Exponential Random Graph Models (ERGMs)

14 Mar 2013 22:38

See exponential families and network data analysis, naturally.

My perspective on these models changed radically in the course of trying to establish that maximum likelihood estimation is consistent for them; but that story is a little long to tell here. See here, or just the paper.

— Although many of the relevant papers appear in the journal Social Networks, published by Elsevier, the company responsible for deliberately publishing pseudo-journals such as The Australasian Journal of Bone and Joint Medicine, I know of no particular reason to believe that their findings are problematic. It would, however, be good if the community could shift to a journal whose publishers do not subvert the peer-review process whenever they find it profitable to do so.

Peter J. Carrington, John Scott and Stanley Wasserman (eds.), Models and Methods in Social Network Analysis [Many, but not all, of the papers are based on using ERGMs.]
Steven M. Goodreau, James A. Kitts and Martina Morris, "Birds of a Feather, Or Friend of a Friend?: Using Exponential Random Graph Models to Investigate Adolescent Social Networks", Demography 46 (2009): 103--125 [In addition to the substantive findings, this is a great introduction to the approach.]
Mark S. Handcock, David R. Hunter, Carter T. Butts, Steven M. Goodreau, and Martina Morris (eds.), "Statistical Modeling of Social Networks with 'statnet'", special volume (24) of the Journal of Statistical Software (2008) [Introduction to a whole issue on the ERGM approach.]

Shankar Bhamidi, Guy Bresler and Allan Sly, "Mixing time of exponential random graphs", Annals of Applied Probability 21 (2011): 2146--2170, arxiv:0812.2265 [Extended abstract in FOCS 2008 conference proceedings]
Sourav Chatterjee and Persi Diaconis, "Estimating and Understanding Exponential Random Graph Models", arxiv:1102.2650 [Results on conditions under which the mean field approximation for ERGMs becomes exact, and they consequently grow indistinguishable from simple Erdos-Renyi models.]
Stephen E. Fienberg, Alessandro Rinaldo and Yi Zhou, "On the Geometry of Discrete Exponential Families with Applications to Exponential Random Graph Models", arxiv:0901.0026
Diego Garlaschelli and Maria I. Loffredo, "Maximum likelihood: extracting unbiased information from complex networks", cond-mat/0609015 [This is a much-needed corrective to the physics literature, but it makes it sound as though exponential families of random graphs were invented in 2004, and they're the first ones to apply maximum likelihood to network analysis. I'm sure, however, that these are inadvertent lapses. Definitely worth reading as a first glimpse of how to do parameter estimation correctly. Thanks to Dave Feldman for pointing it out to me.]
Krista Gile and Mark S. Handcock, "Model-based Assessment of the Impact of Missing Data on Inference for Networks" [Working Paper 66, Center for Statistics and the Social Sciences, University of Washington (2006). PDF preprint.]
Mark S. Handcock, "Assessing degeneracy in statistical models of social networks", CSSS working paper 39 (2003)
Mark S. Handcock and Krista J. Gile, "Modeling social networks from sampled data", Annals of Applied Statistics 4 (2010): 5--25, arxiv:1010.0891
Steve Hanneke and Eric Xing, "Discrete Temporal Models for Social Networks", in Airoldi et al. (eds.) above [Extending exponential-family random graph models to dynamic networks. Makes me extra proud to have taught Steve stochastic processes. PDF preprint]
Steve Hanneke, Wenjie Fu, and Eric P. Xing, "Discrete temporal models of social networks", Electronic Journal of Statistics 4 (2010): 585--605
David R. Hunter and Mark S. Handcock, "Inference in curved exponential family models for networks", Journal of Computational and Graphical Statistics 15 (2006): 565--583 [PDF reprint]
Eric D. Kolaczyk and Pavel N. Krivitsky, "On the question of effective sample size in network modeling", arxiv:1112.0840
Pavel N. Krivitsky, "Exponential-Family Random Graph Models for Valued Networks", Electronic Journal of Statistics 6 (2012): 1100--1128, arxiv:1101.1359
Pavel N. Krivitsky, Mark S. Handcock and Martina Morris, "Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models", Statistical Methodology 8 (2011): 319--339, arxiv:1004.5328
Juyong Park and M. E. J. Newman
- "The Statistical Mechanics of Networks", Physical Review E 70 (2004): 066117, arxiv:cond-mat/0405566 [I particularly like the way diagrammatic perturbation theory is introduced]
- "Solution of the 2-star model of a network", Physical Review E 70 (2004): 066146, arxiv:cond-mat/0405457
- "Solution for the properties of a clustered network", Physical Review E 72 (2006): 026136, arxiv:cond-mat/0412579
Garry Robins, Tom Snijders, Peng Wang, Mark Handcock and Philippa Pattison, "Recent developments in exponential random graph (p*) models for social networks", Social Networks 29 (2007): 192--215 [PDF reprint via Prof. Snijders]
Michael Schweinberberg, "Instability, Sensitivity, and Degeneracy in Discrete Exponential Families", Journal of the American Statistical Association forthcoming [Tech Report 10-07, Penn State, PDF (oddly, a scan of a LaTeX-produced paper]
Lin Yuan, Sergey Kirshner, Robert Givan, "Estimating Densities with Non-Parametric Exponential Families", arxiv:1206.5036

