Equivariant Normalizing Flows for Point Processes and Sets

Marin Biloš, Stephan Günnemann

Keywords: point process, set, normalizing flow, equivariance

Abstract: A point process describes how random sets of exchangeable points are generated. The points usually influence the positions of each other via attractive and repulsive forces. To model this behavior, it is enough to transform the samples from the uniform process with a sufficiently complex equivariant function. However, learning the parameters of the resulting process is challenging since the likelihood is hard to estimate and often intractable. This leads us to our proposed model - CONFET. Based on continuous normalizing flows, it allows arbitrary interactions between points while having tractable likelihood. Experiments on various real and synthetic datasets show the improved performance of our new scalable approach.

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One-sentence Summary: Having permutation equivariant mapping in continuous normalizing flows allows modeling densities over sets.

Reviewed Version (pdf): https://openreview.net/references/pdf?id=VqyzKw-7S