Change Point Detection in the Frequency Domain with Statistical Reliability
This work addresses the need for accurate root-cause analysis in complex systems by enabling statistically reliable change point detection in the frequency domain, representing an incremental advancement in applying existing methods to new domains.
The paper tackles the problem of detecting change points in the frequency domain for condition monitoring in complex systems, extending Selective Inference to provide statistically significant p-values, and demonstrates reliable identification of genuine change points with strong statistical guarantees.
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.