Riemannian SOS-Polynomial Normalizing Flows

Jonathan Schwarz, Felix Draxler, Ullrich Köthe, Christoph Schnörr

Abstract: Sum-of-Squares polynomial normalizing flows have been proposed recently, without taking into account the convexity property and the geometry of the corresponding parameter space. We develop two gradient flows based on the geometry of the parameter space of the cone of SOS-polynomials. Few proof-of-concept experiments using non-Gaussian target distributions validate the computational approach and illustrate the expressiveness of SOS-polynomial normalizing flows.