Feature Clustering for Support Identification in Extreme Regions

Hamid Jalalzai, Rémi Leluc
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:4733-4743, 2021.

Abstract

Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes’ dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-jalalzai21a, title = {Feature Clustering for Support Identification in Extreme Regions}, author = {Jalalzai, Hamid and Leluc, R{\'e}mi}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {4733--4743}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/jalalzai21a/jalalzai21a.pdf}, url = {https://proceedings.mlr.press/v139/jalalzai21a.html}, abstract = {Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes’ dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.} }
Endnote
%0 Conference Paper %T Feature Clustering for Support Identification in Extreme Regions %A Hamid Jalalzai %A Rémi Leluc %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-jalalzai21a %I PMLR %P 4733--4743 %U https://proceedings.mlr.press/v139/jalalzai21a.html %V 139 %X Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common characterization of extremes’ dependence structure is the angular measure. It is a suitable measure to work in extreme regions as it provides meaningful insights concerning the subregions where extremes tend to concentrate their mass. The present paper develops a novel optimization-based approach to assess the dependence structure of extremes. This support identification scheme rewrites as estimating clusters of features which best capture the support of extremes. The dimension reduction technique we provide is applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.
APA
Jalalzai, H. & Leluc, R.. (2021). Feature Clustering for Support Identification in Extreme Regions. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:4733-4743 Available from https://proceedings.mlr.press/v139/jalalzai21a.html.

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