High-Dimensional Change Point Detection using Graph Spanning Ratio

TL;DR

This paper introduces a graph-spanning algorithm for high-dimensional change point detection that is effective for both offline and online data, outperforming existing methods in accuracy and speed across various data types.

Contribution

The paper presents a novel graph-spanning change point detection algorithm applicable to high-dimensional, Euclidean, and graph-structured data with theoretical guarantees.

Findings

Achieves high detection power when change magnitude exceeds the minimax separation rate.

Outperforms existing techniques in accuracy for Gaussian and non-Gaussian data.

Remains effective with small observation windows, suitable for online detection.

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.