论文标题
网络拓扑推断与图形光谱惩罚
Network Topology Inference with Graphon Spectral Penalties
论文作者
论文摘要
我们考虑从其节点支持的数据中推断出图的未观察到的边缘的问题。与现有方法一致，我们提出了一个凸面程序，用于恢复图形laplacian，该图可通过从观察到的数据的二阶时刻获得的一组特征向量可进行对角线化。与现有作品不同，我们将有关绘制基础图的分布的先验知识纳入了知识。特别是，我们考虑了从Graphon模型中绘制图形的情况，并且在要恢复的图表上，我们将凸优化问题补充了凸优化问题。我们介绍了假定Graphon模型已知的情况，并且从辅助网络观测值推断该模型的相关特征的更实际设置。关于合成和现实世界数据的数值实验说明了即使先验不完美的情况，也说明了提出的图形先验的优势。
We consider the problem of inferring the unobserved edges of a graph from data supported on its nodes. In line with existing approaches, we propose a convex program for recovering a graph Laplacian that is approximately diagonalizable by a set of eigenvectors obtained from the second-order moment of the observed data. Unlike existing work, we incorporate prior knowledge about the distribution from where the underlying graph was drawn. In particular, we consider the case where the graph was drawn from a graphon model, and we supplement our convex optimization problem with a provably-valid regularizer on the spectrum of the graph to be recovered. We present the cases where the graphon model is assumed to be known and the more practical setting where the relevant features of the model are inferred from auxiliary network observations. Numerical experiments on synthetic and real-world data illustrate the advantage of leveraging the proposed graphon prior, even when the prior is imperfect.
