Information-theoretic limits of a multiview low-rank symmetric spiked matrix model

Conference Paper

We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently attracted a lot of attention from a number of communities due to their phenomenological richness with statistical-to-computational gaps, while remaining tractable. We rigorously establish the information-theoretic limits through the proof of single-letter formulas for the mutual information and minimum mean-square error. On a technical side we improve the recently introduced adaptive interpolation method, so that it can be used to study low-rank models (i.e., estimation problems of "tall matrices") in full generality, an important step towards the rigorous analysis of more complicated inference and learning models.

Full Text

Duke Authors

Cited Authors

  • Barbier, J; Reeves, G

Published Date

  • June 1, 2020

Published In

Volume / Issue

  • 2020-June /

Start / End Page

  • 2771 - 2776

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781728164328

Digital Object Identifier (DOI)

  • 10.1109/ISIT44484.2020.9173970

Citation Source

  • Scopus