Generative modeling of extremes 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 investigate new parametrizations based on neural networks in order to approximate and sample multi-variate extreme values, especially in the case of heavy-tailed distributions. We discuss two approaches. First, transformations of Feedforward neural networks based on Rectified linear units (ReLU) are used. An analysis of the uniform error between the extreme quantile and its GAN approximation is provided, and shows that second-order parameters of the marginal data distributions play an important role. Second, eLU based NN are used, to efficiently get rid of the bias term in tails approximation, in the presence of arbitrary high-order parameters. These results are illustrated on synthetic and real data.

Domaines: Statistiques [math.ST]

Michaël Allouche, Stéphane Girard, Emmanuel Gobet. Generative modeling of extremes with neural networks. 2023 - Accelerating Generative Models and Nonconvex Optimisation Workshop, The Alan Turing Institute, Mar 2023, London, United Kingdom. ⟨hal-04057231⟩