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Journal Articles Journal of Machine Learning Research Year : 2022

EV-GAN: Simulation of extreme events with ReLU neural networks

Abstract

Feedforward neural networks based on Rectified linear units (ReLU) cannot efficiently approximate quantile functions which are not bounded, especially in the case of heavy-tailed distributions. We thus propose a new parametrization for the generator of a Generative adversarial network (GAN) adapted to this framework, basing on extreme-value theory. An analysis of the uniform error between the extreme quantile and its GAN approximation is provided: We establish that the rate of convergence of the error is mainly driven by the second-order parameter of the data distribution. The above results are illustrated on simulated data and real financial data. It appears that our approach outperforms the classical GAN in a wide range of situations including high-dimensional and dependent data.
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Dates and versions

hal-03250663 , version 1 (04-06-2021)
hal-03250663 , version 2 (16-06-2021)
hal-03250663 , version 3 (22-03-2022)

Identifiers

  • HAL Id : hal-03250663 , version 3

Cite

Michaël Allouche, Stéphane Girard, Emmanuel Gobet. EV-GAN: Simulation of extreme events with ReLU neural networks. Journal of Machine Learning Research, 2022, 23 (150), pp.1--39. ⟨hal-03250663v3⟩
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