Section: New Results

Kernel change-point detection

In collaboration with A. Celisse and Z. Harchaoui, S. Arlot worked on the change-point problem with data belonging to a general set. They built a penalty for choosing the number of change-points in the kernel-based method of Harchaoui and Cappé (2007). This penalty generalizes the one proposed by Lebarbier (2005) for one-dimensional signals. They prove in [4] a non-asymptotic oracle inequality for the proposed method, thanks to a new concentration result for some function of Hilbert-space valued random variables. Experiments on synthetic and real data illustrate the accuracy of our method, showing that it can detect changes in the whole distribution of data, even when the mean and variance are constant. This method has since been used successfully by several authors in various applied contexts.