Wild binary segmentation algorithm for consistent multiple change points detection via the fused LASSO signal approximator†
Woosol Jang1 · Won Son2
12Department of Applied Statistics, Dankook University
Correspondence to: † This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01051039).
1 Graduate student, Department of Applied Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, Republic of Korea.
2 Assistant professor, Department of Information Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, Republic of Korea, E-mail: son.won@dankook.ac.kr
1 Graduate student, Department of Applied Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, Republic of Korea.
2 Assistant professor, Department of Information Statistics, Dankook University, 152, Jukjeon-ro, Suji-gu, Yongin-si, Gyeonggi-do 16890, Republic of Korea, E-mail: son.won@dankook.ac.kr
Received August 1, 2022; Revised September 1, 2022; Accepted September 7, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- It is well known that the fused LASSO signal approximator (FLSA) is inconsistent in multiple change points detection. The FLSA is inconsistent when there exists at least one staircase block whose mean value is not an extreme value, i.e., neither a local maximum nor local minimum. Therefore, if there exists only one true change point, there can be no true staircase blocks. Consequently, the FLSA can find the true change point consistently for those cases. The wild binary segment (WBS) algorithm is one of the famous algorithms which can be applied to multiple change points detection problems. The WBS algorithm randomly samples intervals and we can expect that some of the sampled intervals contain only one true change point. Therefore, the WBS algorithm tries to convert multiple change points detection problems into single change point detection problems. Although the original WBS algorithm is coupled with the CUSUM statistic, other statistics can be utilized. In this paper, we propose a WBS algorithm employing the FLSA for consistent multiple change points detection. Through a numerical study, we find that the newly proposed algorithm can identify the true change points consistently.
- Keywords : CUSUM statistic, fused LASSO signal approximator, multiple change points detection, wild binary segmentation.
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