# Window-Limited CUSUM for Sequential Change Detection

arXiv: https://arxiv.org/abs/2206.06777 · HTML: https://mlsanity.com/paper/2206.06777/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2022.

## Built on by (most cited first, 6 of 6)

- [A Log-Linear Non-Parametric Online Changepoint Detection Algorithm based on Functional Pruning](https://mlsanity.com/paper/2302.02718/) (2023)
- [Neural network-based CUSUM for online change-point detection](https://mlsanity.com/paper/2210.17312/) (2022)
- [Sequential Change Point Detection via Denoising Score Matching](https://mlsanity.com/paper/2501.12667/) (2025)
- [Modeling Discrete Coating Degradation Events via Hawkes Processes](https://mlsanity.com/paper/2504.09706/) (2025)
- [The Cost of Learning Under Multiple Change Points](https://mlsanity.com/paper/2602.11406/) (2026)
- [Quickest Change-point Detection in Generalized Linear Models with Variational Estimation](https://mlsanity.com/paper/2610.16616/) (2026)

## Abstract (arXiv)

We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We propose a joint detection/estimation scheme, which we call Window-Limited CUSUM, that combines the cumulative sum (CUSUM) test with a sliding window-based consistent estimate of the post-change parameters. We characterize the optimal choice of the window size and show that the Window-Limited CUSUM enjoys first-order asymptotic optimality as average run length approaches infinity under the optimal choice of window length. Compared to existing schemes with similar asymptotic optimality properties, our test can be much faster computed because it can recursively update the CUSUM statistic by employing the estimate of the post-change parameters. A parallel variant is also proposed that facilitates the practical implementation of the test. Numerical simulations corroborate our theoretical findings.