Change Point Detection in the Frequency Domain with Statistical Reliability
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915302833389568 |
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| author | Yamada, Akifumi Shiraishi, Tomohiro Nishino, Shuichi Katsuoka, Teruyuki Taji, Kouichi Takeuchi, Ichiro |
| author_facet | Yamada, Akifumi Shiraishi, Tomohiro Nishino, Shuichi Katsuoka, Teruyuki Taji, Kouichi Takeuchi, Ichiro |
| contents | Effective condition monitoring in complex systems requires identifying change points (CPs) in the frequency domain, as the structural changes often arise across multiple frequencies. This paper extends recent advancements in statistically significant CP detection, based on Selective Inference (SI), to the frequency domain. The proposed SI method quantifies the statistical significance of detected CPs in the frequency domain using $p$-values, ensuring that the detected changes reflect genuine structural shifts in the target system. We address two major technical challenges to achieve this. First, we extend the existing SI framework to the frequency domain by appropriately utilizing the properties of discrete Fourier transform (DFT). Second, we develop an SI method that provides valid $p$-values for CPs where changes occur across multiple frequencies. Experimental results demonstrate that the proposed method reliably identifies genuine CPs with strong statistical guarantees, enabling more accurate root-cause analysis in the frequency domain of complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03062 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Change Point Detection in the Frequency Domain with Statistical Reliability Yamada, Akifumi Shiraishi, Tomohiro Nishino, Shuichi Katsuoka, Teruyuki Taji, Kouichi Takeuchi, Ichiro Machine Learning Effective condition monitoring in complex systems requires identifying change points (CPs) in the frequency domain, as the structural changes often arise across multiple frequencies. This paper extends recent advancements in statistically significant CP detection, based on Selective Inference (SI), to the frequency domain. The proposed SI method quantifies the statistical significance of detected CPs in the frequency domain using $p$-values, ensuring that the detected changes reflect genuine structural shifts in the target system. We address two major technical challenges to achieve this. First, we extend the existing SI framework to the frequency domain by appropriately utilizing the properties of discrete Fourier transform (DFT). Second, we develop an SI method that provides valid $p$-values for CPs where changes occur across multiple frequencies. Experimental results demonstrate that the proposed method reliably identifies genuine CPs with strong statistical guarantees, enabling more accurate root-cause analysis in the frequency domain of complex systems. |
| title | Change Point Detection in the Frequency Domain with Statistical Reliability |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.03062 |