Robust Sequential Analysis in Networks

网络中的稳健序列分析

• 批准号: 431431951
• 负责人: Professor Dr.-Ing. Abdelhak Zoubir
• 金额: --
• 依托单位: Department of Electrical and Computer Engineering
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/431431951?language=en
• 关键词: Robust; Sequential; Analysis; Networks

Sequential Analysis is concerned with statistical inference when the number of samples is not given a priori, but chosen based on the data observed so far. Sequential detectors have been shown to significantly reduce the average number of samples compared to equivalent fixed-sample-size detectors. They find application in many fields where a high efficiency is required, in particular in situations where either taking samples is expensive or detection delay is critical. In contrast, the idea underpinning robust statistics is to sacrifice some efficiency under ideal conditions in order to be less sensitive to deviations from the ideal case. That is, robust procedures are designed to perform well in a neighborhood of the assumed model, typically allowing for small, but arbitrary deviations. In our previous work, in particular the DFG project "Robust Sequential Analysis", we investigated the benefits of combining sequential and robust statistics in order to make fast yet statistically reliable decisions. With the Roseanne project, we plan to extend this line of research to distributed systems and networks. The latter are highly relevant for future communication and signal processing systems, in particular in the context of Smart Cities and the Internet of Things. Yet, very few results on robust sequential detection in networks can be found in the literature. Most importantly:1) There is no distributed equivalent to uncertainty models such as outliers or neighborhoods of probability distributions.2) Little is known about the relation between node-wise uncertainty and network-wide uncertainty.3) Techniques from robust centralized detection, such as clipping or censoring, do not reliably robustify distributed detection.4) There are no results on the amount of uncertainty a distributed detector can tolerate without breaking down.As a consequence, in the majority of existing works, robustness is defined in a purely qualitative manner and the results either only apply to small networks or are based on empirically motivated, application specific heuristics. The first aim of this project is to narrow this gap in understanding by providing a solid foundation for a theory of robust sequential detection in networks. Based on this foundation, the second aim is to develop and implement sequential distributed detection algorithms that are robust in a well-defined and quantifiable manner. A successful completion of the project would pave the way for a general and rigorous framework of robust distributed statistics, comparable to the existing body of work on centralized robust detection.The Signal Processing Group is internationally recognized for its work on robust statistics as well as sequential and distributed signal processing. Therefore, we see ourselves in a uniquely favorable position for a successful completion of the proposed project, which brings together these core areas of expertise.

序贯分析涉及的是当样本数量不是先验给定的，而是根据迄今为止观察到的数据选择时的统计推断。顺序检测器已被证明显着减少平均样本数相比，等效的固定样本大小的检测器。它们在需要高效率的许多领域中找到应用，特别是在采样昂贵或检测延迟至关重要的情况下。相反，稳健统计学的基本思想是在理想条件下牺牲一些效率，以便对理想情况的偏差不那么敏感。也就是说，鲁棒的程序被设计为在假设模型的邻域中表现良好，通常允许小的但任意的偏差。在我们以前的工作中，特别是DFG项目“稳健的序贯分析”，我们研究了序贯和稳健统计相结合的好处，以便做出快速而可靠的决策。通过Roseanne项目，我们计划将这一研究领域扩展到分布式系统和网络。后者与未来的通信和信号处理系统高度相关，特别是在智能城市和物联网的背景下。然而，在文献中可以找到的网络中的鲁棒顺序检测的结果很少。最重要的是：1）没有分布等价的不确定性模型，如离群值或概率分布的邻域。2）关于节点的不确定性和网络范围的不确定性之间的关系知之甚少。3）来自鲁棒集中式检测的技术，如裁剪或删失，不可靠地鲁棒分布式检测。4）分布式检测器可以容忍的不确定性的量没有结果而不会崩溃。因此，在大多数现有的作品中，鲁棒性是以纯粹的定性方式定义的，结果要么只适用于小型网络，要么基于经验激励，应用特定的算法。这个项目的第一个目标是缩小这一差距的理解提供了一个坚实的基础，在网络中的鲁棒顺序检测的理论。在此基础上，第二个目标是开发和实现顺序分布式检测算法，这些算法以明确定义和可量化的方式具有鲁棒性。该项目的成功完成将为健全的分布式统计的一般和严格的框架铺平道路，与现有的集中式健全检测工作机构相媲美，信号处理小组在健全的统计以及顺序和分布式信号处理方面的工作得到国际认可。因此，我们认为自己处于成功完成拟议项目的独特有利地位，该项目汇集了这些核心专业领域。