标题： 自适应网络中的分布式检测：精炼渐近性和连通性的作用 显示英文标题

标题： Distributed Detection over Adaptive Networks: Refined Asymptotics and the Role of Connectivity

摘要： 我们研究了自适应网络中的分布式检测问题，分散的代理通过局部交互从流数据中不断学习。 通过采用具有固定步长{\mu }的扩散算法，同时实现了自适应和协作的需求。 在 [1], [2] 中揭示了自适应分布式检测的一些主要特征。 通过利用大偏差分析，证明了所有代理的 I 型和 II 型错误概率随着 1/{\mu }的函数呈指数衰减，并且所有代理共享相同的 I 型和 II 型错误指数。 然而，[1], [2] 中提供的数值证据表明，大偏差理论未能捕捉网络连通性对性能的根本影响，需要额外的工具和努力来获得误差概率的准确预测。 本文解决了这些开放性问题，并在多个方向上扩展了 [1], [2] 的结果。 通过基于精确渐近数学框架的细化渐近分析，我们对自适应网络中分布式检测的普遍行为有了深刻而有力的理解：作为 1/{\mu }的函数，不同代理对应的误差（对数）概率曲线几乎彼此平行（已在 [1], [2] 中发现），然而，这些曲线按照反映每个代理连通度的准则进行排序。 根据组合权重的不同，一个代理的连通度越高，其误差概率曲线就越低。 有趣且有些出乎意料的是，在网络拓扑、组合权重与推理性能之间的相互作用中出现了某些行为。 得出的经验教训是，连通性至关重要。 显示英文摘要

摘要： We consider distributed detection problems over adaptive networks, where dispersed agents learn continually from streaming data by means of local interactions. The simultaneous requirements of adaptation and cooperation are achieved by employing diffusion algorithms with constant step-size {\mu}. In [1], [2] some main features of adaptive distributed detection were revealed. By resorting to large deviations analysis, it was established that the Type-I and Type-II error probabilities of all agents vanish exponentially as functions of 1/{\mu}, and that all agents share the same Type-I and Type-II error exponents. However, numerical evidences presented in [1], [2] showed that the theory of large deviations does not capture the fundamental impact of network connectivity on performance, and that additional tools and efforts are required to obtain accurate predictions for the error probabilities. This work addresses these open issues and extends the results of [1], [2] in several directions. By conducting a refined asymptotic analysis based on the mathematical framework of exact asymptotics, we arrive at a revealing and powerful understanding of the universal behavior of distributed detection over adaptive networks: as functions of 1/{\mu}, the error (log-)probability curves corresponding to different agents stay nearly-parallel to each other (as already discovered in [1], [2]), however, these curves are ordered following a criterion reflecting the degree of connectivity of each agent. Depending on the combination weights, the more connected an agent is, the lower its error probability curve will be. Interesting and somehow unexpected behaviors emerge, in terms of the interplay between the network topology, the combination weights, and the inference performance. The lesson learned is that connectivity matters.