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High-dimensional, multiscale online changepoint detection

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Chen, Y 
Samworth, RJ 

Abstract

We introduce a new method for high-dimensional, online changepoint detection in settings where a p-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst-case computational complexity per new observation are independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal, which is implemented in the R package 'ocd', and we also demonstrate its utility on a seismology data set.

Description

Keywords

average run length, detection delay, high-dimensional changepoint detection, online algorithm, sequential method

Journal Title

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

Conference Name

Journal ISSN

1369-7412
1467-9868

Volume Title

Publisher

Royal Statistical Society

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)