# Bayesian methods for low-rank matrix estimation: short survey and theoretical study

arXiv: https://arxiv.org/abs/1306.3862 · HTML: https://mlsanity.com/paper/1306.3862/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2013.

## Built on by (most cited first, 7 of 7)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [PAC-Bayes Bounds for Multivariate Linear Regression and Linear Autoencoders](https://mlsanity.com/paper/2512.12905/) (2025)
- [A Probabilistic Basis for Low-Rank Matrix Learning](https://mlsanity.com/paper/2510.05447/) (2025)
- [Simulation comparisons between Bayesian and de-biased estimators in low-rank matrix completion](https://mlsanity.com/paper/2103.11749/) (2021)
- [PAC-Bayesian Matrix Completion with a Spectral Scaled Student Prior](https://mlsanity.com/paper/2104.08191/) (2021)
- [Bayesian Analysis for Over-parameterized Linear Model via Effective Spectra](https://mlsanity.com/paper/2305.15754/) (2023)
- [PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory](https://mlsanity.com/paper/2604.17219/) (2026)

## Abstract (arXiv)

The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization.