Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled using variational inference and inducing points. In this paper, we revisit active set approximations. We develop a new stochastic estimate of the log-marginal likelihood based on recently discovered links to cross-validation, and we propose a computationally efficient approximation thereof. We demonstrate that the resulting stochastic active sets (SAS) approximation significantly improves the robustness of GP decoder training, while reducing computational cost. The SAS-GP obtains more structure in the latent space, scales to many datapoints, and learns better representations than variational autoencoders, which is rarely the case for GP decoders.

We develop a module-based method that having a dictionary of well fitted GPs, one could build ensemble GP models without revisiting any data.

While one side of the coin is a boost of interest and investment on deep learning research, theother isanemergent need foritsrobustness, sample efficiency,security,and interpretability.

Despite recent advances in automated machine learning, model selection is still acomplexandcomputationally intensiveprocess.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix ofamultivariate timeseries.

Neural Information Processing Systems http://nips.cc/

Variational inference was employed in prior work to inferz (and w implicitly), and to obtain a point estimate ofθ, as a by-product of optimising the variational lower bound. Critically, in this representation weights are only implicitly parametrized through the use of these latent variables, which transforms inference onweights into inference ofthemuch smaller collection oflatent unit variables.

Table evaluated hyperparameters Dataset Nd GPR |M| - - q() - - free-form Boston 506 13 3.049 Concrete 1030 8 4.864 Ener 768 8 0.441 WineRed1599 11 0.640 Yacht308 6 0.353