Abstract
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