Structured Variational Inference for Coupled Gaussian Processes

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, these 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-GPs setting allowing for fast and scalable inference capturing posterior dependencies.