COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence
This addresses a critical limitation in deep generative models for applications like finance and climate science where extreme events are common, representing an incremental improvement over existing normalizing flow methods.
The paper tackles the problem of modeling multivariate extremes with heavy-tailed marginals and asymmetric tail dependence, proposing COMET Flows which outperform state-of-the-art baselines in capturing these features on synthetic and real-world datasets.
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.