Parallelisation of a Common Changepoint Detection Method

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

doi:10.48550/arxiv.1810.03591

Cited by 1 publication

(1 citation statement)

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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%