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Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learningmodels which leverage the flexibility of deep learning to producewell-calibrated predictions and naturally handle off-the-grid and missing data.CNPs scale to large datasets and train with ease. Due to these features, CNPsappear well-suited to tasks from environmental sciences or healthcare.Unfortunately, CNPs do not produce correlated predictions, making themfundamentally inappropriate for many estimation and decision making tasks.Predicting heat waves or floods, for example, requires modelling dependenciesin temperature or precipitation over time and space. Existing approaches whichmodel output dependencies, such as Neural Processes (NPs; Garnelo et al.,2018b) or the FullConvGNP (Bruinsma et al., 2021), are either complicated totrain or prohibitively expensive. What is needed is an approach which providesdependent predictions, but is simple to train and computationally tractable. Inthis work, we present a new class of Neural Process models that make correlatedpredictions and support exact maximum likelihood training that is simple andscalable. We extend the proposed models by using invertible outputtransformations, to capture non-Gaussian output distributions. Our models canbe used in downstream estimation tasks which require dependent functionsamples. By accounting for output dependencies, our models show improvedpredictive performance on a range of experiments with synthetic and real data.

Practical Conditional Neural Processes Via Tractable Dependent Predictions