多流非平稳过程中的鲁棒最快变化检测
Robust Quickest Change Detection in Multi-Stream Non-Stationary Processes
AI总结：
针对多流非平稳过程中变化前后分布时变且未知的问题，提出基于各流最不利分布律的鲁棒最快变化检测算法，并通过公共卫生、航空场景的模拟与真实数据验证其最优性和有效性。
摘要：
本文研究多流设置下非平稳过程中的鲁棒最快变化检测（QCD）问题。在经典QCD理论中，最优方案被用于检测平稳数据分布中的突发变化，且多数研究集中于单流数据。在非平稳过程中，变化前后的数据分布均随时间变化且无法精确获知，多维数据进一步使这些问题复杂化。研究表明，如果每个维度或数据流的非平稳分布族在明确定义的意义上具有最不利分布律（LFL）或分布，则利用这些LFL设计的算法具有鲁棒最优性。由于变化后模型依赖于变化点，本文定义的LFL概念不同于经典定义。文中给出了公共卫生监测和航空应用中遇到的多流非平稳过程示例，并将所提出的鲁棒算法应用于模拟数据和真实数据，以验证其有效性。
英文摘要：
The problem of robust quickest change detection (QCD) in non-stationary processes under a multi-stream setting is studied. In classical QCD theory, optimal solutions are developed to detect a sudden change in the distribution of stationary data. Most studies have focused on single-stream data. In non-stationary processes, the data distribution both before and after change varies with time and is not precisely known. The multi-dimension data even complicates such issues. It is shown that if the non-stationary family for each dimension or stream has a least favorable law (LFL) or distribution in a well-defined sense, then the algorithm designed using the LFLs is robust optimal. The notion of LFL defined in this work differs from the classical definitions due to the dependence of the post-change model on the change point. Examples of multi-stream non-stationary processes encountered in public health monitoring and aviation applications are provided. Our robust algorithm is applied to simulated and real data to show its effectiveness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
