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

arXiv: https://arxiv.org/abs/2203.10044 · HTML: https://mlsanity.com/paper/2203.10044/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 78 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 17 of 17)

- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination](https://mlsanity.com/paper/1401.6497/) (2014)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements](https://mlsanity.com/paper/1506.06081/) (2015)
- [Matrix Completion on Graphs](https://mlsanity.com/paper/1408.1717/) (2014)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Fast Robust PCA on Graphs](https://mlsanity.com/paper/1507.08173/) (2015)
- [Depth Image Inpainting: Improving Low Rank Matrix Completion with Low Gradient Regularization](https://mlsanity.com/paper/1604.05817/) (2016)
- [Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models](https://mlsanity.com/paper/1708.02455/) (2017)
- [Robust Principal Component Analysis on Graphs](https://mlsanity.com/paper/1504.06151/) (2015)
- [Scalable Probabilistic Matrix Factorization with Graph-Based Priors](https://mlsanity.com/paper/1908.09393/) (2019)
- [Faster Matrix Completion Using Randomized SVD](https://mlsanity.com/paper/1810.06860/) (2018)
- [Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method](https://mlsanity.com/paper/2008.07740/) (2020)
- [Matrix Completion for Low-Observability Voltage Estimation](https://mlsanity.com/paper/1801.09799/) (2018)
- [Biconvex Relaxation for Semidefinite Programming in Computer Vision](https://mlsanity.com/paper/1605.09527/) (2016)
- [Robust Matrix Completion State Estimation in Distribution Systems](https://mlsanity.com/paper/1902.02009/) (2019)

## Built on by (most cited first, 4 of 4)

- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Non-Neighbors Also Matter to Kriging: A New Contrastive-Prototypical Learning](https://mlsanity.com/paper/2401.12681/) (2024)
- [To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion](https://mlsanity.com/paper/2306.11123/) (2023)
- [When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning](https://mlsanity.com/paper/2512.21486/) (2025)

## Abstract (arXiv)

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.