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Change-point detection for sparse and dense functional data in general dimensions
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Padilla, Carlos Misael Madrid, Wang, Daren, Zhao, Zifeng and Yu, Yi (2022) Change-point detection for sparse and dense functional data in general dimensions. In: 36th Conference on Neural Information Processing Systems (NeurIPS 2022), New Orleans, USA, 28 Nov - 09 Dec 2022. Published in: Advances in Neural Information Processing Systems (NeurIPS 2022) (36). ISSN 1049-5258. (In Press)
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Abstract
We study the problem of change-point detection and localisation for functional data sequentially observed on a general d-dimensional space, where we allow the functional curves to be either sparsely or densely sampled. Data of this form naturally arise in a wide range of applications such as biology, neuroscience, climatology and finance. To achieve such a task, we propose a kernel-based algorithm namely functional seeded binary segmentation (FSBS). FSBS is computationally efficient, can handle discretely observed functional data, and is theoretically sound for heavy-tailed and temporally-dependent observations. Moreover, FSBS works for a general d-dimensional domain, which is the first in the literature of changepoint estimation for functional data. We show the consistency of FSBS for multiple change-point estimation and further provide a sharp localisation error rate, which reveals an interesting phase transition phenomenon depending on the number of functional curves observed and the sampling frequency for each curve. Extensive numerical experiments illustrate the effectiveness of FSBS and its advantage over existing methods in the literature under various settings. A real data application is further conducted, where FSBS localises change-points of sea surface temperature patterns in the south Pacific attributed to El Niño. The code to replicate all of our experiments can be found at https://github.com/cmadridp/FSBS.
| Item Type: | Conference Item (Paper) | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
| Library of Congress Subject Headings (LCSH): | Change-point problems, Kernel functions, Algorithms | |||||||||
| Journal or Publication Title: | Advances in Neural Information Processing Systems (NeurIPS 2022) | |||||||||
| ISSN: | 1049-5258 | |||||||||
| Official Date: | 2022 | |||||||||
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| Number: | 36 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 6 October 2022 | |||||||||
| Date of first compliant Open Access: | 6 October 2022 | |||||||||
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| Conference Paper Type: | Paper | |||||||||
| Title of Event: | 36th Conference on Neural Information Processing Systems (NeurIPS 2022) | |||||||||
| Type of Event: | Conference | |||||||||
| Location of Event: | New Orleans, USA | |||||||||
| Date(s) of Event: | 28 Nov - 09 Dec 2022 | |||||||||
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