%0 Generic %1 chatterjee2011estimating %A Chatterjee, Sourav %A Diaconis, Persi %D 2011 %K exponential_model random_graphs statistics %T Estimating and Understanding Exponential Random Graph Models %U http://arxiv.org/abs/1102.2650 %X We introduce a new method for estimating the parameters 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. 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 showing that for many models, the extra sufficient statistics are useless: most realizations look like the results of a simple Erdos-Renyi model. We also find classes of models where the limiting graphs differ from Erdos-Renyi graphs and begin to make the link to models where the natural parameters alternate in sign.

@misc{chatterjee2011estimating, abstract = { We introduce a new method for estimating the parameters 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. 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 showing that for many models, the extra sufficient statistics are useless: most realizations look like the results of a simple Erdos-Renyi model. We also find classes of models where the limiting graphs differ from Erdos-Renyi graphs and begin to make the link to models where the natural parameters alternate in sign. }, added-at = {2011-02-21T07:54:21.000+0100}, author = {Chatterjee, Sourav and Diaconis, Persi}, biburl = {https://www.bibsonomy.org/bibtex/209b030b86e0f95987762c5bdd865b367/peter.ralph}, description = {[1102.2650] Estimating and Understanding Exponential Random Graph Models}, interhash = {697a37481901a107ac74dda68572bba3}, intrahash = {09b030b86e0f95987762c5bdd865b367}, keywords = {exponential_model random_graphs statistics}, note = {cite arxiv:1102.2650 Comment: 41 pages, 8 figures}, timestamp = {2011-02-21T07:54:21.000+0100}, title = {Estimating and Understanding Exponential Random Graph Models}, url = {http://arxiv.org/abs/1102.2650}, year = 2011 }