Copula-Based Normalizing Flows
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.
Keywords
Cite
@article{arxiv.2107.07352,
title = {Copula-Based Normalizing Flows},
author = {Mike Laszkiewicz and Johannes Lederer and Asja Fischer},
journal= {arXiv preprint arXiv:2107.07352},
year = {2021}
}
Comments
Accepted for presentation at the ICML 2021 Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit Likelihood Models (INNF+ 2021)