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High-dimensional change-point estimation: Combining filtering with convex optimization

Soh, Yong Sheng and Chandrasekaran, Venkat (2017) High-dimensional change-point estimation: Combining filtering with convex optimization. Applied and Computational Harmonic Analysis, 43 (1). pp. 122-147. ISSN 1063-5203. https://resolver.caltech.edu/CaltechAUTHORS:20170525-100137066

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Abstract

We consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they have undesirable scaling behavior in the high-dimensional setting. However, many high-dimensional signals encountered in practice frequently possess latent low-dimensional structure. Motivated by this observation, we propose a technique for high-dimensional change-point estimation that combines the filtered derivative approach from previous work with convex optimization methods based on atomic norm regularization, which are useful for exploiting structure in high-dimensional data. Our algorithm is applicable in online settings as it operates on small portions of the sequence of observations at a time, and it is well-suited to the high-dimensional setting both in terms of computational scalability and of statistical efficiency. The main result of this paper shows that our method performs change-point estimation reliably as long as the product of the smallest-sized change (the Euclidean-norm-squared of the difference between signals at a change-point) and the smallest distance between change-points (number of time instances) is larger than a Gaussian width parameter that characterizes the low-dimensional complexity of the underlying signal sequence.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.acha.2015.11.003DOIArticle
http://resolver.caltech.edu/CaltechAUTHORS:20151007-111059602Related ItemConference Paper
https://arxiv.org/abs/1412.3731arXivDiscussion Paper
Additional Information:© 2015 Elsevier Inc. Received 11 December 2014, Revised 3 November 2015, Accepted 6 November 2015, Available online 11 November 2015. This work was supported in part by the following sources: National Science Foundation Career award CCF-1350590, Air Force Office of Scientific Research grant FA9550-14-1-0098, an Okawa Research Grant in Information and Telecommunications, and an A*STAR (Agency for Science, Technology and Research, Singapore) Fellowship. Yong Sheng Soh would like to thank Michael McCoy for useful discussions, and Atul Ingle for pointing out a typographical error in a preliminary version of this paper. The authors would like to thank the reviewers for their useful comments and suggestions.
Funders:
Funding AgencyGrant Number
NSFCCF-1350590
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0098
Okawa Research Grant in Information and TelecommunicationsUNSPECIFIED
Agency for Science, Technology and Research (A*STAR)UNSPECIFIED
Subject Keywords:High-dimensional time series; Convex geometry; Atomic norm thresholding; Filtered derivative
Issue or Number:1
Record Number:CaltechAUTHORS:20170525-100137066
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170525-100137066
Official Citation:Yong Sheng Soh, Venkat Chandrasekaran, High-dimensional change-point estimation: Combining filtering with convex optimization, Applied and Computational Harmonic Analysis, Volume 43, Issue 1, July 2017, Pages 122-147, ISSN 1063-5203, https://doi.org/10.1016/j.acha.2015.11.003. (http://www.sciencedirect.com/science/article/pii/S1063520315001542)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77750
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 May 2017 18:22
Last Modified:03 Oct 2019 18:01

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