Conditional Graph Neural Processes: A Functional Autoencoder Approach
We introduce a novel encoder-decoder architecture to embed functional processes into latent vector spaces. This embedding can then be decoded to sample the encoded functions over any arbitrary domain. This autoencoder generalizes the recently introduced Conditional Neural Process (CNP) model of random processes. Our architecture employs the latest advances in graph neural networks to process irregularly sampled functions. Thus, we refer to our model as Conditional Graph Neural Process (CGNP). Graph neural networks can effectively exploit `local' structures of the metric spaces over which the functions/processes are defined. The contributions of this paper are twofold: (i) a novel graph-based encoder-decoder architecture for functional and process embeddings, and (ii) a demonstration of the importance of using the structure of metric spaces for this type of representations.