Mutual information for low-rank even-order symmetric tensor estimation. (24th September 2020)

• Record Type: Journal Article
• Authors: Luneau, Clément; Barbier, Jean; Macris, Nicolas
• Is Part Of: Information and inference. Volume 10:Number 4(2021)
• Page Start: 1167
• Page End: 1207
• Publication Date: 2020-09-24
• Subjects: mutual information -- tensor decomposition -- adaptive interpolation method -- concentration -- replica formula; Mathematical models -- Periodicals; 519.605
• DOI: 10.1093/imaiai/iaaa022
• Languages: English
• ISSNs: 2049-8764

Abstract

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 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.