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Title: Information-theoretic limits of a multiview low-rank symmetric spiked matrix model
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.  more » « less
Award ID(s):
1750362
NSF-PAR ID:
10221390
Author(s) / Creator(s):
;
Date Published:
Journal Name:
2020 IEEE International Symposium on Information Theory (ISIT)
Page Range / eLocation ID:
2771 to 2776
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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