Learning the dependence structure of rare events: a non-asymptotic study

Nicolas Goix, Anne Sabourin, Stéphan Clémen\ccon
Proceedings of The 28th Conference on Learning Theory, PMLR 40:843-860, 2015.

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 \emphstable tail dependence function (\textscstdf). Learning this structure is the keystone of multivariate extremes. Although extensive studies have proved consistency and asymptotic normality for the empirical version of the \textscstdf, 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 O(k^-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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v40-Goix15, title = {Learning the dependence structure of rare events: a non-asymptotic study}, author = {Goix, Nicolas and Sabourin, Anne and Clémen\ccon, Stéphan}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {843--860}, year = {2015}, editor = {Grünwald, Peter and Hazan, Elad and Kale, Satyen}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Goix15.pdf}, url = {https://proceedings.mlr.press/v40/Goix15.html}, 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 \emphstable tail dependence function (\textscstdf). Learning this structure is the keystone of multivariate extremes. Although extensive studies have proved consistency and asymptotic normality for the empirical version of the \textscstdf, 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 O(k^-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. } }
Endnote
%0 Conference Paper %T Learning the dependence structure of rare events: a non-asymptotic study %A Nicolas Goix %A Anne Sabourin %A Stéphan Clémen\ccon %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Goix15 %I PMLR %P 843--860 %U https://proceedings.mlr.press/v40/Goix15.html %V 40 %X 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 \emphstable tail dependence function (\textscstdf). Learning this structure is the keystone of multivariate extremes. Although extensive studies have proved consistency and asymptotic normality for the empirical version of the \textscstdf, 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 O(k^-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.
RIS
TY - CPAPER TI - Learning the dependence structure of rare events: a non-asymptotic study AU - Nicolas Goix AU - Anne Sabourin AU - Stéphan Clémen\ccon BT - Proceedings of The 28th Conference on Learning Theory DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Goix15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 40 SP - 843 EP - 860 L1 - http://proceedings.mlr.press/v40/Goix15.pdf UR - https://proceedings.mlr.press/v40/Goix15.html AB - 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 \emphstable tail dependence function (\textscstdf). Learning this structure is the keystone of multivariate extremes. Although extensive studies have proved consistency and asymptotic normality for the empirical version of the \textscstdf, 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 O(k^-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. ER -
APA
Goix, N., Sabourin, A. & Clémen\ccon, S.. (2015). Learning the dependence structure of rare events: a non-asymptotic study. Proceedings of The 28th Conference on Learning Theory, in Proceedings of Machine Learning Research 40:843-860 Available from https://proceedings.mlr.press/v40/Goix15.html.

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