Discovering patterns in high-dimensional extremes

Abstract : We present and study unsupervised learning methods of multivariate extreme phenomena in high-dimension. Considering a random vector on which each marginal is heavy-tailed, the study of its behavior in extreme regions is no longer possible via usual methods that involve finite means and variances. Multivariate extreme value theory provides an adapted framework to this study. In particular it gives theoretical basis to dimension reduction through the angular measure. The thesis is divided in two main part: - Reduce the dimension by finding a simplified dependence structure in extreme regions. This step aim at recover subgroups of features that are likely to exceed large thresholds simultaneously. - Model the angular measure with a mixture distribution that follows a predefined dependence structure. These steps allow to develop new clustering methods for extreme points in high dimension.
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Maël Chiapino. Discovering patterns in high-dimensional extremes. Machine Learning [stat.ML]. Télécom ParisTech, 2018. English. ⟨NNT : 2018ENST0035⟩. ⟨tel-02294009⟩

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