  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.
