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Conference Papers Year : 2021

On the approximation of extreme quantiles with ReLU neural networks

Abstract

Feedforward neural networks based on rectified linear units (ReLU) cannot efficiently approximate quantile functions which are not bounded in the Fréchet maximum domain of attraction. We thus propose a new parametrization for the generator of a generative adversarial network (GAN) adapted to this framework of heavy-tailed distributions. We provide an analysis of the uniform error between the extreme quantile and its GAN approximation. It appears 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.
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Dates and versions

hal-03301431 , version 1 (27-07-2021)

Identifiers

  • HAL Id : hal-03301431 , version 1

Cite

Michaël Allouche, Stéphane Girard, Emmanuel Gobet. On the approximation of extreme quantiles with ReLU neural networks. EVA 2021 - 12th International Conference on Extreme Value Analysis, Jun 2021, Edinburgh / Virtual, United Kingdom. ⟨hal-03301431⟩
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