# Change Detection with the Kernel Cumulative Sum Algorithm

arXiv: https://arxiv.org/abs/1903.01661 · HTML: https://mlsanity.com/paper/1903.01661/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 12 of 12)

- [Kernel Two-Sample Tests for Manifold Data](https://mlsanity.com/paper/2105.03425/) (2021)
- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Sequential Multivariate Change Detection with Calibrated and Memoryless False Detection Rates](https://mlsanity.com/paper/2108.00883/) (2021)
- [Change Detection of Markov Kernels with Unknown Pre and Post Change Kernel](https://mlsanity.com/paper/2201.11722/) (2022)
- [Sequential change detection via backward confidence sequences](https://mlsanity.com/paper/2302.02544/) (2023)
- [Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition](https://mlsanity.com/paper/2310.02941/) (2023)
- [Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guarantees](https://mlsanity.com/paper/2311.18769/) (2023)
- [Optimal Sub-sampling to Boost Power of Kernel Sequential Change-point Detection](https://mlsanity.com/paper/2210.15060/) (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)
- [Sustaining model performance for covid-19 detection from dynamic audio data: Development and evaluation of a comprehensive drift-adaptive framework](https://mlsanity.com/paper/2409.19300/) (2024)

## Abstract (arXiv)

Online change detection involves monitoring a stream of data for changes in the statistical properties of incoming observations. A good change detector will detect any changes shortly after they occur, while raising few false alarms. Although there are algorithms with confirmed optimality properties for this task, they rely on the exact specifications of the relevant probability distributions and this limits their practicality. In this work we describe a kernel-based variant of the Cumulative Sum (CUSUM) change detection algorithm that can detect changes under less restrictive assumptions. Instead of using the likelihood ratio, which is a parametric quantity, the Kernel CUSUM (KCUSUM) algorithm compares incoming data with samples from a reference distribution using a statistic based on the Maximum Mean Discrepancy (MMD) non-parametric testing framework. The KCUSUM algorithm is applicable in settings where there is a large amount of background data available and it is desirable to detect a change away from this background setting. Exploiting the random-walk structure of the test statistic, we derive bounds on the performance of the algorithm, including the expected delay and the average time to false alarm.