NSF-BSF:CIF:Small: Searching for the Rare: an Active Inference and Learning Approach

这个项目解决了在大量的可能性中寻找少数感兴趣的稀有事件的问题。罕见的事件可能代表着具有异常回报的机会，也可能是与高成本或潜在灾难性后果相关的异常。这一问题出现在广泛的应用中，从通信和基础设施系统、网络安全到社会经济网络，在网络规模和数据日益丰富的时代尤为重要。该项目的多学科性质也为本科生和研究生提供了丰富的研究经验。科学目标是开发通用设计方法，在假设总数较多、观测噪声较大、对罕见事件的先验知识可能只有“它们与名义上的不同”的情况下，快速可靠地检测到罕见事件。该项目由三个步骤组成，这三个步骤代表了范围和难度的逻辑递进：(1)通过主动假设检验实现关于检测准确性的最佳样本复杂性；(2)通过利用固有的分层结构实现关于搜索空间维度的最佳样本复杂性；(3)通过将在线学习与主动推理相结合来处理未知模型。在有原则的理论框架内的整体治疗从积极假设检验以及统计和机器学习的基本理论中获得灵感并做出贡献。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project addresses the problem of searching for a few rare events of interest among a massive number of possibilities. The rare events may represent opportunities with exceptional returns or anomalies associated with high costs or potential catastrophic consequences. This problem arises in a broad range of applications, ranging from communications and infrastructure systems, cyber-security, to social-economic networks, and is particularly relevant in the era of increasing network size and abundance of data. The multidisciplinary nature of this project also provides a rich research experience for both undergraduate and graduate students.The scientific objective is to develop general design methodologies for detecting rare events quickly and reliably when the total number of hypotheses is large, the observations are noisy, and the prior knowledge on the rare events may be as little as "they are different from the nominal." The project consists of three steps that represent a logical progression in scope and level of difficulty: (i) achieving optimal sample complexity with respect to detection accuracy through active hypothesis testing; (ii) achieving optimal sample complexity with respect to the dimension of the search space by exploiting inherent hierarchical structures; (iii) tackling unknown models by integrating online learning with active inference. The holistic treatment within a principled theoretic framework draws inspirations from and contributes to fundamental theories of active hypothesis testing and statistical and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.