# Bayesian Uncertainty Quantification for Low-Rank Matrix Completion

arXiv: https://arxiv.org/abs/2101.01299 · HTML: https://mlsanity.com/paper/2101.01299/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2021.

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

- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [A Probabilistic Basis for Low-Rank Matrix Learning](https://mlsanity.com/paper/2510.05447/) (2025)
- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)
- [eRPCA: Robust Principal Component Analysis for Exponential Family Distributions](https://mlsanity.com/paper/2310.19787/) (2023)
- [SATORIS-N: Spectral Analysis based Traffic Observation Recovery via Informed Subspaces and Nuclear-norm minimization](https://mlsanity.com/paper/2602.03138/) (2026)
- [PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory](https://mlsanity.com/paper/2604.17219/) (2026)
- [Low-rank Distributional Matrix Completion](https://mlsanity.com/paper/2606.04176/) (2026)

## Abstract (arXiv)

We consider the problem of uncertainty quantification for an unknown low-rank matrix X, given a partial and noisy observation of its entries. This quantification of uncertainty is essential for many real-world problems, including image processing, satellite imaging, and seismology, providing a principled framework for validating scientific conclusions and guiding decision-making. However, existing literature has mainly focused on the completion (i.e., point estimation) of the matrix X, with little work on investigating its uncertainty. To this end, we propose in this work a new Bayesian modeling framework, called BayeSMG, which parametrizes the unknown X via its underlying row and column subspaces. This Bayesian subspace parametrization enables efficient posterior inference on matrix subspaces, which represents interpretable phenomena in many applications. This can then be leveraged for improved matrix recovery. We demonstrate the effectiveness of BayeSMG over existing Bayesian matrix recovery methods in numerical experiments, image inpainting, and a seismic sensor network application.