论文标题
在部分可观察性下进行拓扑推断的无偏对称矩阵估计器
An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability
论文作者
论文摘要
网络拓扑推断是网络科学的许多应用中的一个基本问题，例如找到虚假新闻的来源，大脑连接网络检测等。许多现实世界中的情况遇到了一个关键问题，只有有限的部分观察到的节点才能可用。这封信考虑了部分可观察性框架下的网络拓扑推断问题。基于矢量自回旋模型，我们提出了一个具有高斯噪声和拉普拉斯组合规则的对称网络拓扑的新型无偏估计器。从理论上讲，我们证明它以概率收敛到网络组合矩阵。此外，通过利用高斯混合模型算法，开发了一种称为网络推理高斯算法的有效算法来推断网络结构。最后，与最先进的方法相比，数值实验证明了所提出的算法在较小的样本量的情况下具有更好的性能。
Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem that only a limited part of observed nodes are available. This letter considers the problem of network topology inference under the framework of partial observability. Based on the vector autoregressive model, we propose a novel unbiased estimator for the symmetric network topology with the Gaussian noise and the Laplacian combination rule. Theoretically, we prove that it converges to the network combination matrix in probability. Furthermore, by utilizing the Gaussian mixture model algorithm, an effective algorithm called network inference Gauss algorithm is developed to infer the network structure. Finally, compared with the state-of-the-art methods, numerical experiments demonstrate the proposed algorithm enjoys better performance in the case of small sample sizes.
