# Matrix completion based on Gaussian parameterized belief propagation

arXiv: https://arxiv.org/abs/2105.00233 · HTML: https://mlsanity.com/paper/2105.00233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 3 of 3)

- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [A Note on Alternating Minimization Algorithm for the Matrix Completion Problem](https://mlsanity.com/paper/1602.02164/) (2016)
- [Approximate matrix completion based on cavity method](https://mlsanity.com/paper/1907.00138/) (2019)

## Built on by (most cited first, 1 of 1)

- [Graphical model for factorization and completion of relatively high rank tensors by sparse sampling](https://mlsanity.com/paper/2510.17886/) (2025)

## Abstract (arXiv)

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same first and second moments. We also derive a memory-friendly version of the proposed algorithm by applying a perturbation treatment commonly used in the literature of approximate message passing. In addition, a damping technique, which is demonstrated to be crucial for optimal performance, is introduced without computational strain, and the relationship to the message-passing version of alternating least squares, a method reported to be optimal in certain settings, is discussed. Experiments on synthetic datasets show that while the proposed algorithm quantitatively exhibits almost the same performance under settings where the earlier algorithm is optimal, it is advantageous when the observed datasets are corrupted by non-Gaussian noise. Experiments on real-world datasets also emphasize the performance differences between the two algorithms.