标题： 无线网络拓扑推断：马尔可夫链方法 显示英文标题

标题： Wireless Network Topology Inference: A Markov Chains Approach

摘要： 我们解决使用有限观测数据推断无线网络拓扑的问题。 具体来说，我们假设可以检测节点是否在发送，但无法获得有关发送的其他信息。 我们提出了一种新颖的网络估计方法，其基础是以下抽象问题：通过在每个时间步观察多个“匿名”链的遍历状态，来估计有限离散时间马尔可夫链的参数。 我们开发了一个一致估计量，在算子范数下近似链的转移矩阵，所需样本数量大致与状态空间的大小成线性关系。 将此估计方法应用于无线网络，我们的数值实验表明，所提出的方法在广泛参数范围内准确地推断网络拓扑，特别是在高网络拥塞条件下，其表现始终优于转移熵。 显示英文摘要

摘要： 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.