Opening the way for deep Gaussian processes on massive data

stitute two of the most important foci of modern machine learning research. In this preliminary work we propose a neat solution for combining the afore-mentioned domains into a single principled framework based on Gaussian processes. Speficically, we invisti-gate algorithms for training deep generative models with hidden layers connected with non-linear Gaus-sian process (GP) mappings. Building on recent devel-opments on (stochastic) variational approximations, the models are fitted on massive data and the hidden variables are marginalised out in a Bayesian manner to allow for efficient propagation of the uncertainty throughout the network of variables. Defining deep Gaussian process networks is challeng-ing even for few data. Consider n observed datapoint