AAAI Conference 2020 Conference Paper
Scalable Probabilistic Matrix Factorization with Graph-Based Priors
- Jonathan Strahl
- Jaakko Peltonen
- Hirsohi Mamitsuka
- Samuel Kaski
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 contested edges improves prediction accuracy and scalability. We identify the contested edges through a highlyefficient 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 nonzeros. 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 sideinformation is often inaccurate). A 300 thousand dimensional graph with three million edges (Yahoo music sideinformation) can be analyzed in under ten minutes on a standard laptop computer demonstrating the efficiency of our graph update.