Robust Sequential Analysis in Networks

序列分析关注的是统计推断，当样本数量不是先验的，而是根据迄今为止观察到的数据选择的时候。与等效的固定样本大小的检测器相比，顺序检测器已被证明可以显着减少平均样本数量。它们在需要高效率的许多领域都有应用，特别是在采样昂贵或检测延迟至关重要的情况下。相反，支撑健壮统计的思想是在理想条件下牺牲一些效率，以便对与理想情况的偏差不那么敏感。也就是说，健壮的程序被设计成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。在我们之前的工作中，特别是在DFG项目“稳健的序列分析”中，我们研究了将序列统计和稳健统计相结合的好处，以便做出快速而统计可靠的决策。在Roseanne项目中，我们计划将这条研究线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，特别是在智慧城市和物联网的背景下。然而，文献中很少有关于网络鲁棒序列检测的结果。最重要的是：1)不确定性模型没有分布的等价物，如概率分布的离群值或邻域。2)对节点不确定性和网络不确定性之间的关系知之甚少。3)鲁棒集中式检测技术，如剪切或审查，不能可靠地鲁棒分布式检测。4)没有关于分布式检测器在不崩溃的情况下可以容忍的不确定性量的结果。因此，在大多数现有的工作中，鲁棒性是以纯粹定性的方式定义的，结果要么只适用于小型网络，要么基于经验动机，特定于应用的启发式。该项目的第一个目标是通过为网络中鲁棒顺序检测理论提供坚实的基础来缩小这种理解上的差距。在此基础上，第二个目标是开发和实现具有良好定义和可量化的鲁棒性的顺序分布式检测算法。该项目的成功完成将为健壮的分布式统计数据的一般和严格框架铺平道路，可与现有的集中健壮检测工作相媲美。信号处理组是国际公认的鲁棒统计以及顺序和分布式信号处理的工作。因此，我们认为自己在成功完成拟议项目方面处于独特的有利地位，该项目汇集了这些核心专业领域。

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.