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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.<\/jats:p>","DOI":"10.1162\/rest_a_01023","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T21:29:24Z","timestamp":1619126964000},"page":"113-124","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":9,"title":["Approximate Variational Estimation for a Model of Network Formation"],"prefix":"10.1162","volume":"105","author":[{"given":"Angelo","family":"Mele","sequence":"first","affiliation":[{"name":"Johns Hopkins University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingjiong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Florida State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2023,1,6]]},"reference":[{"key":"2023010623082240300_B1","first-page":"1981","article-title":"Mixed Membership Stochastic Blockmodels,","volume":"9","author":"Airoldi","year":"2008","journal-title":"Journal of Machine Learning Research"},{"key":"2023010623082240300_B2","article-title":"Approximating Partition Functions for Exponential-Family Random Graph Models","volume-title":"Advances in Neural Information Processing Systems","author":"Amir","year":"2012"},{"key":"2023010623082240300_B3","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1017\/apr.2018.13","article-title":"On the Phase Transition Curve in a Directed Exponential Random Graph Model,","volume":"50","author":"Aristoff","year":"2018","journal-title":"Advances in Applied Probability"},{"key":"2023010623082240300_B4","article-title":"Discrete Games in Endogenous Networks: Theory and Policy","author":"Badev","year":"2013"},{"issue":"6144","key":"2023010623082240300_B5","doi-asserted-by":"publisher","DOI":"10.1126\/science.1236498","article-title":"The Diffusion of Microfinance","volume":"341","author":"Banerjee","year":"2013","journal-title":"Science"},{"issue":"2","key":"2023010623082240300_B6","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1111\/j.2517-6161.1974.tb00999.x","article-title":"Spatial Interaction and the Statistical Analysis of Lattice Systems","volume":"36","author":"Besag","year":"1974","journal-title":"Journal of the Royal Statistical Society Series B (Methodological)"},{"issue":"6","key":"2023010623082240300_B7","doi-asserted-by":"publisher","first-page":"2146","DOI":"10.1214\/10-AAP740","article-title":"Mixing Time of Exponential Random Graphs","volume":"21","author":"Bhamidi","year":"2011","journal-title":"Annals of Applied Probability"},{"issue":"4","key":"2023010623082240300_B8","doi-asserted-by":"publisher","first-page":"1922","DOI":"10.1214\/13-AOS1124","article-title":"Asymptotic Normality of Maximum Likelihood and Its Variational Approximation for Stochastic Blockmodels","volume":"41","author":"Bickel","year":"2013","journal-title":"Ann. 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