A computationally efficient nonparametric approach for changepoint detection

Abstract

In this paper we build on an approach proposed by for nonparametric changepoint detection. This approach defines the best segmentation for a data set as the one which minimises a penalised cost function, with the cost function defined in term of minus a non-parametric loglikelihood for data within each segment. Minimising this cost function is possible using dynamic programming, but their algorithm had a computational cost that is cubic in the length of the data set. To speed up computation, resorted to a screening procedure which means that the estimated segmentation is no longer guaranteed to be the global minimum of the cost function. We show that the screening procedure adversely affects the accuracy of the changepoint detection method, and show how a faster dynamic programming algorithm, pruned exact linear time (PELT) (Killick et al. 2012), can be used to find the optimal segmentation with a computational cost that can be close to linear in the amount of data. PELT requires a penalty to avoid under/over-fitting the model which can have a detrimental effect on the quality of the detected changepoints. To overcome this issue we use a relatively new method, changepoints over a range of penalties (Haynes et al. 2016), which finds all of the optimal segmentations for multiple penalty values over a continuous range. We apply our method to detect changes in heart-rate during physical activity. Electronic supplementary materialThe online version of this article

Narrowest-Over-Threshold Detection of Multiple Change Points and Change-Point-Like Features

“…For change point detection in the mean, the selected competitors from the Comprehensive R Archive Network are changepoint (Killick and Eckley, 2014;Killick et al, 2016) implementing the PELT methodology that was proposed by Killick, Fearnhead and Eckley (2012), changepoint.np implementing a non-parametric extension of the PELT methodology that was studied in Haynes et al (2017), wbs (Baranowski and Fryzlewicz, 2015) implementing WBS proposed by Fryzlewicz (2014), ecp (James and Matteson, 2014) implementing the e.cp3o method that was proposed by James and Matteson (2015), strucchange (Zeileis et al, 2002) implementing the methodology of Bai and Perron (2003), Segmentor3IsBack (Cleynen et al, 2013) implementing the technique that was proposed by Rigaill (2015), nmcdr (Zou and Lancezhange, 2014) implementing NMCD, the non-parametric multiple change point detection methodology of , stepR (Pein et al, 2018) implementing the simultaneous multiscale change point estimator SMUCE that was proposed by Frick et al (2014) and FDRSeg (Li et al, 2017) implementing the method called FDRSeg proposed by Li et al (2016). We refer to the corresponding methods as PELT, NP-PELT, WBS, e.cp3o, B&P, S3IB, NMCD, SMUCE and FDRSeg respectively.…”

“…A non‐parametric version of the PELT method was investigated by Haynes et al . (). Another general approach is based on the idea of binary segmentation (BS) (Vostrikova, ), which can be viewed as a greedy approach with a limited computational cost.…”

“…However, there are exceptions, such as the pruned exact linear time (PELT) method (Killick, Fearnhead and Eckley, 2012), which achieves a linear computational cost, but requires the further assumption that change points are separated by time intervals drawn independently from some probability distribution: a scenario in which considerations of statistical consistency are not generally possible. A nonparametric version of the PELT method was investigated by Haynes et al (2017). Another general approach is based on the idea of binary segmentation (BS) (Vostrikova, 1981), which can be viewed as a greedy approach with a limited computational cost.…”

Selective review of offline change point detection methods

“…Precisely, for two indexes t and s (t < s < T ), the pruning rule is given by: An extension of Pelt is described in [9] to solve the linearly penalized change point detection for a range of smoothing parameter values [β min , β max ]. Pelt has been applied on DNA sequences [16,17], physiological signals [89], and oceanographic data [111].…”

High-dimensional changepoint detection via a geometrically inspired mapping

“…If p is small, we may not want to make the Normal assumption. In this case, we recommend using a non-parametric test statistic, such as the empirical distribution from Zou et al (2014) (where consistency has also been shown) as embedded within PELT in Haynes et al (2017b).…”