Copula-Based Normalizing Flows

TL;DR

This paper introduces a generalized normalizing flow model that uses copula-based base distributions, significantly enhancing flexibility and stability for modeling complex, heavy-tailed data distributions.

Contribution

It proposes a novel copula-based approach for the base distribution in normalizing flows, improving their expressiveness and robustness.

Findings

Enhanced flexibility and stability in modeling heavy-tailed data

Significant improvements over vanilla normalizing flows

Increased local Lipschitz-stability of the learned flow

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.