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Mathematical Finance and Probability Seminars

Variational approximations for exponential random graph models

Location:  Hill 705
Date & time: Tuesday, 11 October 2016 at 11:45AM - 11:45AM

Lingjiong Zhu, Florida State University: We study a model of strategic network formation with heterogeneous players, that converges to an exponential random graph model. The likelihood of observing a specific network is known up to an intractable normalizing constant, which is infeasible to compute. The standard estimation method uses an MCMC algorithm that generates the samples from the exponential random graph model to provide an estimate of the normalizing constant. We provide an alternative tractable method of estimation for a large class of exponential random graph models. We show that a mean-field variational approximation of the likelihood provides a lower bound for the normalizing constant, which becomes exact as the network size grows to infinity. We also provide exact bounds for the approximation error of the variational mean-field for fixed network size. Special cases including the model featuring extreme homophily will also be discussed.

This is based on the joint work with Angelo Mele (Carey Business School, Johns Hopkins University).

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

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