Estimation of extreme quantiles from heavy-tailed distributions with neural networks

Michaël Allouche (1) , Stéphane Girard (2) , Emmanuel Gobet (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension

We propose new parametrizations for neural networks in order to estimate extreme quantiles in both non-conditional and conditional heavy-tailed settings. All proposed neural network estimators feature a bias correction based on an extension of the usual second-order condition to an arbitrary order. The convergence rate of the uniform error between extreme log-quantiles and their neural network approximation is established. The finite sample performances of the non-conditional neural network estimator are compared to other bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. The source code is available at https://github.com/michael-allouche/nn-quantile-extrapolation.git. Finally, the conditional neural network estimators are implemented to investigate the behaviour of extreme rainfalls as functions of their geographical location in the southern part of France.

Mots clés: neural networks; Extreme Value Theory; heavy-tailed distribution; quantile estimation; conditional quantile estimation

Domaines: Machine Learning [stat.ML]

Michaël Allouche, Stéphane Girard, Emmanuel Gobet. Estimation of extreme quantiles from heavy-tailed distributions with neural networks. Statistics and Computing, 2023, 34 (12), pp.1-35. ⟨hal-03751980⟩