Kernel Change point Analysis

Niveau: Supérieur
Kernel Change-point Analysis Zaıd Harchaoui LTCI, TELECOM ParisTech and CNRS 46, rue Barrault, 75634 Paris cedex 13, France Francis Bach Willow Project, INRIA-ENS 45, rue d'Ulm, 75230 Paris, France Eric Moulines LTCI, TELECOM ParisTech and CNRS 46, rue Barrault, 75634 Paris cedex 13, France Abstract We introduce a kernel-based method for change-point analysis within a sequence of temporal observations. Change-point analysis of an unlabelled sample of obser- vations consists in, first, testing whether a change in the distribution occurs within the sample, and second, if a change occurs, estimating the change-point instant after which the distribution of the observations switches from one distribution to another different distribution. We propose a test statistic based upon the maximum kernel Fisher discriminant ratio as a measure of homogeneity between segments. We derive its limiting distribution under the null hypothesis (no change occurs), and establish the consistency under the alternative hypothesis (a change occurs). This allows to build a statistical hypothesis testing procedure for testing the pres- ence of a change-point, with a prescribed false-alarm probability and detection probability tending to one in the large-sample setting. If a change actually occurs, the test statistic also yields an estimator of the change-point location.

• kernel change-point


• limiting distribution


• null hypothesis


• based method


• statistical hypothesis testing


• change-point problem


• point analysis


• alarm probability