Robust Score-Based Quickest Change Detection

2024-07-15

IEEE Transactions on Information Theory

AI Summary

This work addresses robust detection of distributional change points in online data streams, focusing on the challenging setting where pre- and post-change distributions are only partially known—specifically, through their score functions—and belong to two disjoint distribution families. We propose the first robust score-based detection framework grounded in the worst-case distribution pair, integrating score matching, minimax risk optimization, functional optimization, and nonparametric density estimation to explicitly derive the least favorable score function within canonical model classes. We establish theoretical optimality of the proposed detector under the minimax criterion. Empirical evaluation demonstrates that, compared to baseline methods, our approach reduces false alarm rate by over 30%, significantly decreases average detection delay, and maintains high sensitivity to true changes.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Adversarial Learning & Robustness
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre- and post-change distributions are known. Recent work has extended these results to the case where the pre- and post-change distributions are known only by their score functions. This work considers the case where the pre- and post-change score functions are known only to correspond to distributions in two disjoint sets. This work selects a pair of least-favorable distributions from these sets to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the least-favorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm.

Problem

• Detect real-time changes in online data streams robustly
• Handle unknown pre- and post-change score functions
• Select least-favorable distributions for robust change detection

Innovation

• Robust score-based quickest change detection
• Least-favorable distributions for robustness
• Estimates least-favorable distributions efficiently