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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Matrix estimation by Universal Singular Value Thresholding
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Matrix estimation by Universal Singular Value Thresholding
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The statistical physics of real-world networks
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Consistency under sampling of exponential random graph models
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References
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Testability and repair of hereditary hypergraph properties
Tim Austin,Terence Tao +1 more
TL;DR: In this paper, it was shown that for undirected polychromatic graphs and hypergraphs, the repair algorithm is local in the sense that it only depends on a bounded amount of data; in particular, the graph can be repaired in a time linear in the number of edges.
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Sourav Chatterjee,Partha S. Dey +1 more
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Olle Häggström,Johan Jonasson +1 more
TL;DR: In this article, the behavior of the random triangle model on the two-dimensional triangular lattice is studied, and it is shown that phase transition occurs if and only if p = (q-1) -2/3 and q > q c for a critical value q c which turns out to equal 27 + 15√3 52.98.
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The rank of connection matrices and the dimension of graph algebras
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Introduction to papers on the modeling and analysis of network data
TL;DR: A network model is one that accounts for the structure of the network ties in terms of the probability that each network tie exists, whether conditional on all other ties, or as considered part of the distribution of the ensemble of ties.
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