# E-detectors: a nonparametric framework for sequential change detection

arXiv: https://arxiv.org/abs/2203.03532 · HTML: https://mlsanity.com/paper/2203.03532/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 56 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 14 of 14)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Safe Testing](https://mlsanity.com/paper/1906.07801/) (2019)
- [Admissible anytime-valid sequential inference must rely on nonnegative martingales](https://mlsanity.com/paper/2009.03167/) (2020)
- [Universal Inference](https://mlsanity.com/paper/1912.11436/) (2019)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Testing randomness](https://mlsanity.com/paper/1906.09256/) (2019)
- [Testing exchangeability: fork-convexity, supermartingales, and e-processes](https://mlsanity.com/paper/2102.00630/) (2021)
- [Scan B-Statistic for Kernel Change-Point Detection](https://mlsanity.com/paper/1507.01279/) (2015)
- [High-dimensional, multiscale online changepoint detection](https://mlsanity.com/paper/2003.03668/) (2020)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [Catoni-style confidence sequences for heavy-tailed mean estimation](https://mlsanity.com/paper/2202.01250/) (2022)
- [Nonparametric iterated-logarithm extensions of the sequential generalized likelihood ratio test](https://mlsanity.com/paper/2010.08082/) (2020)
- [Quickest Detection of Dynamic Events in Networks](https://mlsanity.com/paper/1807.06143/) (2018)

## Built on by (most cited first, 30 of 32)

- [Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach](https://mlsanity.com/paper/2408.07511/) (2024)
- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [Prediction-Powered E-Values](https://mlsanity.com/paper/2502.04294/) (2025)
- [WATCH: Adaptive Monitoring for AI Deployments via Weighted-Conformal Martingales](https://mlsanity.com/paper/2505.04608/) (2025)
- [Adaptive Learn-then-Test: Statistically Valid and Efficient Hyperparameter Selection](https://mlsanity.com/paper/2409.15844/) (2024)
- [On Continuous Monitoring of Risk Violations under Unknown Shift](https://mlsanity.com/paper/2506.16416/) (2025)
- [Who Drifted: the System or the Judge? Anytime-Valid Attribution in LLM Evaluation Pipelines](https://mlsanity.com/paper/2606.15474/) (2026)
- [Post-detection inference for sequential changepoint localization](https://mlsanity.com/paper/2502.06096/) (2025)
- [Theoretical guarantees for change localization using conformal p-values](https://mlsanity.com/paper/2510.08749/) (2025)
- [Auditing Pay-Per-Token in Large Language Models](https://mlsanity.com/paper/2510.05181/) (2025)
- [Asymptotically optimal sequential change detection for bounded means](https://mlsanity.com/paper/2602.05272/) (2026)
- [Testing For Distribution Shifts with Conditional Conformal Test Martingales](https://mlsanity.com/paper/2602.13848/) (2026)
- [Prediction-Powered Risk Monitoring of Deployed Models for Detecting Harmful Distribution Shifts](https://mlsanity.com/paper/2602.02229/) (2026)
- [Adaptive auditing of AI systems with anytime-valid guarantees](https://mlsanity.com/paper/2605.07002/) (2026)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)
- [CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning](https://mlsanity.com/paper/2607.20129/) (2026)
- [A complete characterization of sequential testability and change detectability in i.i.d. models](https://mlsanity.com/paper/2609.05752/) (2026)
- [When Is Enough Enough in Self-Evolving LLM Systems?](https://mlsanity.com/paper/2610.04756/) (2026)
- [Deceptive Risk Minimization: Out-of-Distribution Generalization by Deceiving Distribution Shift Detectors](https://mlsanity.com/paper/2509.12081/) (2025)
- [Detecting Object Tracking Failure via Sequential Hypothesis Testing](https://mlsanity.com/paper/2602.12983/) (2026)
- [When Your Model Stops Working: Anytime-Valid Calibration Monitoring](https://mlsanity.com/paper/2603.13156/) (2026)
- [Optimal sequential tests yield log-optimal e-processes](https://mlsanity.com/paper/2605.12720/) (2026)
- [Online Safety Monitoring for LLMs](https://mlsanity.com/paper/2607.02510/) (2026)
- [Calibrated e-CUSUM Decoding for Quantized Reasoning Models: Why Token Log-Probability Is the Wrong Observable for Decoding Monitors](https://mlsanity.com/paper/2607.11317/) (2026)
- [When the Martingale Never Stops Firing: Anytime-Valid Gating on Real Forecast Streams](https://mlsanity.com/paper/2608.30502/) (2026)
- [Distribution-free inference on the number of changepoints](https://mlsanity.com/paper/2609.08234/) (2026)
- [When May a Bandit Leave Its Anchor? E-Process-Authorized Thompson Sampling under Non-stationarity](https://mlsanity.com/paper/2610.03646/) (2026)
- [The Premise Is the Problem: Exchangeability Failure in Self-Monitored Test-Time Adaptation](https://mlsanity.com/paper/2610.07038/) (2026)

## Abstract (arXiv)

Sequential change detection is a classical problem with a variety of applications. However, the majority of prior work has been parametric, for example, focusing on exponential families. We develop a fundamentally new and general framework for sequential change detection when the pre- and post-change distributions are nonparametrically specified (and thus composite). Our procedures come with clean, nonasymptotic bounds on the average run length (frequency of false alarms). In certain nonparametric cases (like sub-Gaussian or sub-exponential), we also provide near-optimal bounds on the detection delay following a changepoint. The primary technical tool that we introduce is called an e-detector, which is composed of sums of e-processes -- a fundamental generalization of nonnegative supermartingales -- that are started at consecutive times. We first introduce simple Shiryaev-Roberts and CUSUM-style e-detectors, and then show how to design their mixtures in order to achieve both statistical and computational efficiency. Our e-detector framework can be instantiated to recover classical likelihood-based procedures for parametric problems, as well as yielding the first change detection method for many nonparametric problems. As a running example, we tackle the problem of detecting changes in the mean of a bounded random variable without i.i.d. assumptions, with an application to tracking the performance of a basketball team over multiple seasons.