High-dimensional change-point estimation: Combining filtering with convex optimization
- Creators
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Soh, Yong Sheng
- Chandrasekaran, Venkat
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.
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.Attached Files
Submitted - 1412.3731.pdf
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Additional details
- Eprint ID
- 77750
- DOI
- 10.1016/j.acha.2015.11.003
- Resolver ID
- CaltechAUTHORS:20170525-100137066
- NSF
- CCF-1350590
- Air Force Office of Scientific Research (AFOSR)
- FA9550-14-1-0098
- Okawa Research
- Agency for Science, Technology and Research (A*STAR)
- Created
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2017-05-25Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field