# Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models

arXiv: https://arxiv.org/abs/1708.02455 · HTML: https://mlsanity.com/paper/1708.02455/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2017.

## Built on by (most cited first, 11 of 11)

- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Concentration properties of fractional posterior in 1-bit matrix completion](https://mlsanity.com/paper/2404.08969/) (2024)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)
- [Variational Bayesian inference for CP tensor completion with side information](https://mlsanity.com/paper/2206.12486/) (2022)
- [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)
- [Uncertainty-Based Non-Parametric Active Peak Detection](https://mlsanity.com/paper/2205.02376/) (2022)
- [A Bayesian Methodology for Estimation for Sparse Canonical Correlation](https://mlsanity.com/paper/2310.19621/) (2023)
- [Variational Bayesian Inference for Tensor Robust Principal Component Analysis](https://mlsanity.com/paper/2412.18717/) (2024)
- [Bayesian Matrix Completion Under Geometric Constraints](https://mlsanity.com/paper/2601.22765/) (2026)

## Abstract (arXiv)

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.