# Fast Online Changepoint Detection via Functional Pruning CUSUM statistics

arXiv: https://arxiv.org/abs/2110.08205 · HTML: https://mlsanity.com/paper/2110.08205/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [High-dimensional, multiscale online changepoint detection](https://mlsanity.com/paper/2003.03668/) (2020)
- [Continuous online sequence learning with an unsupervised neural network model](https://mlsanity.com/paper/1512.05463/) (2015)
- [On Optimal Multiple Changepoint Algorithms for Large Data](https://mlsanity.com/paper/1409.1842/) (2014)
- [Changepoint Detection in the Presence of Outliers](https://mlsanity.com/paper/1609.07363/) (2016)
- [Fast Nonconvex Deconvolution of Calcium Imaging Data](https://mlsanity.com/paper/1802.07380/) (2018)
- [Detecting Abrupt Changes in the Presence of Local Fluctuations and Autocorrelated Noise](https://mlsanity.com/paper/2005.01379/) (2020)
- [Asynchronous Multi-Sensor Change-Point Detection for Seismic Tremors](https://mlsanity.com/paper/1901.08196/) (2019)
- [A computationally efficient, high-dimensional multiple changepoint procedure with application to global terrorism incidence](https://mlsanity.com/paper/2011.03599/) (2020)
- [Is a Finite Intersection of Balls Covered by a Finite Union of Balls in Euclidean Spaces ?](https://mlsanity.com/paper/1804.06699/) (2018)
- [Subset Multivariate Collective And Point Anomaly Detection](https://mlsanity.com/paper/1909.01691/) (2019)
- [A new approach for open-end sequential change point monitoring](https://mlsanity.com/paper/1906.03225/) (2019)

## Built on by (most cited first, 10 of 10)

- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Keeping Medical AI Healthy and Trustworthy: A Review of Detection and Correction Methods for System Degradation](https://mlsanity.com/paper/2506.17442/) (2025)
- [A Constant-per-Iteration Likelihood Ratio Test for Online Changepoint Detection for Exponential Family Models](https://mlsanity.com/paper/2302.04743/) (2023)
- [Optimal Online Change Detection via Random Fourier Features](https://mlsanity.com/paper/2505.17789/) (2025)
- [Monitoring Machine Learning Forecasts for Platform Data Streams](https://mlsanity.com/paper/2401.09144/) (2024)
- [RIO-CPD: A Riemannian Geometric Method for Correlation-aware Online Change Point Detection](https://mlsanity.com/paper/2407.09698/) (2024)
- [Predictive maintenance solution for industrial systems -- an unsupervised approach based on log periodic power law](https://mlsanity.com/paper/2408.05231/) (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)
- [An Efficient Likelihood Ratio Test for Online Changepoint Detection in the Presence of Autocorrelation](https://mlsanity.com/paper/2607.16106/) (2026)
- [High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretability](https://mlsanity.com/paper/2609.24278/) (2026)

## Abstract (arXiv)

Many modern applications of online changepoint detection require the ability to process high-frequency observations, sometimes with limited available computational resources. Online algorithms for detecting a change in mean often involve using a moving window, or specifying the expected size of change. Such choices affect which changes the algorithms have most power to detect. We introduce an algorithm, Functional Online CuSUM (FOCuS), which is equivalent to running these earlier methods simultaneously for all sizes of window, or all possible values for the size of change. Our theoretical results give tight bounds on the expected computational cost per iteration of FOCuS, with this being logarithmic in the number of observations. We show how FOCuS can be applied to a number of different change in mean scenarios, and demonstrate its practical utility through its state-of-the art performance at detecting anomalous behaviour in computer server data.