Paper
Global Sequential Testing for Multi-Stream Auditing
Authors
Beepul Bharti, Ambar Pal, Jeremias Sulam
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.21479v1</id>\n <title>Global Sequential Testing for Multi-Stream Auditing</title>\n <updated>2026-02-25T01:10:45Z</updated>\n <link href='https://arxiv.org/abs/2602.21479v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.21479v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ML'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <published>2026-02-25T01:10:45Z</published>\n <arxiv:primary_category term='stat.ML'/>\n <author>\n <name>Beepul Bharti</name>\n </author>\n <author>\n <name>Ambar Pal</name>\n </author>\n <author>\n <name>Jeremias Sulam</name>\n </author>\n </entry>"
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