可分解图模型中通信效率最快变化检测的排序
Ordering for Communication-Efficient Quickest Change Detection in a Decomposable Graphical Model
摘要：
一个最快的变化检测问题被认为是在一个传感器网络的观察，其统计依赖结构的变化之前和之后的传感器描述的可分解的图形模型（DGM）。分布式计算方法，这个问题提出了能够产生最佳的集中式测试统计量。DGM导致以适当的方式将节点收集到相当于图中的团的局部组中，使得可以在每个团内计算汇总所有团传感器数据的团统计。集团统计被发送到决策者，以产生最佳的集中式测试统计。为了进一步提高通信效率，提出了一种有序传输方法，其中团统计到融合中心的传输是有序的，然后在积累了足够的信息时自适应地停止。该过程总是保证提供最佳的变化检测性能，尽管没有传输来自所有集团的所有统计数据。有序传输保存的传输的平均数的下限提供和的情况下，很少发生变化的下限接近约一半的集团提供了良好的行为之间的距离测量的传感器观测的分布之前和之后的变化是足够大的。我们还扩展的方法的情况下，图结构是不同的每个假设。数值结果表明，显着节省使用有序传输的方法，并验证了理论研究结果。
英文摘要：
A quickest change detection problem is considered in a sensor network with observations whose statistical dependency structure across the sensors before and after the change is described by a decomposable graphical model (DGM). Distributed computation methods for this problem are proposed that are capable of producing the optimum centralized test statistic. The DGM leads to the proper way to collect nodes into local groups equivalent to cliques in the graph, such that a clique statistic which summarizes all the clique sensor data can be computed within each clique. The clique statistics are transmitted to a decision maker to produce the optimum centralized test statistic. In order to further improve communication efficiency, an ordered transmission approach is proposed where transmissions of the clique statistics to the fusion center are ordered and then adaptively halted when sufficient information is accumulated. This procedure is always guaranteed to provide the optimal change detection performance, despite not transmitting all the statistics from all the cliques. A lower bound on the average number of transmissions saved by ordered transmissions is provided and for the case where the change seldom occurs the lower bound approaches approximately half the number of cliques provided a well behaved distance measure between the distributions of the sensor observations before and after the change is sufficiently large. We also extend the approach to the case when the graph structure is different under each hypothesis. Numerical results show significant savings using the ordered transmission approach and validate the theoretical findings.
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