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 this https URL

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

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

We propose a novel probabilistic model to facilitate the learning of
multivariate tail dependence of multiple financial assets. Our method allows
one to construct from known random vectors, e.g., standard normal,
sophisticated joint heavy-tailed random vectors featuring not only distinct
marginal tail heaviness, but also flexible tail dependence structure. The
novelty lies in that pairwise tail dependence between any two dimensions is
modeled separately from their correlation, and can vary respectively according
to its own parameter rather than the correlation parameter, which is an
essential advantage over many commonly used methods such as multivariate $t$ or
elliptical distribution. It is also intuitive to interpret, easy to track, and
simple to sample comparing to the copula approach. We show its flexible tail
dependence structure through simulation. Coupled with a GARCH model to
eliminate serial dependence of each individual asset return series, we use this
novel method to model and forecast multivariate conditional distribution of
stock returns, and obtain notable performance improvements in multi-dimensional
coverage tests. Besides, our empirical finding about the asymmetry of tails of
the idiosyncratic component as well as the market component is interesting and
worth to be well studied in the future.

本文提出一种新颖的概率模型，用于学习多元金融资产的尾部依赖，其方法可以构建新的随机向量，并且相较于常见的方法，具有更灵活、直观、易于追踪和简单抽样等优势，结合 GARCH 模型进行预测和检验，发现资产收益率的尾部具有不对称性，对此进行了初步研究。