Notes on what you can infer through various sampling processes on graphs, as made famous by social network research. Paintbox processes? Edge exchangeability? Projectivity? We are notably terrible at this.
Nothing but chaos awaiting filing for now.
I am currently watching an overview seminar by Li Chun Zhang. He covers (Patone and Zhang 2020; Sanguiao Sande and Zhang 2020; L.-C. Zhang and Nguyen 2020; L.-C. Zhang and Oguz-Alper 2020; L.-C. Zhang and Patone 2017) and credits Thompson and Frank, althougcodeh I donβt know which Thompson and which Frank.
Exponential random graph models
A.k.a. ERGMs.
References
Achlioptas, Dimitris, Aaron Clauset, David Kempe, and Cristopher Moore. 2005. βOn the Bias of Traceroute Sampling: Or, Power-Law Degree Distributions in Regular Graphs.β In Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, 694β703. STOC β05. New York, NY, USA: ACM.
Cranmer, Skyler J, Bruce A Desmarais, and Jason W Morgan. 2021. Inferential network analysis.
Draves, Benjamin, and Daniel L. Sussman. 2020. βBias-Variance Tradeoffs in Joint Spectral Embeddings.β arXiv:2005.02511 [Math, Stat], May.
Green, Alden, and Cosma Rohilla Shalizi. 2017. βBootstrapping Exchangeable Random Graphs.β arXiv:1711.00813 [Stat], November.
Hunter, David R., Pavel N. Krivitsky, and Michael Schweinberger. 2012. βComputational Statistical Methods for Social Network Models.β Journal of Computational and Graphical Statistics 21 (4): 856β82.
Jaeger, Manfred, and Oliver Schulte. 2021. βA Complete Characterization of Projectivity for Statistical Relational Models.β In Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, 4283β90. IJCAIβ20. Yokohama, Yokohama, Japan.
Kandiros, Vardis, Yuval Dagan, Nishanth Dikkala, Surbhi Goel, and Constantinos Daskalakis. 2021. βStatistical Estimation from Dependent Data.β In International Conference on Machine Learning, 5269β78. PMLR.
Kitsak, Maksim. n.d. βIdentifying Influential Spreaders in Complex Networks.β
Krivitsky, Pavel N., and Mark S. Handcock. 2014. βA Separable Model for Dynamic Networks.β Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76 (1): 29β46.
Krivitsky, Pavel N., and Martina Morris. 2017. βInference For Social Network Models From Egocentrically Sampled Data, With Application To Understanding Persistent Racial Disparities In Hiv Prevalence In The Us.β The Annals of Applied Statistics 11 (1): 427β55.
Laga, Ian, Le Bao, and Xiaoyue Niu. 2020. βThirty Years of The Network Scale up Method.β arXiv:2011.12516 [Stat], November.
Levin, Keith, Avanti Athreya, Minh Tang, Vince Lyzinski, Youngser Park, and Carey E. Priebe. 2019. βA Central Limit Theorem for an Omnibus Embedding of Multiple Random Graphs and Implications for Multiscale Network Inference.β arXiv:1705.09355 [Stat], June.
Lin, Qiaohui, Robert Lunde, and Purnamrita Sarkar. 2020. βOn the Theoretical Properties of the Network Jackknife.β arXiv:2004.08935 [Math, Stat], April.
Patone, Martina, and Li-Chun Zhang. 2020. βIncidence Weighting Estimation Under Bipartite Incidence Graph Sampling.β arXiv:2004.04257 [Math, Stat], April.
Salamanos, Nikos, Elli Voudigari, and Emmanuel J. Yannakoudakis. n.d. βDeterministic Graph Exploration for Efficient Graph Sampling.β Social Network Analysis and Mining 7 (1).
Sanguiao Sande, Luis, and Li-Chun Zhang. 2020. βDesign-Unbiased Statistical Learning in Survey Sampling.β Sankhya: The Indian Journal of Statistics, October.
Shalizi, Cosma Rohilla, and Alessandro Rinaldo. 2013. βConsistency Under Sampling of Exponential Random Graph Models.β Annals of Statistics 41 (2): 508β35.
Snijders, Tom A. B. 2010. βConditional Marginalization for Exponential Random Graph Models.β The Journal of Mathematical Sociology 34 (4): 239β52.
Stumpf, Michael P. H., Carsten Wiuf, and Robert M. May. 2005. βSubnets of Scale-Free Networks Are Not Scale-Free: Sampling Properties of Networks.β Proceedings of the National Academy of Sciences of the United States of America 102 (12): 4221β24.
Vega-Oliveros, Didier. n.d. βInο¬uence Maximization Based on the Least Inο¬uential Spreaders.β
Yannakoudakis, Emmanuel J., Elli Voudigari, and Nikos Salamanos. 2020. βIdentifying Influential Spreaders by Graph Sampling.β Salamanos N, Voudigari E, Yannakoudakis EJ (2016) Identifying Influential Spreaders by Graph Sampling. In: Proceedings of the 5th International Workshop on Complex Networks and Their Applications, Milan, Italy, November 30 - December 02, 2016.
Zhang, L.-C., and M. Patone. 2017. βGraph Sampling.β METRON 75 (3): 277β99.
Zhang, Li-Chun, and Nancy Nguyen. 2020. βAn Appraisal of Common Reweighting Methods for Nonresponse in Household Surveys Based on Norwegian Labour Force Survey and Statistics on Income and Living Conditions Survey.β Journal of Official Statistics 36 (1): 151β72.
Zhang, Li-Chun, and Melike Oguz-Alper. 2020. βBIG Sampling.β arXiv:2003.09467 [Math, Stat], March.
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