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

Soh, Yong Sheng and Chandrasekaran, Venkat (2015) High-dimensional change-point estimation: Combining filtering with convex optimization. In: 2015 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 151-155. ISBN 978-1-4673-7704-1. https://resolver.caltech.edu/CaltechAUTHORS:20151007-111059602

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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. A full version of this paper is available online [1].


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2015.7282435 DOIArticle
http://resolver.caltech.edu/CaltechAUTHORS:20170525-100137066Related ItemJournal Article
https://arxiv.org/abs/1412.3731arXivDiscussion Paper
Additional Information:© 2015 IEEE.
Subject Keywords:High-dimensional time series; convex geometry;atomic norm thresholding; filtered derivative
Record Number:CaltechAUTHORS:20151007-111059602
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20151007-111059602
Official Citation:Soh, Yong Sheng; Chandrasekaran, Venkat, "High-dimensional change-point estimation: Combining filtering with convex optimization," in Information Theory (ISIT), 2015 IEEE International Symposium on , vol., no., pp.151-155, 14-19 June 2015 doi: 10.1109/ISIT.2015.7282435
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60874
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Oct 2015 19:11
Last Modified:03 Oct 2019 09:01

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