Robust Sequential Analysis in Networks

序贯分析关注的是当样本的数量不是先验的，而是根据到目前为止观察到的数据来选择的统计推断。与同等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著减少样本的平均数量。它们在许多需要高效率的领域中得到应用，特别是在采集样品昂贵或检测延迟很关键的情况下。相比之下，支撑稳健统计的理念是牺牲理想条件下的一些效率，以降低对偏离理想情况的敏感度。也就是说，健壮的程序被设计成在假设模型的附近执行得很好，通常允许很小的但任意的偏差。在我们以前的工作中，特别是DFG项目“稳健顺序分析”，我们调查了将顺序统计和稳健统计相结合的好处，以便做出快速且在统计上可靠的决策。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，在文献中很少能找到关于网络中的稳健序列检测的结果。最重要的是：1)没有分布式等价的不确定性模型，如离群点或概率分布的邻域。2)节点不确定性和网络范围不确定性之间的关系知之甚少。3)稳健集中式检测技术，如裁剪或审查，不能可靠地增强分布式检测的健壮性。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的结果。因此，在大多数现有的工作中，健壮性是以纯粹定性的方式定义的，结果要么仅适用于小型网络，要么基于经验驱动的、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稳健的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连续的分布式检测算法，这些算法以定义良好和可量化的方式具有健壮性。该项目的成功完成将为建立一个全面和严格的稳健分布统计框架铺平道路，这一框架可与现有的集中稳健检测工作相媲美。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。

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.