BayesProject: Fast computation of a projection direction for multivariate changepoint detection
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BayesProject: Fast computation of a projection direction for multivariate changepoint detection Georg Hahn1
· Paul Fearnhead1 · Idris A. Eckley1
Received: 16 July 2019 / Accepted: 23 July 2020 © The Author(s) 2020
Abstract This article focuses on the challenging problem of efficiently detecting changes in mean within multivariate data sequences. Multivariate changepoints can be detected by projecting a multivariate series to a univariate one using a suitable projection direction that preserves a maximal proportion of signal information. However, for some existing approaches the computation of such a projection direction can scale unfavourably with the number of series and might rely on additional assumptions on the data sequences, thus limiting their generality. We introduce BayesProject, a computationally inexpensive Bayesian approach to compute a projection direction in such a setting. The proposed approach allows the incorporation of prior knowledge of the changepoint scenario, when such information is available, which can help to increase the accuracy of the method. A simulation study shows that BayesProject is robust, yields projections close to the oracle projection direction and, moreover, that its accuracy in detecting changepoints is comparable to, or better than, existing algorithms while scaling linearly with the number of series. Keywords Multivariate data sequence · Segmentation · Dimension reduction · Structural break · Breakpoint · Cusum
1 Introduction Changepoint detection is an area of research with immediate practical applications in the monitoring of financial data (Bai and Perron 1998; Frick et al. 2014), network traffic data (Lévy-Leduc and Roueff 2009; Lung-Yut-Fong et al. 2012), as well as bioinformatics (Maidstone et al. 2017; Guédon 2013), environmental (Nam et al. 2015) and signal or speech processing applications (Desobry et al. 2005; Haynes et al. 2017). For instance, a sudden change in (mean) activity of one or more data streams in a network could hint at an intruder sending data to an unknown host from several infected computers. In general, a user is faced with the task to monitor several data streams simultaneously, ideally in real time, with the aim of detecting a change occurring in at least one series as soon as it occurs. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11222-020-09966-2) contains supplementary material, which is available to authorized users.
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Georg Hahn [email protected] Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK
Starting with the work of Page (1954), considerable contributions have been made to the literature on changepoint detection in the areas of both methodology and applications. Of particular interest for the work we present are the developments in multivariate changepoint detection. Other aspects of changepoint detection address nonparametric asymptotic tests (Aue et al. 2009), scan and segmentation algorithms based on Chi-squared statistics (Zhang et al. 20
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