Abstract Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in capturing many network features of interest, recent work highlights difficulties related to the models’ ill behavior, such as most of the probability mass being concentrated on a very small subset of the parameter space. This behavior limits both the applicability of an ERGM as a model for real data and inference and parameter estimation via the usual Markov chain Monte Carlo algorithms. To address this problem, we propose a new exponential family of models for random graphs that build on the standard ERGM framework. Specifically, we solve the problem of computational intractability and “degenerate” model behavior by an interpretable support restriction. We introduce a new parameter based on the graph-theoretic notion of degeneracy, a measure of sparsity whose value is commonly low in real-world networks. The new model family is supported on the sample space of graphs with bounded degeneracy and is called degeneracy-restricted ERGMs, or DERGMs for short. Since DERGMs generalize ERGMs—the latter is obtained from the former by setting the degeneracy parameter to be maximal—they inherit good theoreticalmore »
This content will become publicly available on August 26, 2023
Highly scalable maximum likelihood and conjugate Bayesian inference for ERGMs on graph sets with equivalent vertices
The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing more »
- De Vico Fallani, Fabrizio
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- PLOS ONE
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- National Science Foundation
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