CRS and Alessandro Rinaldo, "Consistency under Sampling of Exponential Random Graph Models", Annals of Statistics forthcoming, arxiv:1111.3054 [More]

David Aristoff, Charles Radin, "Emergent structures in large networks", arxiv:1110.1912
Arun Chandrasekhar, Matthew O. Jackson, "Tractable and Consistent Random Graph Models", arxiv:1210.7375
Alexander Engstrom, Patrik Noren, "Polytopes from Subgraph Statistics", arxiv:1011.3552
A. Caimo, N. Friel, "Bergm: Bayesian Exponential Random Graphs in R", arxiv:1201.2770
Richard G. Everitt, "Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks", Journal of Computational and Graphical Statistic 21 (2012): 940--960
Katherine Faust and John Skvoretz, "Comparing Networks Across Space and Time, Size and Species", Sociological Methodology 32 (2002): 267--299
Andreas Flache and Tobias Stark, "Preference or opportunity? Why do we find more friendship segregation in more heterogeneous schools?", arxiv:0901.2825
Agata Fronczak, "Exponential random graph models", arxiv:1210.7828
Neha Gondal, "The local and global structure of knowledge production in an emergent research field: An exponential random graph analysis", Social Networks forthcoming (2011)
Ruth M. Hummel, David R. Hunter and Mark S. Handcock, "Improving Simulation-Based Algorithms for Fitting ERGMs", Journal of Computational and Graphical Statistics 21 (2012): 920--939
David R. Hunter, Pavel N. Krivitsky and Michael Schweinberger, "Computational Statistical Methods for Social Network Models", Journal of Computational and Graphical Statistics 21 (2012): 856--882
Pavel N. Krivitsky and Mark S. Handcock, "A Separable Model for Dynamic Networks", arxiv:1011.1937
Dean Lusher, Johan Koskinen, and Garry Robins (eds.), Exponential Random Graph Models for Social Networks: Theory, Methods, and Applications [Blurb]
Saisuke Okabayashi and Charles J. Geyer, "Long range search for maximum likelihood in exponential families", Electronic Journal of Statistics 6 (2012): 123--147
Charles Radin, Mei Yin, "Phase transitions in exponential random graphs", arxiv:1108.0649
Tiago P. Peixoto, "The entropy of stochastic blockmodel ensembles", Physical Review E 85 (2012): 056122, arxiv:1112.6028
Michael Schweinberger, "Statistical modelling of network panel data: Goodness of fit", British Journal of Mathematical and Statistical Psychology 65 (2012): 263--281
Sean L. Simpson, Satoru Hayasaka, Paul J. Laurienti, "Selecting an exponential random graph model for complex brain networks", arxiv:1007.3230
Thomas Suesse, "Marginalized Exponential Random Graph Models", Journal of Computational and Graphical Statistics 21 (2012): 883--900