# Maximum Mean Discrepancy on Exponential Windows for Online Change Detection

arXiv: https://arxiv.org/abs/2205.12706 · HTML: https://mlsanity.com/paper/2205.12706/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 71 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 10 of 10)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [An Evaluation of Change Point Detection Algorithms](https://mlsanity.com/paper/2003.06222/) (2020)
- [Graph Kernels: State-of-the-Art and Future Challenges](https://mlsanity.com/paper/2011.03854/) (2020)
- [Characteristic and Universal Tensor Product Kernels](https://mlsanity.com/paper/1708.08157/) (2017)
- [Optimal Rates for Random Fourier Features](https://mlsanity.com/paper/1506.02155/) (2015)
- [NEWMA: a new method for scalable model-free online change-point detection](https://mlsanity.com/paper/1805.08061/) (2018)
- [WATCH: Wasserstein Change Point Detection for High-Dimensional Time Series Data](https://mlsanity.com/paper/2201.07125/) (2022)
- [Kernel Two-Sample Tests for Manifold Data](https://mlsanity.com/paper/2105.03425/) (2021)

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

- [Population-Aligned Persona Generation for LLM-based Social Simulation](https://mlsanity.com/paper/2509.10127/) (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)
- [Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology](https://mlsanity.com/paper/2605.22886/) (2026)
- [Cloud-Native Evaluation-as-a-Service: A Microservices Architecture for Scalable AI Monitoring with Conformal Guarantees](https://mlsanity.com/paper/2607.21623/) (2026)
- [Kernel-based External Validity of Experimental Studies](https://mlsanity.com/paper/2610.13625/) (2026)

## Abstract (arXiv)

Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of observations within the stream to each other via hypothesis testing. Maximum mean discrepancy (MMD), a (semi-)metric on the space of probability distributions, provides powerful non-parametric two-sample tests on kernel-enriched domains. In particular, MMD is able to detect any disparity between distributions under mild conditions. However, classical MMD estimators suffer from a quadratic runtime complexity, which renders their direct use for change detection in data streams impractical. In this article, we propose a new change detection algorithm, called Maximum Mean Discrepancy on Exponential Windows (MMDEW), that combines the benefits of MMD with an efficient computation based on exponential windows. We prove that MMDEW enjoys polylogarithmic runtime and logarithmic memory complexity and show empirically that it outperforms the state of the art on benchmark data streams.