标题： 无线网络拓扑推断：基于马尔可夫链的方法 显示英文标题

标题： Wireless Network Topology Inference: A Markov Chains Approach

摘要： 在这项工作中，我们研究了利用有限观测数据推断无线网络拓扑的问题。 具体来说，我们假设可以检测到节点何时正在发送数据，但无法获得有关发送的任何进一步信息。 我们提出了一种新颖的网络估计程序，基于以下抽象问题：通过观察每个时间步长下链式结构的多个“匿名”副本访问哪些状态，来估计一个有限离散时间马尔可夫链的参数。 我们开发了一致性估计器，以算子范数近似链的转移矩阵，所需样本数量大致随状态空间大小线性增长。 将此估计程序应用于无线网络时，我们的数值实验表明，所提出的方法在广泛的参数范围内准确地推断了网络拓扑，并且在高网络拥塞条件下尤其优于传递熵。 显示英文摘要

摘要： In this work, we address the problem of inferring the topology of a wireless network using limited observational data. Specifically, we assume that we can detect when a node is transmitting, but no further information regarding the transmission is available. We propose a novel network estimation procedure grounded in the following abstract problem: estimating the parameters of a finite discrete-time Markov chain by observing, at each time step, which states are visited by multiple ``anonymous'' copies of the chain. We develop a consistent estimator that approximates the transition matrix of the chain in the operator norm, with the number of required samples scaling roughly linearly with the size of the state space. Applying this estimation procedure to wireless networks, our numerical experiments demonstrate that the proposed method accurately infers network topology across a wide range of parameters, consistently outperforming transfer entropy, particularly under conditions of high network congestion.