CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.
CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.
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DOI：
10.1214/12-aos1044
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发表时间：
2013-04
影响因子：
4.5
通讯作者：
Rinaldo A
中科院分区：
文献类型：
--
作者：
Shalizi CR;Rinaldo A
网络数据的日益可用性和科学对分布式系统的兴趣导致了网络结构统计模型的快速发展。然而，通常，这些是整个网络的模型，而数据仅由采样的子网络组成。通过将模型应用于子网络来估计整个网络的参数，这是我们感兴趣的。这假定模型在抽样下是一致的，或者，根据随机过程理论，它定义了一个射影族。关注流行的指数随机图模型（ERGM），我们证明了这个看似微不足道的条件实际上被许多流行的和科学上吸引人的模型所违反，并且满足它极大地限制了ERGM的表达能力。这些结果实际上是关于相关随机变量指数族的更一般结果的特例，我们也证明了这些结果。利用这些结果，我们提供了ergm中最大似然估计一致性的易于检查的条件，并讨论了一些可能的建设性响应。
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.