提出更高效的多流审计方法，显著缩短检测时间。
Global Sequential Testing for Multi-Stream Auditing
- 用平均与乘积规则合并鞅序列，提升检测效率。
- 稀疏情形下停时为 $O(\ln \frac{k}{α})$，稠密情形下降至 $O(\frac{1}{k}\ln \frac{1}{α})$。
- 适合高维、多源数据的实时系统风险监测。
在众多高风险领域，持续审计机器学习系统至关重要，需随新数据流入快速判断其是否按设计运行。该任务可建模为具有 $k$ 个数据流的全局序贯假设检验问题，其中全局零假设表示系统在所有 $k$ 个流上均正常运行。在备择假设下，标准的全局序贯检验采用 Bonferroni 校正，其期望停时为 $O(\ln \frac{k}{α})$（当 $k$ 较大且显著性水平为 $α$ 时）。本文证明，通过基于平均与乘积规则合并鞅序列的高效序贯检验方法，可实现更短的停时，从而增强对零假设的检验力。理论分析表明，在稀疏替代情形（仅少数非零流）下，均衡测试可保持 $O(\ln \frac{k}{α})$ 的误差率；而在稠密替代情形（多数非零流）下，停时可优化至 $O(\frac{1}{k}\ln \frac{1}{α})$。实验在合成数据与真实世界数据上验证了理论结果。
原文摘要 · Abstract (English)
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 $O\left(\ln \frac{k}α\right)$ 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 $O\left(\ln \frac{k}α\right)$ in the sparse regime (just a few non-null streams) while achieving $O\left(\frac{1}{k}\ln \frac{1}α\right)$ under dense alternatives (many non-null steams). We validate our theory through experiments on both synthetic and real-world data.
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