Information-theoretic limits of a multiview low-rank symmetric spiked matrix model
This work provides foundational theoretical insights for communities studying statistical-to-computational gaps in high-dimensional inference, though it is incremental as it extends existing methods to more general cases.
The authors tackled the problem of establishing information-theoretic limits for multiview low-rank symmetric spiked matrix models, which generalize high-dimensional inference problems used in principal component analysis, and they rigorously proved single-letter formulas for mutual information and minimum mean-square error.
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.