Data-Adaptive Symmetric CUSUM for Sequential Change Detection.

Area of Science:

• Statistics
• Signal Processing
• Data Science

Background:

• Sequential change point detection in streaming data is challenging, especially with simultaneous mean and variance shifts.
• Traditional methods like CUSUM and GLR lack symmetry, complicating threshold setting for multiple distribution changes.
• Adaptive thresholding is difficult when signal distributions change dynamically.

Purpose of the Study:

• To introduce a novel, symmetric change point detection algorithm for streaming data.
• To address the limitations of existing methods in handling simultaneous mean and variance changes.
• To enable reliable sequential detection of multiple change points with a single threshold.

Main Methods:

• Development of the Data-Adaptive Symmetric CUSUM (DAS-CUSUM) procedure.
• Theoretical analysis of expected detection delay and average run length under normal distributions.
• Empirical validation using simulated and real-world streaming datasets.

Main Results:

• DAS-CUSUM demonstrates symmetry, facilitating a single detection threshold.
• The proposed method effectively detects sequential change points even with mean and variance shifts.
• Experimental results confirm the practical utility and performance of DAS-CUSUM.

Conclusions:

• DAS-CUSUM provides a robust and symmetric solution for sequential change point detection in streaming environments.
• The method simplifies threshold management for detecting multiple changes across different data distributions.
• DAS-CUSUM offers a significant advancement for real-time signal monitoring and analysis.