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

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

Many real-world systems produce a batch of observations at each time step, like hospital labs analyzing thousands of cells per patient or platforms processing millions of daily comments. Existing change-point detection methods aggregate each batch into summary numbers like the mean, hiding important shifts in distributional shape. We treat each batch as a full probability distribution. Using optimal transport, our detector represents each one by how a fixed pre-change reference must be reshaped to match it. This linearizes the otherwise curved space of distributions, letting classical monitoring tools apply directly with provable false-alarm control. On flow-cytometry leukemia data, Reddit vaccine discussions, and synthetic benchmarks, our method catches complex distributional shifts faster than baselines at matched false-alarm rates, enabling sensitive monitoring in diagnostics, public-opinion analytics, and deployed ML systems.