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Statistical mechanics of networks: Estimation and uncertainty

Desmarais, B.A. ; Cranmer, S.J.

Physica A, 2012-02, Vol.391 (4), p.1865-1876 [Peer Reviewed Journal]

Elsevier B.V

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  • Title:
    Statistical mechanics of networks: Estimation and uncertainty
  • Author: Desmarais, B.A. ; Cranmer, S.J.
  • Subjects: Bootstrap ; Computer simulation ; Congress ; Dynamic network ; Dynamics ; ERGM ; Mathematical models ; Networks ; Resampling ; Statistical mechanics ; Uncertainty
  • Is Part Of: Physica A, 2012-02, Vol.391 (4), p.1865-1876
  • Notes: ObjectType-Article-2
    SourceType-Scholarly Journals-1
    ObjectType-Feature-1
    content type line 23
  • Description: Exponential random graph models (ERGMs) are powerful tools for formulating theoretical models of network generation or learning the properties of empirical networks. They can be used to construct models that exactly reproduce network properties of interest. However, tuning these models correctly requires computationally intractable maximization of the probability of a network of interest—maximum likelihood estimation (MLE). We discuss methods of approximate MLE and show that, though promising, simulation based methods pose difficulties in application because it is not known how much simulation is required. An alternative to simulation methods, maximum pseudolikelihood estimation (MPLE), is deterministic and has known asymptotic properties, but standard methods of assessing uncertainty with MPLE perform poorly. We introduce a resampling method that greatly outperforms the standard approach to characterizing uncertainty with MPLE. We also introduce ERGMs for dynamic networks—temporal ERGM (TERGM). In an application to modeling cosponsorship networks in the United States Senate, we show how recently proposed methods for dynamic network modeling can be integrated into the TERGM framework, and how our resampling method can be used to characterize uncertainty about network dynamics. ► We review methods for exponential random graph models. ► We present an algorithm for summarizing uncertainty in estimates. ► We introduce temporal exponential random graph models to physics. ► We compare temporal exponential random graph models to physics training models. ► Methods are illustrated through modeling and forecasting Senate cosponsorship.
  • Publisher: Elsevier B.V
  • Language: English
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