  Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive
family of meta-learning models which produce well-calibrated predictions,
enable fast inference at test time, and are trainable via a simple maximum
likelihood procedure. A limitation of CNPs is their inability to model
dependencies in the outputs. This significantly hurts predictive performance
and renders it impossible to draw coherent function samples, which limits the
applicability of CNPs in down-stream applications and decision making. Neural
Processes (NPs; Garnelo et al., 2018) attempt to alleviate this issue by using
latent variables, relying on these to model output dependencies, but introduces
difficulties stemming from approximate inference. One recent alternative
(Bruinsma et al., 2021), which we refer to as the FullConvGNP, models
dependencies in the predictions while still being trainable via exact
maximum-likelihood. Unfortunately, the FullConvGNP relies on expensive
2D-dimensional convolutions, which limit its applicability to only
one-dimensional data. In this work, we present an alternative way to model
output dependencies which also lends itself maximum likelihood training but,
unlike the FullConvGNP, can be scaled to two- and three-dimensional data. The
proposed models exhibit good performance in synthetic experiments.
