Repository logo
 

High-dimensional change point estimation via sparse projection

Published version
Peer-reviewed

Type

Article

Change log

Authors

Wang, T 
Samworth, RJ 

Abstract

Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse subset of the coordinates. The challenge is to borrow strength across the coordinates in order to detect smaller changes than could be observed in any individual component series. We propose a two-stage procedure called 'inspect' for estimation of the changepoints: first, we argue that a good projection direction can be obtained as the leading left singular vector of the matrix that solves a convex optimisation problem derived from the CUSUM transformation of the time series. We then apply an existing univariate changepoint estimation algorithm to the projected series. Our theory provides strong guarantees on both the number of estimated changepoints and the rates of convergence of their locations, and our numerical studies validate its highly competitive empirical performance for a wide range of data generating mechanisms. Software implementing the methodology is available in the R package 'InspectChangepoint'.

Description

Keywords

Change point estimation, Convex optimization, Dimension reduction, Piecewise stationary, Segmentation, Sparsity

Journal Title

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Conference Name

Journal ISSN

1369-7412
1467-9868

Volume Title

80

Publisher

Wiley
Sponsorship
Engineering and Physical Sciences Research Council (EP/J017213/1)
Leverhulme Trust (PLP-2014-353)
Engineering and Physical Sciences Research Council (EP/N031938/1)
Alan Turing Institute (unknown)