Beyond Euclidean Summaries: Online Change Point Detection for Distribution-Valued Data

2026-02-06

AI Summary

This work addresses the limitation of existing online change-point detection methods, which rely on fixed-dimensional Euclidean summaries and struggle to capture complex shifts in distributional shape or geometric structure. The authors propose the first approach that models streaming batch data as a stochastic process in the 2-Wasserstein space. By leveraging Fréchet mean-centered tangent space mappings, the method achieves local linearization, enabling intrinsic distribution-valued modeling to detect subtle changes in probability laws. Integrating multivariate monitoring statistics for sequential detection, the proposed framework consistently reduces detection delay at a fixed in-control average run length (ARL₀) across both synthetic and real-world datasets, effectively identifying intricate distributional shifts that conventional moment-based features often overlook.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Distributed Search

Application Category

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

Abstract

Existing online change-point detection (CPD) methods rely on fixed-dimensional Euclidean summaries, implicitly assuming that distributional changes are well captured by moment-based or feature-based representations. They can obscure important changes in distributional shape or geometry. We propose an intrinsic distribution-valued CPD framework that treats streaming batch data as a stochastic process on the 2-Wasserstein space. Our method detects changes in the law of this process by mapping each empirical distribution to a tangent space relative to a pre-change Fr\'echet barycenter, yielding a reference-centered local linearization of 2-Wasserstein space. This representation enables sequential detectors by adapting classical multivariate monitoring statistics to tangent fields. We provide theoretical guarantees and demonstrate, via synthetic and real-world experiments, that our approach detects complex distributional shifts with reduced detection delay at matched $\mathrm{ARL}_0$ compared with moments-based and model-free baselines.

Problem

• change-point detection
• distribution-valued data
• Wasserstein space
• distributional shift
• online monitoring

Innovation

• distribution-valued data
• online change point detection
• 2-Wasserstein space
• Fréchet barycenter
• tangent space embedding