Scalable Bayesian Non-linear Matrix Completion

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 nonlinear combinations in massive-scale matrices. Bayesian approaches have been proven beneficial in linear matrix completion, but not applied in the more general nonlinear case, due to limited scalability. We introduce a Bayesian nonlinear 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. 1 Introduction In matrix completion--one of the most widely used approaches for collaborative filtering--the objective is to predict missing elements of a partially observed data matrix.