Network representation using graph root distributions
Network representation using graph root distributions
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DOI：
10.1214/20-aos1976
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发表时间：
2018-02
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影响因子：
--
通讯作者：
Jing Lei
中科院分区：
文献类型：
--
作者：
Jing Lei
可交换随机图是网络数据统计分析的重要概率框架。该框架的核心是图样本分布的参数化，现有的方法存在着非平凡的可识别性问题。本文给出了一般可交换随机图的一种新的参数化方法，其中节点是线性空间中具有不定内积的独立随机向量，两节点之间的边概率等于相应节点向量的内积。因此，可交换随机图的分布可以用这个线性空间上的节点抽样分布来表示，我们称之为图根分布。研究了这种表示的存在唯一性，图根分布与可交换随机图抽样分布之间的拓扑关系，以及图根分布的统计估计。
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. At the core of this framework is the parameterization of graph sampling distributions, where existing methods suffer from non-trivial identifiability issues. In this work we develop a new parameterization for general 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 can be represented by a node sampling distribution on this linear space, which we call the "graph root distribution". We study existence and uniqueness of such representations, the topological relationship between the graph root distribution and the exchangeable random graph sampling distribution, and the statistical estimation of graph root distributions.