## Electronic Journal of Statistics

### Consistent change-point detection with kernels

#### Abstract

In this paper we study the kernel change-point algorithm (KCP) proposed by Arlot, Celisse and Harchaoui [5], which aims at locating an unknown number of change-points in the distribution of a sequence of independent data taking values in an arbitrary set. The change-points are selected by model selection with a penalized kernel empirical criterion. We provide a non-asymptotic result showing that, with high probability, the KCP procedure retrieves the correct number of change-points, provided that the constant in the penalty is well-chosen; in addition, KCP estimates the change-points location at the optimal rate. As a consequence, when using a characteristic kernel, KCP detects all kinds of change in the distribution (not only changes in the mean or the variance), and it is able to do so for complex structured data (not necessarily in $\mathbb{R}^{d}$). Most of the analysis is conducted assuming that the kernel is bounded; part of the results can be extended when we only assume a finite second-order moment. We also demonstrate KCP on both synthetic and real data.

#### Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 4440-4486.

Dates
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.ejs/1545123630

Digital Object Identifier
doi:10.1214/18-EJS1513

Subjects
Secondary: 62G20: Asymptotic properties

#### Citation

Garreau, Damien; Arlot, Sylvain. Consistent change-point detection with kernels. Electron. J. Statist. 12 (2018), no. 2, 4440--4486. doi:10.1214/18-EJS1513. https://projecteuclid.org/euclid.ejs/1545123630

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