Copula-Based Normalizing Flows
This is an incremental improvement for researchers in density estimation and generative modeling, addressing a specific bottleneck in normalizing flows.
The paper tackles the limited expressive power of normalizing flows due to their Gaussian base distribution by proposing a copula-based generalization, resulting in dramatic improvements in flexibility, stability, and effectiveness for heavy-tailed data.
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.