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.
翻译:普通化的流,一种流行的深层基因模型,往往不能代表现实世界进程中观察到的极端现象。特别是,现有的正常化流动结构努力模拟多种变异极端,其特点是变异性边缘分布和变异性之间不对称尾部依赖性。鉴于这一缺陷,我们提议COT(COpula 多重变异Extreme)流,它分解了模拟联合分布的过程,分为两个部分:(一) 模拟其边际分布,和(二) 模拟其椰子分布。 ICOT流通过将边缘极端四分点的准尾部信念与中点的经验性内核密度功能相结合,捕捉到重尾部分布的重尾部分布。此外,ICT流通过观察这种依赖性在地貌空间诱导出一个低度的多元结构,在多变异性极端之间捕捉取不对称尾部依赖性。 合成和真实世界数据集的实验结果表明,ICOT流动在捕捉重尾部边缘和不对称尾部依赖性与其它州/州/州/州/州/州/州/州/州/州/州/州/州/州/州/州/ 都可使用的基本结构所有可用的GAT。