随机网络中选择重要节点的高效采样
Efficient Sampling for Selecting Important Nodes in Random Network
AI总结：
本文提出了一种基于贝叶斯学习的动态采样方法，用于高效确定随机网络中重要节点的平稳概率。
摘要：
我们考虑在随机网络中选择重要节点的问题，其中节点以一定的转移概率相互连接。节点的重要性由马尔可夫链中相应节点的平稳概率来表征，这类似于谷歌的PageRank方法。与确定性网络不同，随机网络中的转移概率是未知的，但可以通过采样进行估计。在贝叶斯学习框架下，我们应用一阶泰勒展开和正态近似，以提供计算高效的平稳概率后验近似。为了最大化正确选择的概率，我们提出了一种动态采样程序，该程序不仅使用不同节点之间某些交互参数的后验均值和方差，还使用平稳概率对每个交互参数的敏感性。数值实验结果展示了所提采样程序的优越性。
英文摘要：
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the corresponding nodes in a Markov chain defined over the network, as in Google's PageRank. Unlike deterministic network, the transition probabilities in random network are unknown but can be estimated by sampling. Under a Bayesian learning framework, we apply the first-order Taylor expansion and normal approximation to provide a computationally efficient posterior approximation of the stationary probabilities. In order to maximize the probability of correct selection, we propose a dynamic sampling procedure which uses not only posterior means and variances of certain interaction parameters between different nodes, but also the sensitivities of the stationary probabilities with respect to each interaction parameter. Numerical experiment results demonstrate the superiority of the proposed sampling procedure.
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。
