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- W3099640877 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 ErdH{o}s-R'{e}nyi model. We also find classes of models where the limiting graphs differ from ErdH{o}s-R'{e}nyi graphs. A limitation of our approach, inherited from the limitation of graph limit theory, is that it works only for dense graphs." @default.
- W3099640877 created "2020-11-23" @default.
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- W3099640877 date "2013-10-01" @default.
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- W3099640877 title "Estimating and understanding exponential random graph models" @default.
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- W3099640877 doi "https://doi.org/10.1214/13-aos1155" @default.
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