Informative Clusters for Multivariate Extremes

Capturing the dependence structure of multivariate extreme data is a major challenge in many fields involving the management of risks that come from multiple sources, e.g., portfolio monitoring, environmental risk management, insurance and anomaly detection. The present paper develops a novel optimization-based approach called MEXICO, standing for Multivariate EXtreme Informative Clustering by Optimization. It aims at exhibiting a sparsity pattern within the dependence structure of extremes. This is achieved by estimating some disjoint clusters of features that tend to be large simultaneously through an optimization method on the probability simplex. This dimension reduction technique can be applied to statistical learning tasks such as feature clustering and anomaly detection. Numerical experiments provide strong empirical evidence of the relevance of our approach.