Global Sequential Testing for Multi-Stream Auditing

• URL: http://arxiv.org/abs/2602.21479v1
• Date: Wed, 25 Feb 2026 01:10:45 GMT
• Title: Global Sequential Testing for Multi-Stream Auditing
• Authors: Beepul Bharti, Ambar Pal, Jeremias Sulam,
• Abstract summary: It is critical to continuously audit the performance of machine learning systems and detect any unusual behavior quickly.<n>This can be modeled as a sequential hypothesis testing problem with $k$ incoming streams of data and a global null hypothesis.<n>We construct new sequential tests by using ideas of merging test martingales with different trade-offs in expected stopping times under different, sparse or dense alternative hypotheses.
• Score: 13.390852646411929
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Across many risk-sensitive areas, it is critical to continuously audit the performance of machine learning systems and detect any unusual behavior quickly. This can be modeled as a sequential hypothesis testing problem with $k$ incoming streams of data and a global null hypothesis that asserts that the system is working as expected across all $k$ streams. The standard global test employs a Bonferroni correction and has an expected stopping time bound of $O\left(\ln\frac{k}α\right)$ when $k$ is large and the significance level of the test, $α$, is small. In this work, we construct new sequential tests by using ideas of merging test martingales with different trade-offs in expected stopping times under different, sparse or dense alternative hypotheses. We further derive a new, balanced test that achieves an improved expected stopping time bound that matches Bonferroni's in the sparse setting but that naturally results in $O\left(\frac{1}{k}\ln\frac{1}α\right)$ under a dense alternative. We empirically demonstrate the effectiveness of our proposed tests on synthetic and real-world data.

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