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

arXiv: https://arxiv.org/abs/2602.07252 · HTML: https://mlsanity.com/paper/2602.07252/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency](https://mlsanity.com/paper/2608.08424/) (2026)

## Abstract (arXiv)

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 ARL0 compared with moments-based and model-free baselines. The code is available at https://github.com/yyzeng43/IDD-icml .