  Deep Gaussian processes provide a flexible approach to probabilistic
modelling of data using either supervised or unsupervised learning. For
tractable inference approximations to the marginal likelihood of the model must
be made. The original approach to approximate inference in these models used
variational compression to allow for approximate variational marginalization of
the hidden variables leading to a lower bound on the marginal likelihood of the
model [Damianou and Lawrence, 2013]. In this paper we extend this idea with a
nested variational compression. The resulting lower bound on the likelihood can
be easily parallelized or adapted for stochastic variational inference.
