Copula-Based Normalizing Flows Article Swipe

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Copula (linguistics) Gaussian Empirical distribution function Stability (learning theory) Distribution (mathematics) Base (topology) Lipschitz continuity Mathematics Computer science Econometrics Mathematical optimization Applied mathematics Statistics Mathematical analysis Physics Machine learning Quantum mechanics

Mike Laszkiewicz , Johannes Lederer , Asja Fischer ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2107.07352 · OA: W3182295533

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.