Consistency under sampling of exponential random graph models
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It is shown 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.Abstract:
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.read more
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References
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Journal ArticleDOI
Birds of a Feather: Homophily in Social Networks
TL;DR: The homophily principle as mentioned in this paper states that similarity breeds connection, and that people's personal networks are homogeneous with regard to many sociodemographic, behavioral, and intrapersonal characteristics.
Book
Networks: An Introduction
TL;DR: This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.
Book
Foundations of modern probability
TL;DR: In this article, the authors discuss the relationship between Markov Processes and Ergodic properties of Markov processes and their relation with PDEs and potential theory. But their main focus is on the convergence of random processes, measures, and sets.
Book
Graphical Models, Exponential Families, and Variational Inference
TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Book
Networks, Crowds, and Markets: Reasoning about a Highly Connected World
Easley David,Kleinberg Jon +1 more
TL;DR: In this article, an introductory undergraduate textbook takes an interdisciplinary look at economics, sociology, computing and information science, and applied mathematics to understand networks and behavior, addressing fundamental questions about how the social, economic, and technological worlds are connected.