annual Allerton Conference on Communication, Control, and Computing, 2017