Detecting abrupt changes in the distribution along the time in complex objects

Nom de l'orateur
Alain Celisse
Etablissement de l'orateur
Université de Lille
Date et heure de l'exposé
Lieu de l'exposé
salle des séminaires

In this talk we discuss the change-point detection problem when dealing with complex data.

Our goal is to present a new procedure involving positive semidefinite kernels and allowing us for detecting abrupt changes arising in the full distribution of the observations along the time (and not only in their means).

The two-stage procedure we introduce involves dynamic programming and a new $l_0$-type penalty derived from a new concentration inequality applying to vectors in a reproducing kernel Hilbert space. The performance of the resulting change-point detection procedure is theoretically grounded by means of a non-asymptotic model selection result (oracle inequality).

We will also illustrate the practical behavior of our kernel change-point procedure on a wide range of simulated data. In particular we empirically validate our penalty since the resulting penalized criterion recovers the true (number of) change-points with high probability.

We will finally discuss the influence of the kernel on the results in practice.