THOMAS Maud

We present and study methods for unsupervised learning of multivariate extreme phenomena in high dimension. In the case where each of the marginal distributions of a random vector is heavy-tailed, the study of its behavior in extreme regions (i.e. far from the origin) can no longer be done via the usual methods which assume a finite mean and variance. Extreme value theory then offers a framework adapted to this study, by giving in particular a theoretical basis to the reduction of dimension through the angular measurement. The thesis is structured around two main steps: - Reducing the dimension of the problem by finding a summary of the dependence structure in the extreme regions. In particular, this step aims at finding the subgroups of components that are likely to exceed a high threshold simultaneously. - Modeling the angular measurement by a mixing density that follows a predetermined dependency structure. These two steps allow the development of unsupervised classification methods through the construction of a similarity matrix for the extreme points.