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

TL;DR

This paper introduces an innovative online change-point detection method for distribution-valued data using 2-Wasserstein space, improving detection of complex distributional shifts over traditional Euclidean summary-based methods.

Contribution

It develops an intrinsic distribution-valued CPD framework that operates directly on the space of distributions, providing theoretical guarantees and enhanced detection capabilities.

Findings

Detects complex distributional shifts with reduced delay

Outperforms moments-based and model-free baselines in experiments

Provides theoretical guarantees for change detection

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. The code is available at https://github.com/yyzeng43/IDD-icml .