Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference

TL;DR

This paper introduces a Bayesian low-rank matrix completion method with dual-graph embedding that automatically learns hyper-parameters, ensuring low-rankness and improving performance without manual tuning across multiple data tasks.

Contribution

It proposes a novel prior for dual-graph regularization, enabling automatic hyper-parameter learning and efficient variational inference for matrix completion.

Findings

Achieves state-of-the-art results on synthetic and real datasets.

Automatically learns hyper-parameters, removing the need for tuning.

Effectively promotes low-rankness with dual-graph information.

Abstract

Recently, there is a revival of interest in low-rank matrix completion-based unsupervised learning through the lens of dual-graph regularization, which has significantly improved the performance of multidisciplinary machine learning tasks such as recommendation systems, genotype imputation and image inpainting. While the dual-graph regularization contributes a major part of the success, computational costly hyper-parameter tunning is usually involved. To circumvent such a drawback and improve the completion performance, we propose a novel Bayesian learning algorithm that automatically learns the hyper-parameters associated with dual-graph regularization, and at the same time, guarantees the low-rankness of matrix completion. Notably, a novel prior is devised to promote the low-rankness of the matrix and encode the dual-graph information simultaneously, which is more challenging than the single-graph counterpart. A nontrivial conditional conjugacy between the proposed priors and likelihood function is then explored such that an efficient algorithm is derived under variational inference framework. Extensive experiments using synthetic and real-world datasets demonstrate the state-of-the-art performance of the proposed learning algorithm for various data analysis tasks.