Copula-Based Normalizing FlowsDownload PDF

Published: 15 Jun 2021, Last Modified: 22 Oct 2023INNF+ 2021 posterReaders: Everyone
Keywords: Base Distribution, Copula, Expressiveness
TL;DR: We propose to generalize the Gaussian base distribution in a normalizing flow to a more elaborate copula distribution.
Abstract: Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution. We, therefore, propose to generalize the base distribution to a more elaborate copula distribution to capture the properties of the target distribution more accurately. In a first empirical analysis, we demonstrate that this replacement can dramatically improve the vanilla normalizing flows in terms of flexibility, stability, and effectivity for heavy-tailed data. Our results suggest that the improvements are related to an increased local Lipschitz-stability of the learned flow.
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