Séance Séminaire

Séminaire de Probabilités et Statistique

Change-points detection in the distribution of high dimensional objects

Nowadays statiscians deal with very high dimensional or even inifite dimensional objects such as next generation sequencing data or functions for instance. The goal of the present work is to propose a unified strategy to handle such objects relying on Reproducing Kernel Hilbert Space (RKHS) structures.
The main focus is given to off-line change-points detection in the distribution of the fixed-design data mapped onto the RKHS through the choice of a kernel (Gaussian, Laplace,...). We will describe some theoretical settings (mainly homoscedastic and sometimes weakly heteroscedastic) in which oracle inequalities can be derived for the estimator of the mean element in the RKHS. Finally, the performance of the proposed strategy will be assessed on synthetic and real data.