Mutual information for low-rank even-order symmetric tensor estimation

Jean François Emmanuel Barbier, Clément Dominique Luneau, Nicolas Macris
OXFORD UNIV PRESS, 2021
Article

Résumé

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 non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.

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