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

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