  We present a new family of exchangeable stochastic processes, the Functional
Neural Processes (FNPs). FNPs model distributions over functions by learning a
graph of dependencies on top of latent representations of the points in the
given dataset. In doing so, they define a Bayesian model without explicitly
positing a prior distribution over latent global parameters; they instead adopt
priors over the relational structure of the given dataset, a task that is much
simpler. We show how we can learn such models from data, demonstrate that they
are scalable to large datasets through mini-batch optimization and describe how
we can make predictions for new points via their posterior predictive
distribution. We experimentally evaluate FNPs on the tasks of toy regression
and image classification and show that, when compared to baselines that employ
global latent parameters, they offer both competitive predictions as well as
more robust uncertainty estimates.
