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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 at https://github.com/andrewmcdonald27/COMETFlows.
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Heavy-Tailed Density Estimation
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mildsmoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem ofsparse information in the tail of the distribution getting washed away by unrelated features of a hefty bulk.The proposed Bayesian method avoids this problem by incorporating smoothness and tail regularizationthrough a carefully specified semiparametric prior distribution, and is able to consistently estimate boththe density function and its tail index at near minimax optimal rates of contraction. A joint, likelihood drivenestimation of the bulk and the tail is shown to help improve uncertainty assessment in estimating the tailindex parameter and offer more accurate and reliable estimates of the high tail quantiles compared tothresholding methods. Supplementary materials for this article are available online.
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- Award ID(s):
- 2014861
- PAR ID:
- 10484531
- Publisher / Repository:
- Taylor & Francis
- Date Published:
- Journal Name:
- Journal of the American Statistical Association
- ISSN:
- 0162-1459
- Page Range / eLocation ID:
- 1 to 13
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1080/01621459.2022.2104727
