Papers Published
- Barbier, J; Reeves, G, Information-theoretic limits of a multiview low-rank symmetric spiked matrix model,
IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June
(June, 2020),
pp. 2771-2776 [doi] .
(last updated on 2024/04/22)Abstract:
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.