New Adaptive Approaches for Change-Point Detection

We consider the change-point problem in time series of observations belonging to general sets. We propose a test of the presence of a change-point that relies on a positive semi-definite kernel between observations. We also propose the counterpart for the retrospective estimation of multiple change-points. Owing to our reproducing kernel Hilbert space construction, the proposed methods can handle observations living in general sets, as long as a meaningful positive semi-definite kernel can be defined between two observations. We prove non-asymptotic statistical guarantees for both methods. We illustrate the potential of the approach on several real-world applications, including user-generated video summarization and automatic structuring of videos.