Universal Functional Regression with Neural Operator Flows

arXiv:2404.02986v1 Announce Type: new
Abstract: Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that remains mathematically tractable for functional regression. To do this, we develop Neural Operator Flows (OpFlow), an infinite-dimensional extension of normalizing flows. OpFlow is an invertible operator that maps the (potentially unknown) data function space into a Gaussian process, allowing for …

abstract aim arxiv cs.lg distribution function functional learn notion prior process regression spaces stat.ml tractable type universal