Parallelization of a Common Changepoint Detection Method

Tickle, Sam; Eckley, Idris A.; Fearnhead, Paul; Haynes, Kaylea

doi:10.1080/10618600.2019.1647216

Cited by 15 publications

(15 citation statements)

References 20 publications

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“…It can be shown (e.g. Tickle et al, 2018) that the Schwarz' information criterion is asymptotically equivalent to the ℓ 0 penalization. Note that the results obtained there are asymptotic, while ours are non-asymptotic and allow all parameters to vary as the sample size n. Another related area is the reduced isotonic regression problem, which assumes the monotonic signal is piecewise-constant and which aims to recover the signal.…”

Section: Introductionmentioning

confidence: 99%

Univariate mean change point detection: Penalization, CUSUM and optimality

Wang¹,

Yu²,

Rinaldo³

2020

Electron. J. Statist.

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The problem of univariate mean change point detection and localization based on a sequence of n independent observations with piecewise constant means has been intensively studied for more than half century, and serves as a blueprint for change point problems in more complex settings. We provide a complete characterization of this classical problem in a general framework in which the upper bound σ 2 on the noise variance, the minimal spacing ∆ between two consecutive change points and the minimal magnitude κ of the changes, are allowed to vary with n. We first show that consistent localization of the change points, when the signal-to-noise ratio κdiverges with n at the rate of at least log(n), we demonstrate that two computationally-efficient change point estimators, one based on the solution to an ℓ 0 -penalized least squares problem and the other on the popular wild binary segmentation algorithm, are both consistent and achieve a localization rate of the order σ 2 κ 2 log(n). We further show that such rate is minimax optimal, up to a log(n) term.

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Section: Introductionmentioning

confidence: 99%

Univariate mean change point detection: Penalization, CUSUM and optimality

Wang¹,

Yu²,

Rinaldo³

2020

Electron. J. Statist.

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“…Indeed, employing a pruning step as per the PELT procedure of Killick et al (2012) results in an expected cost of O (qd). As shown in Tickle et al (2020), this can be improved further to a worst-case cost of O (qd) using parallelisation. Therefore, the worst-case computational complexity of the post-processing step is O (nd).…”

Section: Subset Pseudo-code Post-processing and Computational Discussionmentioning

confidence: 99%

A computationally efficient, high-dimensional multiple changepoint procedure with application to global terrorism incidence

Tickle

Eckley

Fearnhead

2020

Preprint

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Detecting changepoints in datasets with many variates is a data science challenge of increasing importance. Motivated by the problem of detecting changes in the incidence of terrorism from a global terrorism database, we propose a novel approach to multiple changepoint detection in multivariate time series. Our method, which we call SUBSET, is a model-based approach which uses a penalised likelihood to detect changes for a wide class of parametric settings. We provide theory that guides the choice of penalties to use for SUBSET, and that shows it has high power to detect changes regardless of whether only a few variates or many variates change. Empirical results show that SUBSET out-performs many existing approaches for detecting changes in mean in Gaussian data; additionally, unlike these alternative methods, it can be easily extended to non-Gaussian settings such as are appropriate for modelling counts of terrorist events.

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“…The criterion to optimize contains a penalty that is linear in the number of change-points. It is classically set to 2kσ 2 log(n) for change-in-mean problem [34,31], with σ2 the estimated noise variance and k the number of changes. For change-in-slope problem, theorems for a similar penalty have been given in asymptotic regime [36].…”

Section: Parameter Estimationmentioning

confidence: 99%

“…This penalty controls the amount of evidence we need to add a change: the greater this quantity, the less is k. We emphasise that k is an unknown quantity. The penalty value is often set to 2σ 2 log(n) [34,31,36] with σ2 an estimation of the variance σ 2 .…”

Section: Optimization Problemmentioning

confidence: 99%

Change-in-Slope Optimal Partitioning Algorithm in a Finite-Size Parameter Space

Runge¹,

Pascucci²,

Deschamps³

2020

Preprint

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We consider the problem of detecting change-points in univariate time series by fitting a continuous piecewise linear signal using the residual sum of squares. Values of the inferred signal at slope breaks are restricted to a finite set of size m. Using this finite parameter space, we build a dynamic programming algorithm with a controlled time complexity of O(m 2 n 2 ) for n data points. Some accelerating strategies can be used to reduce the constant before n 2 . The adapted classic inequality-based pruning is outperformed by a simpler "channel" method on simulations. Besides, our finite parameter space setting allows an easy introduction of constraints on the inferred signal. For example, imposing a minimal angle between consecutive segment slopes provides robustness to model misspecification and outliers. We test our algorithm with an isotonic constraint on an antibiogram image analysis problem for which algorithmic efficiency is a cornerstone in the emerging context of mobile-health and embedded medical devices. For this application, a finite state approach can be a valid compromise.

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Parallelization of a Common Changepoint Detection Method

Cited by 15 publications

References 20 publications

Univariate mean change point detection: Penalization, CUSUM and optimality

Univariate mean change point detection: Penalization, CUSUM and optimality

A computationally efficient, high-dimensional multiple changepoint procedure with application to global terrorism incidence

Change-in-Slope Optimal Partitioning Algorithm in a Finite-Size Parameter Space

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