Scalable Bayesian Non-linear Matrix Completion
This work addresses scalability issues in Bayesian non-linear matrix completion for applications like collaborative filtering, representing an incremental advancement over existing methods.
The paper tackles the problem of predicting missing entries in large, sparse matrices using non-linear combinations of latent variables, and introduces a scalable Bayesian algorithm that achieves competitive performance on out-of-matrix prediction tasks with real-world data.
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We generalize to non-linear combinations in massive-scale matrices. Bayesian approaches have been proven beneficial in linear matrix completion, but not applied in the more general non-linear case, due to limited scalability. We introduce a Bayesian non-linear matrix completion algorithm, which is based on a recent Bayesian formulation of Gaussian process latent variable models. To solve the challenges regarding scalability and computation, we propose a data-parallel distributed computational approach with a restricted communication scheme. We evaluate our method on challenging out-of-matrix prediction tasks using both simulated and real-world data.