High-Dimensional Change Point Detection using Graph Spanning Ratio

2025-12-08

AI Summary

This paper addresses offline and online change-point detection in high-dimensional Euclidean and graph-structured data under unknown distributions. We propose a nonparametric method based on the graph-based likelihood ratio—a novel statistic introduced for the first time into the change-point detection framework. Theoretically, our method achieves the minimax lower bound on the separation rate, significantly enhancing detection sensitivity—especially under short windows. By integrating graph-spanning algorithms with nonparametric modeling that guarantees controllable error probabilities, the approach imposes no distributional assumptions and accommodates multivariate, heterogeneous data. Extensive experiments demonstrate superior performance over state-of-the-art methods in both Gaussian and non-Gaussian settings; notably, it maintains high detection power even with limited sample sizes, making it well-suited for real-time, accurate monitoring applications.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and graph-structured data with unknown distributions, while maintaining control over error probabilities. Theoretically, we demonstrate that the algorithm achieves high detection power when the magnitude of the change surpasses the lower bound of the minimax separation rate, which scales on the order of $sqrt{nd}$. Our method outperforms other techniques in terms of accuracy for both Gaussian and non-Gaussian data. Notably, it maintains strong detection power even with small observation windows, making it particularly effective for online environments where timely and precise change detection is critical.

Problem

• Detects change points in high-dimensional offline and online data
• Applies to unknown distributions in Euclidean and graph-structured data
• Maintains accuracy and detection power with small observation windows

Innovation

• Graph-spanning algorithm for offline and online change detection
• Applicable to Euclidean and graph-structured data with unknown distributions
• Maintains detection power with small observation windows for online use