基于图根分布的网络表示
Network Representation Using Graph Root Distributions
摘要：
可交换随机图是网络数据统计分析的重要概率框架。在这项工作中，我们开发了一个替代的参数化的一大类可交换的随机图，其中的节点是独立的随机向量在一个线性空间配备了一个不定的内积，和两个节点之间的边缘概率等于相应的节点向量的内积。因此，这个子类中可交换随机图的分布可以用这个线性空间上的一个节点抽样分布来表示，我们称之为图的根分布。我们研究了这种表示的存在性和可识别性，图根分布和可交换随机图抽样分布之间的拓扑关系，以及图根分布的估计。
英文摘要：
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in this subclass can be represented by a node sampling distribution on this linear space, which we call the graph root distribution. We study existence and identifiability of such representations, the topological relationship between the graph root distribution and the exchangeable random graph sampling distribution, and estimation of graph root distributions.
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