  Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models
for meta-learning that map data sets directly to predictive stochastic
processes. We provide a rigorous analysis of the standard maximum-likelihood
objective used to train conditional NPs. Moreover, we propose a new member to
the Neural Process family called the Gaussian Neural Process (GNP), which
models predictive correlations, incorporates translation equivariance, provides
universal approximation guarantees, and demonstrates encouraging performance.
