# Scan B-Statistic for Kernel Change-Point Detection

arXiv: https://arxiv.org/abs/1507.01279 · HTML: https://mlsanity.com/paper/1507.01279/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2015.

## Built on by (most cited first, 29 of 29)

- [E-detectors: a nonparametric framework for sequential change detection](https://mlsanity.com/paper/2203.03532/) (2022)
- [Kernel Robust Hypothesis Testing](https://mlsanity.com/paper/2203.12777/) (2022)
- [Nonparametric and Online Change Detection in Multivariate Datastreams using QuantTree](https://mlsanity.com/paper/2208.14801/) (2022)
- [Quickest Change Detection for Unnormalized Statistical Models](https://mlsanity.com/paper/2302.00250/) (2023)
- [Memory-free Online Change-point Detection: A Novel Neural Network Approach](https://mlsanity.com/paper/2207.03932/) (2022)
- [Post-detection inference for sequential changepoint localization](https://mlsanity.com/paper/2502.06096/) (2025)
- [InDiD: Instant Disorder Detection via Representation Learning](https://mlsanity.com/paper/2106.02602/) (2021)
- [Detecting Change Intervals with Isolation Distributional Kernel](https://mlsanity.com/paper/2212.14630/) (2022)
- [Selective Inference for Changepoint detection by Recurrent Neural Network](https://mlsanity.com/paper/2311.14964/) (2023)
- [Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel](https://mlsanity.com/paper/2201.11722/) (2022)
- [Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition](https://mlsanity.com/paper/2310.02941/) (2023)
- [Sequential Change Point Detection via Denoising Score Matching](https://mlsanity.com/paper/2501.12667/) (2025)
- [Change Point Detection in the Frequency Domain with Statistical Reliability](https://mlsanity.com/paper/2502.03062/) (2025)
- [Optimal Online Change Detection via Random Fourier Features](https://mlsanity.com/paper/2505.17789/) (2025)
- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data](https://mlsanity.com/paper/2106.11541/) (2021)
- [PERCEPT: a new online change-point detection method using topological data analysis](https://mlsanity.com/paper/2203.04246/) (2022)
- [Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees](https://mlsanity.com/paper/2311.18769/) (2023)
- [Cadence: A Practical Time-series Partitioning Algorithm for Unlabeled IoT Sensor Streams](https://mlsanity.com/paper/2112.03360/) (2021)
- [Noise-contrastive Online Change Point Detection](https://mlsanity.com/paper/2206.10143/) (2022)
- [Class Distribution Monitoring for Concept Drift Detection](https://mlsanity.com/paper/2210.08470/) (2022)
- [Dynamic Interpretable Change Point Detection](https://mlsanity.com/paper/2211.03991/) (2022)
- [An Evaluation of Real-time Adaptive Sampling Change Point Detection Algorithm using KCUSUM](https://mlsanity.com/paper/2402.10291/) (2024)
- [RIO-CPD: A Riemannian Geometric Method for Correlation-aware Online Change Point Detection](https://mlsanity.com/paper/2407.09698/) (2024)
- [Score-based change point detection via tracking the best of infinitely many experts](https://mlsanity.com/paper/2408.14073/) (2024)
- [Real-time Fuel Leakage Detection via Online Change Point Detection](https://mlsanity.com/paper/2410.09741/) (2024)
- [WWAggr: A Window Wasserstein-based Aggregation for Ensemble Change Point Detection](https://mlsanity.com/paper/2506.08066/) (2025)
- [Detecting Fluent Optimization-Based Adversarial Prompts via Sequential Entropy Changes](https://mlsanity.com/paper/2605.19966/) (2026)
- [Kernel-based External Validity of Experimental Studies](https://mlsanity.com/paper/2610.13625/) (2026)

## Abstract (arXiv)

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task which enjoy fewer assumptions on the distributions than the parametric approach and can handle high-dimensional data. In this paper we focus on the scenario when the amount of background data is large, and propose two related computationally efficient kernel-based statistics for change-point detection, which are inspired by the recently developed B-statistics. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using the change-of-measure technique, which focuses on characterizing the tail of the detection statistics rather than obtaining its asymptotic distribution under the null distribution. Such approximations are crucial to control the false alarm rate, which corresponds to the significance level in offline change-point detection and the average-run-length in online change-point detection. Our approximations are shown to be highly accurate. Thus, they provide a convenient way to find detection thresholds for both offline and online cases without the need to resort to the more expensive simulations or bootstrapping. We show that our methods perform well on both synthetic data and real data.