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.

提出COMET流方法用于建模极值现象，将建模联合分布过程分为建模边际分布和建模copula分布两部分，其中结合parametric tail belief和kernel density function来表达重尾边缘分布；同时利用inducing low-dimensional manifold structure来表达多元极值中的非对称尾依赖，并给出相关实验结果。

COMET流: 迈向多元极值和尾相关性的生成建模