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 Fréchet 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.

翻译：现有的在线变点检测方法依赖于固定维度的欧几里得摘要，这隐含地假设基于矩或基于特征的表示能充分捕捉分布变化。然而，这些方法可能会掩盖分布形状或几何结构中的重要变化。我们提出了一种本征的分布值变点检测框架，将流式批处理数据视为2-Wasserstein空间上的随机过程。该方法通过将每个经验分布映射到相对于变化前Fr\'echet重心的一个切空间，实现了2-Wasserstein空间的以参考为中心的局部线性化，从而检测该过程律的变化。这种表示通过将经典多元监测统计量适配到切向量场，实现了序列检测器。我们提供了理论保证，并通过合成与真实世界实验证明，在匹配的$\mathrm{ARL}_0$条件下，与基于矩和无模型的基线方法相比，我们的方法能以更低的检测延迟识别复杂的分布漂移。