Multivariate extreme events : dimension reduction by thresholding or feature clustering
vendredi 15 avril 2016, 9h30 - 10h30
The dependence structure of extreme events of multivariate nature is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. environmental risk management or anomaly detection. In a high dimen- sional context (d > 50), dimension reduction is a natural first step. However, analyz- ing the tails of a dataset requires specific approaches that standard algorithms such as PCA do not accommodate. One convenient (nonparametric) characterization of ex- tremal dependence in the framework of multivariate Extreme Value Theory (EVT) is the angular measure, defined on the positive orthant of the d − 1 dimensional hyper- sphere, which provides direct information about the probable ‘directions’ of extremes, that is, the relative contribution of each feature/coordinate of the ‘largest’ observa- tions. In a wide range of applications, one may expect that only some small groups of components may be concomitantly extreme (e.g. nearest neighbors on the grid of a climate model), so that only the corresponding sub-spheres have non zero mass. In this talk, we present ongoing work aiming at identifying such groups, so as to reduce the dimension of the problem.