Determining the presence of an anomaly or whether a system is safe or not is a problem with wide applicability. The model adopted for this problem is that of verifying whether a multi-component system has anomalies or not. Components can be probed over time individually or as groups in a data-driven manner. The collected observations are noisy and contain information on whether the selected group contains an anomaly or not. The aim is to minimize the probability of incorrectly declaring the system to be free of anomalies while ensuring that the probability of correctly declaring it to be safe is sufficiently large. This problem is modeled as an active hypothesis testing problem in the Neyman-Pearson setting. Asymptotically optimal rates and strategies are characterized. The general strategies are data driven and outperform previously proposed asymptotically optimal methods in the finite sample regime. Furthermore, novel component-selection are designed and analyzed in the non-asymptotic regime. For a specific class of problems admitting a key form of symmetry, strong non-asymptotic converse and achievability bounds are provided which are tighter than previously proposed bounds.

中文翻译：

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固定范围主动假设检验和异常检测

确定异常的存在或系统是否安全是一个具有广泛适用性的问题。该问题采用的模型是验证多分量系统是否存在异常。组件可以随着时间的推移单独或以数据驱动的方式作为组进行探测。收集到的观察结果是嘈杂的，并且包含有关所选组是否包含异常的信息。目的是最小化错误地宣布系统没有异常的可能性，同时确保正确地宣布系统安全的可能性足够大。这个问题在 Neyman-Pearson 设置中被建模为一个主动假设检验问题。描述了渐近最优速率和策略。一般策略是数据驱动的，并且在有限样本方案中优于先前提出的渐近最优方法。此外，在非渐近状态下设计和分析了新的组件选择。对于承认关键对称形式的特定类别的问题，提供了比先前提出的边界更严格的强非渐近逆和可实现边界。