Matrix completion based on Gaussian parameterized belief propagation

TL;DR

This paper introduces a Gaussian parameterized belief propagation algorithm for noisy matrix completion, improving robustness to non-Gaussian noise and enhancing performance on real-world datasets.

Contribution

It presents a novel message-passing algorithm based on Gaussian approximations for matrix completion, including a memory-efficient version and damping technique for improved performance.

Findings

Performs comparably to existing algorithms under Gaussian noise

Outperforms in non-Gaussian noise scenarios

Effective on real-world datasets

Abstract

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.