Scalable Probabilistic Matrix Factorization with Graph-Based Priors

TL;DR

This paper introduces a scalable probabilistic matrix factorization method that improves prediction accuracy by removing contested edges from graph side-information, enhancing efficiency and scalability in matrix completion tasks.

Contribution

It presents a novel approach to identify and remove contested edges using graphical lasso approximation, improving matrix factorization performance without added computational cost.

Findings

Removing contested edges improves prediction accuracy.

The method scales efficiently to large graphs.

Real data experiments show faster analysis with better results.

Abstract

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 $\textit{contested}$ 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.