Marginal Tail-Adaptive Normalizing Flows

Autor:	Laszkiewicz, Mike, Lederer, Johannes, Fischer, Asja
Rok vydání:	2022
Předmět:	Computer Science - Machine Learning Mathematics - Statistics Theory Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential. Comment: Accepted at ICML2022 Thirty-ninth International Conference on Machine Learning
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.10311 Zobrazit plný text záznamu View this record from Arxiv