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Approximate Variational Estimation for a Model of Network Formation

Author

Listed:
  • Angelo Mele

    (Johns Hopkins University)

  • Lingjiong Zhu

    (Florida State University)

Abstract

We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations; however, convergence may be exponentially slow. We propose a deterministic method, based on a variational mean-field approximation of the ERGM's normalizing constant. We compute lower and upper bounds for the approximation error for any network size, adapting nonlinear large deviation results. This translates into bounds on the distance between true likelihood and mean-field likelihood. Monte Carlo simulations suggest that in practice, our deterministic method performs better than our conservative theoretical approximation bounds imply, for a large class of models.

Suggested Citation

  • Angelo Mele & Lingjiong Zhu, 2023. "Approximate Variational Estimation for a Model of Network Formation," The Review of Economics and Statistics, MIT Press, vol. 105(1), pages 113-124, January.
    • Handle: RePEc:tpr:restat:v:105:y:2023:i:1:p:113-124
    DOI: 10.1162/rest_a_01023
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    Cited by:

    1. Bryan S. Graham & Andrin Pelican, 2023. "Scenario Sampling for Large Supermodular Games," Papers 2307.11857, arXiv.org.
    2. Gaonkar, Shweta & Mele, Angelo, 2023. "A model of inter-organizational network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 214(C), pages 82-104.
    3. Bryan S. Graham & Andrin Pelican, 2023. "Scenario sampling for large supermodular games," CeMMAP working papers 15/23, Institute for Fiscal Studies.
    4. Laura Battaglia & Timothy M. Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for regression with variables generated from unstructured data," CeMMAP working papers 10/24, Institute for Fiscal Studies.
    5. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated by AI or Machine Learning," Papers 2402.15585, arXiv.org, revised Dec 2024.

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