Estimating and understanding exponential random graph models
Sourav Chatterjee,Persi Diaconis +1 more
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In this paper, the authors introduce a method for the theoretical analysis of exponential random graph models based on a large deviation approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and Varadhan [European J. Combin. 32 (2011) 1000-1017].Abstract:
We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and Varadhan [European J. Combin. 32 (2011) 1000–1017]. The theory explains a host of difficulties encountered by applied workers: many distinct models have essentially the same MLE, rendering the problems “practically” ill-posed. We give the first rigorous proofs of “degeneracy” observed in these models. Here, almost all graphs have essentially no edges or are essentially complete. We supplement recent work of Bhamidi, Bresler and Sly [2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS) (2008) 803–812 IEEE] showing that for many models, the extra sufficient statistics are useless: most realizations look like the results of a simple Erdős–Renyi model. We also find classes of models where the limiting graphs differ from Erdős–Renyi graphs. A limitation of our approach, inherited from the limitation of graph limit theory, is that it works only for dense graphs.read more
Citations
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Richard Kenyon,Mei Yin +1 more
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Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
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Asymptotics in directed exponential random graph models with an increasing bi-degree sequence
Ting Yan,Chenlei Leng,Ji Zhu +2 more
TL;DR: It is established the uniform consistency and the asymptotic normality for the maximum likelihood estimate, when the number of parameters grows and only one realized observation of the graph is available, for directed exponential random graph models.
References
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Paul W. Holland,Samuel Leinhardt +1 more
TL;DR: An exponential family of distributions that can be used for analyzing directed graph data is described, and several special cases are discussed along with some possible substantive interpretations.
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