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

• URL: http://arxiv.org/abs/2205.01224v1
• Date: Mon, 2 May 2022 21:37:54 GMT
• Title: COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence
• Authors: Andrew McDonald, Pang-Ning Tan, Lifeng Luo
• Abstract summary: COMET Flows decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. Results on both synthetic and real-world datasets demonstrate the effectiveness of COMET Flows.
• Score: 13.041607703862724
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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