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

arXiv: https://arxiv.org/abs/2005.08017 · HTML: https://mlsanity.com/paper/2005.08017/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2020.

## Built on by (most cited first, 8 of 8)

- [Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticity](https://mlsanity.com/paper/2106.11950/) (2021)
- [Optimal Algorithms for the Inhomogeneous Spiked Wigner Model](https://mlsanity.com/paper/2302.06665/) (2023)
- [Approximate Message Passing for the Matrix Tensor Product Model](https://mlsanity.com/paper/2306.15580/) (2023)
- [Spectral Phase Transition and Optimal PCA in Block-Structured Spiked models](https://mlsanity.com/paper/2403.03695/) (2024)
- [A Noise Sensitivity Exponent Controls Large Statistical-to-Computational Gaps in Single- and Multi-Index Models](https://mlsanity.com/paper/2603.17896/) (2026)
- [Mismatched estimation of non-symmetric rank-one matrices corrupted by structured noise](https://mlsanity.com/paper/2302.03306/) (2023)
- [Computational and statistical lower bounds for low-rank estimation under general inhomogeneous noise](https://mlsanity.com/paper/2510.08541/) (2025)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)

## Abstract (arXiv)

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.