Scalable Probabilistic Matrix Factorization with Graph-Based Priors
This addresses matrix completion tasks where graph data may be noisy, offering incremental improvements in efficiency and accuracy for applications like recommendation systems.
The paper tackled the problem of inaccurate graph side-information in matrix factorization by removing contested edges that disagree with latent-feature relations, resulting in improved prediction accuracy and scalability, with analysis of a 300,000-dimensional graph with 3 million edges in under 10 minutes.
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.