Copula-Based Normalizing Flows

Mike Laszkiewicz, Johannes Lederer, Asja Fischer

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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2107.07352/code)