指数随机图模型
数学
随机图
指数族
估计员
统计推断
强一致性
指数函数
一致性(知识库)
随机几何图
组合数学
推论
应用数学
离散数学
图形
折线图
统计
电压图
数学分析
计算机科学
人工智能
作者
Michael Schweinberger,Jonathan R. Stewart
摘要
Statistical inference for exponential-family models of random graphs with dependent edges is challenging.We stress the importance of additional structure and show that additional structure facilitates statistical inference.A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods.We develop the first concentration and consistency results for maximum likelihood and M-estimators of a wide range of canonical and curved exponential-family models of random graphs with local dependence.All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well.In addition, we show that additional structure can facilitate subgraphto-graph estimation, and present concentration results for subgraph-to-graph estimators.As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.
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