High-Dimensional Change Point Detection via Graph Spanning Ratio

Change point detection (CPD) identifies abrupt and significant changes in sequential data, with applications in human activity recognition, financial markets, cybersecurity, manufacturing, and autonomous systems. Traditional CPD methods often face computational challenges in high-dimensional settings and typically provide limited explanations for detected changes, which can restrict their practical usability. This paper introduces a CPD framework that improves scalability and interpretability by leveraging the Sliced Wasserstein (SW) distance. Our contributions are fourfold: (1) we transform multivariate sequential data into one-dimensional scores using the SW distance, making the resulting representation compatible with existing CPD methods; (2) we analyze the distributional behavior of random slices of the SW distance and show that, under suitable assumptions, they can be approximated by a Gamma distribution, providing a principled basis for threshold calibration; (3) we propose a self-adapting online CPD algorithm that combines this SW-based score with an adaptive quantile-based threshold; (4) we introduce a model-specific framework for generating contrastive explanations for annotated change points. Empirically, our method reduces false positives by at least $48\%$ on average compared with popular online and offline CPD baselines, while maintaining competitive or superior detection performance. Code is available at https://github.com/jsve96/SWCPD_Code. At the same time, it produces interpretable change-point annotations, making it practical for deployment in high-stakes applications.

Statistical change point (CP) detection methods typically rely on likelihood-based inference and ignore contextual information about plausible CP locations beyond the observed sequence. Although informative priors provide a natural way to incorporate such information, general and computationally efficient methods for doing so are lacking, especially for multiple CP detection. To address this gap, we propose a prior-informed CP detection algorithm (Pi-Change) that incorporates prior information on CP locations through a time-varying penalty term. We prove that the proposed penalty can be embedded in the Pruned Exact Linear Time framework while preserving the dynamic programming recursion and pruning rule required for efficient multiple CP detection. Across simulation studies and three time-series applications, Pi-Change discourages spurious CPs unsupported by prior information, remains robust to prior misspecification, and improves detection accuracy. More broadly, Pi-Change extends multiple CP detection beyond purely data-driven fitting by incorporating partial prior knowledge in a computationally efficient and interpretable way. It is particularly useful when CPs arise from heterogeneous mechanisms or are associated with known external events, helping quantify the delay between an event and the resulting structural change.

Traditional change point detection in dynamic networks assumes abrupt transitions between stationary states, overlooking scenarios of continuous evolution which arise in most real-world applications, such as social networks or physical systems. We address this gap by formally defining regimes as periods of coherent dynamics in temporal graphs, which we characterize as trajectories along geodesics in a suitably defined graph space. This original perspective allows us to define regime changes as significant drifts in dynamics, either toward new trajectories or with pace changes. We leverage graph regression methods to measure the cumulative distance of sequences of observed graphs from the estimated geodesics between their endpoints, in the relevant graph space, which we can combine with change point detection algorithms. We present experiments on dynamic networks, with changing trajectories and varying speeds, in which we outperform state of the art change point detection models. Then, we analyse mobility data during the Covid-19 pandemic, and show that our assumptions on regular network evolution lead to change points that are more aligned to external events compared to the outcomes of baseline methods. Our work is the first to model and detect changes between evolving regimes in graph space, providing a realistic and powerful tool for analyzing complex temporal graph data.