# Scalable Probabilistic Matrix Factorization with Graph-Based Priors

arXiv: https://arxiv.org/abs/1908.09393 · HTML: https://mlsanity.com/paper/1908.09393/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [GLocal-K: Global and Local Kernels for Recommender Systems](https://mlsanity.com/paper/2108.12184/) (2021)
- [Non-Neighbors Also Matter to Kriging: A New Contrastive-Prototypical Learning](https://mlsanity.com/paper/2401.12681/) (2024)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)
- [To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completion](https://mlsanity.com/paper/2306.11123/) (2023)
- [Probabilistic Embeddings with Laplacian Graph Priors](https://mlsanity.com/paper/2204.01846/) (2022)
- [RSAttAE: An Information-Aware Attention-based Autoencoder Recommender System](https://mlsanity.com/paper/2502.06705/) (2025)
- [Graph Regularized Probabilistic Matrix Factorization for Drug-Drug Interactions Prediction](https://mlsanity.com/paper/2210.10784/) (2022)

## Abstract (arXiv)

In matrix factorization, available graph side-information may not be well suited for the matrix completion problem, having edges that disagree with the latent-feature relations learnt from the incomplete data matrix. We show that removing these textitcontested edges improves prediction accuracy and scalability. We identify the contested edges through a highly-efficient graphical lasso approximation. The identification and removal of contested edges adds no computational complexity to state-of-the-art graph-regularized matrix factorization, remaining linear with respect to the number of non-zeros. Computational load even decreases proportional to the number of edges removed. Formulating a probabilistic generative model and using expectation maximization to extend graph-regularised alternating least squares (GRALS) guarantees convergence. Rich simulated experiments illustrate the desired properties of the resulting algorithm. On real data experiments we demonstrate improved prediction accuracy with fewer graph edges (empirical evidence that graph side-information is often inaccurate). A 300 thousand dimensional graph with three million edges (Yahoo music side-information) can be analyzed in under ten minutes on a standard laptop computer demonstrating the efficiency of our graph update.