# Global Sequential Testing for Multi-Stream Auditing

arXiv: https://arxiv.org/abs/2602.21479 · HTML: https://mlsanity.com/paper/2602.21479/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 47 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 24 of 24)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Black-Box Reductions for Parameter-free Online Learning in Banach Spaces](https://mlsanity.com/paper/1802.06293/) (2018)
- [Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals](https://mlsanity.com/paper/1811.11419/) (2018)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [The age of secrecy and unfairness in recidivism prediction](https://mlsanity.com/paper/1811.00731/) (2018)
- [There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"](https://mlsanity.com/paper/2102.05569/) (2021)
- [Tight Concentrations and Confidence Sequences from the Regret of Universal Portfolio](https://mlsanity.com/paper/2110.14099/) (2021)
- [Nonparametric Two-Sample Testing by Betting](https://mlsanity.com/paper/2112.09162/) (2021)
- [Auditing Fairness by Betting](https://mlsanity.com/paper/2305.17570/) (2023)
- [Algorithmic Auditing and Social Justice: Lessons from the History of Audit Studies](https://mlsanity.com/paper/2109.06974/) (2021)
- [Online Rules for Control of False Discovery Rate and False Discovery Exceedance](https://mlsanity.com/paper/1603.09000/) (2016)
- [From Transparency to Accountability and Back: A Discussion of Access and Evidence in AI Auditing](https://mlsanity.com/paper/2410.04772/) (2024)
- [Online multiple testing with e-values](https://mlsanity.com/paper/2311.06412/) (2023)
- [Instance-Log-Optimality of Portfolio-Based E-Processes and their Sequential Hypothesis Tests](https://mlsanity.com/paper/2504.02818/) (2025)
- [Who Followed the Blueprint? Analyzing the Responses of U.S. Federal Agencies to the Blueprint for an AI Bill of Rights](https://mlsanity.com/paper/2404.19076/) (2024)
- [Online Detection of LLM-Generated Texts via Sequential Hypothesis Testing by Betting](https://mlsanity.com/paper/2410.22318/) (2024)
- [Asynchronous Online Testing of Multiple Hypotheses](https://mlsanity.com/paper/1812.05068/) (2018)
- [Peeking with PEAK: Sequential, Nonparametric Composite Hypothesis Tests for Means of Multiple Data Streams](https://mlsanity.com/paper/2402.06122/) (2024)
- [An Auditing Test To Detect Behavioral Shift in Language Models](https://mlsanity.com/paper/2410.19406/) (2024)
- [On Confidence Sequences for Bounded Random Processes via Universal Gambling Strategies](https://mlsanity.com/paper/2207.12382/) (2022)
- [From Individual Experience to Collective Evidence: A Reporting-Based Framework for Identifying Systemic Harms](https://mlsanity.com/paper/2502.08166/) (2025)

## Built on by (most cited first, 1 of 1)

- [Always-On Experimentation](https://mlsanity.com/paper/2609.38695/) (2026)

## Abstract (arXiv)

Across many risk-sensitive areas, it is critical to continuously audit machine learning systems as we receive more data to quickly determine if they are performing as designed. This auditing task can be modeled as a sequential hypothesis testing problem with k data streams and a global null hypothesis that asserts the system operates as intended across all k streams. Under the alternative, the standard global sequential test, which uses a Bonferroni correction, has an expected stopping time of Oleft(ln frackαright) for large k and significance level α. In this work, we demonstrate that efficient sequential tests, relying on merging martingales via averaging and products rules, provide improved stopping times, and thus more powerful tests against the null. Using these results, we show that a balanced test can match the Bonferroni rate of Oleft(ln frackαright) in the sparse regime (just a few non-null streams) while achieving Oleft(frac1kln frac1αright) under dense alternatives (many non-null steams). We validate our theory through experiments on both synthetic and real-world data.