# Online Kernel CUSUM for Change-Point Detection

arXiv: https://arxiv.org/abs/2211.15070 · HTML: https://mlsanity.com/paper/2211.15070/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 80 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [Kernel Thinning](https://mlsanity.com/paper/2105.05842/) (2021)
- [Kernel Change-point Detection with Auxiliary Deep Generative Models](https://mlsanity.com/paper/1901.06077/) (2019)
- [Generalized Kernel Thinning](https://mlsanity.com/paper/2110.01593/) (2021)
- [A new graph-based two-sample test for multivariate and object data](https://mlsanity.com/paper/1307.6294/) (2013)
- [On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives](https://mlsanity.com/paper/1909.03302/) (2019)
- [Change Detection with the Kernel Cumulative Sum Algorithm](https://mlsanity.com/paper/1903.01661/) (2019)
- [Sequential change-point detection based on nearest neighbors](https://mlsanity.com/paper/1604.03611/) (2016)
- [Localizing Changes in High-Dimensional Regression Models](https://mlsanity.com/paper/2010.10410/) (2020)
- [Online change-point detection with kernels](https://mlsanity.com/paper/2002.02704/) (2020)
- [Inferring serial correlation with dynamic backgrounds](https://mlsanity.com/paper/2101.10962/) (2021)
- [Sequential Multivariate Change Detection with Calibrated and Memoryless False Detection Rates](https://mlsanity.com/paper/2108.00883/) (2021)
- [Nonparametric Detection of Anomalous Data Streams](https://mlsanity.com/paper/1405.2294/) (2014)
- [Asymptotically Optimal One- and Two-Sample Testing with Kernels](https://mlsanity.com/paper/1908.10037/) (2019)
- [Localizing Changes in High-Dimensional Vector Autoregressive Processes](https://mlsanity.com/paper/1909.06359/) (2019)

## Built on by (most cited first, 7 of 7)

- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Sequential change detection via backward confidence sequences](https://mlsanity.com/paper/2302.02544/) (2023)
- [Optimal Online Change Detection via Random Fourier Features](https://mlsanity.com/paper/2505.17789/) (2025)
- [Change detection with conformal martingales: new optimal constructions, and suboptimality of existing methods](https://mlsanity.com/paper/2609.27179/) (2026)
- [RIO-CPD: A Riemannian Geometric Method for Correlation-aware Online Change Point Detection](https://mlsanity.com/paper/2407.09698/) (2024)
- [Change Detection in Multivariate data streams: Online Analysis with Kernel-QuantTree](https://mlsanity.com/paper/2410.13778/) (2024)
- [ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency](https://mlsanity.com/paper/2608.08424/) (2026)

## Abstract (arXiv)

We present a computationally efficient online kernel Cumulative Sum (CUSUM) method for change-point detection that utilizes the maximum over a set of kernel statistics to account for the unknown change-point location. Our approach exhibits increased sensitivity to small changes compared to existing kernel-based change-point detection methods, including Scan-B statistic, corresponding to a non-parametric Shewhart chart-type procedure. We provide accurate analytic approximations for two key performance metrics: the Average Run Length (ARL) and Expected Detection Delay (EDD), which enable us to establish an optimal window length to be on the order of the logarithm of ARL to ensure minimal power loss relative to an oracle procedure with infinite memory. Moreover, we introduce a recursive calculation procedure for detection statistics to ensure constant computational and memory complexity, which is essential for online implementation. Through extensive experiments on both simulated and real data, we demonstrate the competitive performance of our method and validate our theoretical results.