COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence

TL;DR

COMET Flows introduce a novel generative modeling approach that effectively captures multivariate extremes and asymmetric tail dependence by decomposing the joint distribution into marginals and copula components, improving over existing normalizing flows.

Contribution

The paper proposes COMET Flows, a new method that models heavy-tailed marginals and tail dependence separately, addressing limitations of current normalizing flow architectures in extreme value modeling.

Findings

Outperforms baseline models in capturing heavy tails and tail dependence.

Effectively models synthetic and real-world multivariate extremes.

Demonstrates robustness across different datasets.

Abstract

Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET Flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available on GitHub at https://github.com/andrewmcdonald27/COMETFlows.