change-point detection

Current time-series anomaly detection research predominantly focuses on static, batch-processing settings, overlooking critical industrial requirements—namely, streaming computation, human-in-the-loop interaction, point-process modeling, conditional anomaly identification, and multi-series collective analysis. Method: This paper systematically identifies five long-neglected industrial challenges and introduces two novel paradigms: *conditional anomalies* and *collective time-series analysis*. We propose an interpretable, interactive, and scalable framework integrating stream processing architecture, interactive feedback mechanisms, point-process statistical modeling, conditional dependency graph learning, and collective clustering techniques. Contribution/Results: Our work establishes a practical industrial adoption roadmap, catalyzes the development of new benchmark datasets and standardized evaluation protocols, and bridges the gap between theoretical research and real-world deployment in time-series anomaly detection.

This work addresses the limitations of existing online change-point detection methods, which typically assume independent and identically distributed (i.i.d.) data and thus struggle with real-world time series exhibiting autocorrelation, often resulting in high false alarm rates or detection delays. To overcome this, the authors extend the generalized likelihood ratio (GLR) test to p-th order autoregressive (AR(p)) processes and integrate it with an enhanced FOCUS algorithm, yielding a computationally efficient online detector termed AR(p)-FOCUS. This approach is the first to explicitly model temporal dependencies within the GLR framework, achieving significantly improved detection performance while maintaining an average per-iteration computational complexity of O(log n). Empirical evaluations demonstrate that AR(p)-FOCUS outperforms conventional i.i.d.-based methods on autocorrelated data and exhibits strong effectiveness and practicality on real-world telecommunications datasets.

Online univariate change-point detection in high-dimensional data streams suffers from prohibitively high computational complexity in likelihood ratio computation, hindering real-time processing. Method: This paper establishes the first theoretical connection between multivariate change-point detection and computational geometry, proposing an exact online algorithm based on convex hulls and half-space intersections. For sparse change-point structures, it constructs the likelihood ratio statistic in near-linear time (O(n log^{p+1} n)). Furthermore, it introduces a tunable-accuracy approximation algorithm that reduces complexity to (O(np log^{ ilde{p}+1} n)) for (p > 5). Contribution/Results: We prove statistical consistency of the proposed detector. Empirical evaluation on NBA tracking data and real-world datasets demonstrates superior accuracy and real-time performance compared to state-of-the-art methods.

This work addresses the problem of efficient online change-point detection in both univariate and multivariate data streams by introducing a novel method grounded in the Focus algorithm family. Leveraging the generalized likelihood ratio test, the approach enables exact detection of a single change point without requiring approximations. By exploiting the relationship between candidate change-point locations and the geometric structure of the data, it achieves a computational complexity of approximately $\log(n)^d$ per iteration. Notably, this is the first method to support exponential-family models, nonparametric settings, and autoregressive data under no approximation assumptions, integrating natural exponential-family modeling, empirical cumulative distribution functions, and geometric optimization techniques. The accompanying R/Python software package substantially enhances the efficiency and applicability of change-point detection in high-dimensional streaming data.

This paper addresses the core challenge in change detection for nonstationary processes—where the post-change distribution evolves over time and is a priori unknown. Method: We propose a robust sequential detection framework based on the least favorable distribution, integrating minimax decision theory, nonstationary statistical modeling, and sequential hypothesis testing to construct an adaptive CUSUM-type algorithm capable of real-time, robust response to dynamic distributional shifts. Contribution/Results: To our knowledge, this is the first work to establish asymptotically minimax-optimal theoretical guarantees for sequential change detection under nonstationarity. Empirical evaluation on real-world public health and military monitoring datasets, as well as extensive simulations, demonstrates that our method reduces average detection delay by 23% compared to conventional approaches, while maintaining stable and controllable false alarm rates—thereby validating both theoretical soundness and practical superiority.

This work addresses the challenge of detecting subtle changes in cross-variable and temporal dependency structures within multivariate time series in an online setting. The authors propose a distribution-free, minimally parameterized, and interpretable nonparametric method that recursively estimates Dynamic Mode Decomposition (DMD) operators and monitors their truncated eigenvalue sequences to capture abrupt shifts in dependency patterns. To handle the permutation invariance inherent in eigendecompositions, the approach innovatively incorporates an optimal linear assignment strategy. Furthermore, it introduces an augmented monitoring scheme tailored for complex-valued time series. Experimental results on both synthetic and real-world datasets—including video and text streams—demonstrate that the proposed method matches or outperforms state-of-the-art alternatives, exhibiting strong generalization capability and practical deployment potential.

This study addresses the challenge of rapid change-point detection in high-dimensional multisensor systems under structural constraints and limited sensing resources. By integrating sparse modeling, heterogeneous data fusion, and a resource-adaptive sequential sampling strategy, the work extends classical change-point detection theory to large-scale, resource-constrained sensing scenarios and incorporates machine learning to handle cases with unknown system models. The proposed approach unifies sparse signal processing, multi-stream statistical decision-making, and resource-constrained optimization to enable simultaneous detection of multiple change points. This framework significantly enhances both applicability and scalability in high-dimensional, heterogeneous, and resource-limited environments while maintaining high detection efficiency.

This work addresses the lack of reliable uncertainty quantification in online trend estimation for nonstationary time series by proposing a general online bootstrap method applicable to trend estimators expressed as time-window-weighted sample means—such as exponential smoothing and moving averages. Built upon asymptotic theory, the method provides the first uniform-in-time coverage guarantees for trend inference under nonstationarity, enabling adaptive anomaly detection and A/B testing in streaming data settings. Empirical evaluations demonstrate that the framework achieves well-calibrated uncertainty estimates and scales effectively across diverse nonstationary scenarios, offering a practical and real-time solution for accurate uncertainty quantification in large-scale online time series analysis.

This paper addresses offline and online change-point detection in high-dimensional Euclidean and graph-structured data under unknown distributions. We propose a nonparametric method based on the graph-based likelihood ratio—a novel statistic introduced for the first time into the change-point detection framework. Theoretically, our method achieves the minimax lower bound on the separation rate, significantly enhancing detection sensitivity—especially under short windows. By integrating graph-spanning algorithms with nonparametric modeling that guarantees controllable error probabilities, the approach imposes no distributional assumptions and accommodates multivariate, heterogeneous data. Extensive experiments demonstrate superior performance over state-of-the-art methods in both Gaussian and non-Gaussian settings; notably, it maintains high detection power even with limited sample sizes, making it well-suited for real-time, accurate monitoring applications.

Online change detection (OCD) in linear systems under model uncertainty—particularly for streaming data—remains challenging, as existing methods often assume perfect model knowledge and suffer from poor scalability. Method: We propose RoS-Guard, a robust OCD algorithm that employs compact relaxation and optimization-based reconstruction to explicitly account for model uncertainty. It introduces a differentiable architecture via neural network unfolding and leverages GPU parallelization for efficient computation. Contribution/Results: RoS-Guard is the first method to theoretically guarantee both a prescribed expected false alarm rate and an upper bound on the worst-case average detection delay. Experiments demonstrate that, on large-scale systems, it achieves several-fold speedup over conventional OCD algorithms while maintaining high detection accuracy and strong robustness to model mismatch.