Consistency under sampling of exponential random graph models
指数随机图模型的抽样一致性AI 解读 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要直接讨论整体网络、抽样子网络及指数随机图模型的参数估计，属于网络方向。
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指数随机图模型的抽样一致性
- 研究问题
- 只观察到抽样子网络时，将整体网络模型直接用于子网络，是否能保持模型的抽样一致性并支持整体参数估计？
- 方法与思路
- 作者以投影族性质分析指数随机图模型，并推广到具有依赖关系的指数族，进而讨论最大似然估计的一致性条件。
- 材料陈述的贡献
- 摘要称许多常用模型不满足抽样一致性，而满足该性质会限制模型表达力；作者还给出易检查的估计一致性条件。
- 阅读关注点
- 应核对抽样机制与投影性的定义，区分模型抽样一致性和估计量一致性，并查看哪些网络统计量导致性质失效。
- 阅读边界
- 来源为稿件版本未注明的 OpenAlex 索引摘要；具体条件和建设性方案未提供，不能推断刊本变化或所有网络抽样情形。
原文摘要
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling, or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM’s expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.