arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2003.11062cs.ITmath.IT
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减少通信的多重变点检测贝叶斯方法

Bayesian Methods for Multiple Change-Point Detection with Reduced Communication

Eyal Nitzan, Topi Halme, Visa Koivunen

AI总结:

针对通信受限传感器网络中的多重变点检测,提出两种基于后验概率选择传感器子集的贝叶斯程序,可控制FDR并实现不随传感器数增长的ADD。

摘要:

在许多现代应用中,大规模传感器网络被用于执行统计推断任务。本文提出利用传感器网络进行多重变点检测的贝叶斯方法,其中融合中心(FC)可以接收来自每个传感器的数据流。由于通信限制,FC在每个时隙仅监测传感器的一个子集。由于变点数量可能较多,我们采用错误发现率(FDR)准则来控制误报率,同时最小化平均检测延迟(ADD)。我们提出两种贝叶斯检测程序,通过监测已发生变点的后验概率最高的传感器子集来处理通信限制。该监测策略旨在利用相应的后验概率,最小化每个变点发生与其被宣布之间的延迟。所提出的两种程序中,一种比第二种更保守,即其FDR更低,但代价是ADD更高。分析表明,两种程序都能将FDR控制在规定的容忍水平以下,并且具有可扩展性,即它们达到的ADD不会随传感器数量渐近增加。此外,研究证明所提出的检测程序有助于在降低ADD与减少发现前抽取的平均观测数之间进行权衡。数值仿真验证了分析结果,并展示了所提程序的性质。

英文摘要:

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this paper, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while minimizing the average detection delay (ADD). We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain an ADD that does not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced average number of observations drawn until discovery. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures.

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。

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