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December 2018 Tail-greedy bottom-up data decompositions and fast multiple change-point detection
Piotr Fryzlewicz
Ann. Statist. 46(6B): 3390-3421 (December 2018). DOI: 10.1214/17-AOS1662

Abstract

This article proposes a “tail-greedy”, bottom-up transform for one-dimensional data, which results in a nonlinear but conditionally orthonormal, multiscale decomposition of the data with respect to an adaptively chosen unbalanced Haar wavelet basis. The “tail-greediness” of the decomposition algorithm, whereby multiple greedy steps are taken in a single pass through the data, both enables fast computation and makes the algorithm applicable in the problem of consistent estimation of the number and locations of multiple change-points in data. The resulting agglomerative change-point detection method avoids the disadvantages of the classical divisive binary segmentation, and offers very good practical performance. It is implemented in the R package breakfast, available from CRAN.

Citation

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Piotr Fryzlewicz. "Tail-greedy bottom-up data decompositions and fast multiple change-point detection." Ann. Statist. 46 (6B) 3390 - 3421, December 2018. https://doi.org/10.1214/17-AOS1662

Information

Received: 1 March 2017; Revised: 1 September 2017; Published: December 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06965692
MathSciNet: MR3852656
Digital Object Identifier: 10.1214/17-AOS1662

Subjects:
Primary: 62G05

Keywords: bottom-up methods , multiscale methods , segmentation , Sparsity , Tail-greediness , thresholding

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6B • December 2018
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