Title: Structured Variational Inference for Coupled Gaussian Processes,
Abstract: Sparse variational approximations allow for principled and scalable inference
in Gaussian Process (GP) models. In settings where several GPs are part of the
generative model, theses GPs are a posteriori coupled. For many applications
such as regression where predictive accuracy is the quantity of interest, this
coupling is not crucial. Howewer if one is interested in posterior uncertainty,
it cannot be ignored. A key element of variational inference schemes is the
choice of the approximate posterior parameterization. When the number of latent
variables is large, mean field (MF) methods provide fast and accurate posterior
means while more structured posterior lead to inference algorithm of greater
computational complexity. Here, we extend previous sparse GP approximations and
propose a novel parameterization of variational posteriors in the multi-GP
setting allowing for fast and scalable inference capturing posterior
dependencies.