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* Corresponding author 1 LTCI - Laboratoire Traitement et Communication de l-Information

Abstract : Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the so-called stable tail dependence function STDF. Learning this structure is the keystone of multivariate extremes. Although extensive studies have proved consistency and asymptotic normality for the empirical version of the STDF, non-asymptotic bounds are still missing. The main purpose of this paper is to fill this gap. Taking advantage of adapted VC-type concentration inequalities, upper bounds are derived with expected rate of convergence in Ok^-1-2. The concentration tools involved in this analysis rely on a more general study of maximal deviations in low probability regions, and thus directly apply to the classification of extreme data.

Keywords : Unsupervised Learning VC theory extreme data classification concentration inequalities multivariate extremes stable tail dependence function





Author: Nicolas Goix - Anne Sabourin - Stéphan Clémençon -

Source: https://hal.archives-ouvertes.fr/



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