Approximate Variational Estimation for a Model of Network Formation

51 Pages Posted: 2 Feb 2017 Last revised: 6 Apr 2019

See all articles by Angelo Mele

Angelo Mele

Johns Hopkins University - Carey Business School

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: April 4, 2019

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, using nonlinear large deviations results. This translates into bounds on the distance between true likelihood and mean-field likelihood, as well as bounds on the distance between approximate parameter estimates from the MLE, assuming the likelihood is not very flat. In small networks, a simple Monte Carlo exercise shows that our deterministic method provides similar estimates as the simulation-based methods with the advantage of converging in quadratic time.

Keywords: Networks, Microeconometrics, Large networks, Variational Inference, Large deviations, Graph limits, Mean-Field Approximations

JEL Classification: C13, C57, C21, D85

Suggested Citation

Mele, Angelo and Zhu, Lingjiong, Approximate Variational Estimation for a Model of Network Formation (April 4, 2019). Available at SSRN: https://ssrn.com/abstract=2909829 or http://dx.doi.org/10.2139/ssrn.2909829

Angelo Mele (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

HOME PAGE: http://www.meleangelo.com

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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