  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.
