Graph sampling

Estimating functionals of graphs



Notes on what you can infer through various sampling processes on graphs, as made famous by social network research. Paintbox processes here? Edge exchangeability? Projectivity? We are notably terrible at this.

Nothing but chaos awaiting filing here 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 don’t 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. “On the Bias of Traceroute Sampling: Or, Power-Law Degree Distributions in Regular Graphs.” In Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, 694–703. STOC ’05. New York, NY, USA: ACM. https://doi.org/10.1145/1060590.1060693.
Cranmer, Skyler J, Bruce A Desmarais, and Jason W Morgan. 2021. Inferential Network Analysis. https://doi.org/10.1017/9781316662915.
Draves, Benjamin, and Daniel L. Sussman. 2020. “Bias-Variance Tradeoffs in Joint Spectral Embeddings.” May 11, 2020. http://arxiv.org/abs/2005.02511.
Green, Alden, and Cosma Rohilla Shalizi. 2017. “Bootstrapping Exchangeable Random Graphs.” November 2, 2017. http://arxiv.org/abs/1711.00813.
Hunter, David R., Pavel N. Krivitsky, and Michael Schweinberger. 2012. “Computational Statistical Methods for Social Network Models.” Journal of Computational and Graphical Statistics 21 (4): 856–82. https://doi.org/10.1080/10618600.2012.732921.
Jaeger, Manfred, and Oliver Schulte. 2020. “A Complete Characterization of Projectivity for Statistical Relational Models.” April 23, 2020. http://arxiv.org/abs/2004.10984.
Kandiros, Vardis, Yuval Dagan, Nishanth Dikkala, Surbhi Goel, and Constantinos Daskalakis. 2021. “Statistical Estimation from Dependent Data.” In International Conference on Machine Learning, 5269–78. PMLR. http://proceedings.mlr.press/v139/kandiros21a.html.
Kitsak, Maksim. n.d. “Identifying Influential Spreaders in Complex Networks.” Accessed June 24, 2019. https://www.academia.edu/14492654/Identifying_influential_spreaders_in_complex_networks.
Krivitsky, Pavel N., and Mark S. Handcock. 2014. “A Separable Model for Dynamic Networks.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76 (1): 29–46. https://doi.org/10.1111/rssb.12014.
Krivitsky, Pavel N., and Martina Morris. 2017. “Inference For Social Network Models From Egocentrically Sampled Data, With Application To Understanding Persistent Racial Disparities In Hiv Prevalence In The Us.” The Annals of Applied Statistics 11 (1): 427–55. https://doi.org/10.1214/16-AOAS1010.
Laga, Ian, Le Bao, and Xiaoyue Niu. 2020. “Thirty Years of The Network Scale up Method.” November 25, 2020. http://arxiv.org/abs/2011.12516.
Levin, Keith, Avanti Athreya, Minh Tang, Vince Lyzinski, Youngser Park, and Carey E. Priebe. 2019. “A Central Limit Theorem for an Omnibus Embedding of Multiple Random Graphs and Implications for Multiscale Network Inference.” June 25, 2019. http://arxiv.org/abs/1705.09355.
Lin, Qiaohui, Robert Lunde, and Purnamrita Sarkar. 2020. “On the Theoretical Properties of the Network Jackknife.” April 21, 2020. http://arxiv.org/abs/2004.08935.
Patone, Martina, and Li-Chun Zhang. 2020. “Incidence Weighting Estimation Under Bipartite Incidence Graph Sampling.” April 8, 2020. http://arxiv.org/abs/2004.04257.
Salamanos, Nikos, Elli Voudigari, and Emmanuel J. Yannakoudakis. n.d. “Deterministic Graph Exploration for Efficient Graph Sampling.” Social Network Analysis and Mining 7 (1). Accessed June 24, 2019. https://www.academia.edu/33645796/Deterministic_graph_exploration_for_efficient_graph_sampling.
Sanguiao Sande, Luis, and Li-Chun Zhang. 2020. “Design-Unbiased Statistical Learning in Survey Sampling.” Sankhya: The Indian Journal of Statistics, October. https://doi.org/10.1007/s13171-020-00224-1.
Shalizi, Cosma Rohilla, and Alessandro Rinaldo. 2013. “Consistency Under Sampling of Exponential Random Graph Models.” Annals of Statistics 41 (2): 508–35. https://doi.org/10.1214/12-AOS1044.
Snijders, Tom A. B. 2010. “Conditional Marginalization for Exponential Random Graph Models.” The Journal of Mathematical Sociology 34 (4): 239–52. https://doi.org/10.1080/0022250X.2010.485707.
Stumpf, Michael P. H., Carsten Wiuf, and Robert M. May. 2005. “Subnets of Scale-Free Networks Are Not Scale-Free: Sampling Properties of Networks.” Proceedings of the National Academy of Sciences of the United States of America 102 (12): 4221–24. https://doi.org/10.1073/pnas.0501179102.
Vega-Oliveros, Didier. n.d. “Influence Maximization Based on the Least Influential Spreaders.” Accessed June 24, 2019. https://www.academia.edu/14829584/Influence_maximization_based_on_the_least_influential_spreaders.
Yannakoudakis, Emmanuel J., Elli Voudigari, and Nikos Salamanos. 2020. “Identifying Influential Spreaders by Graph Sampling.” 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. https://www.academia.edu/29619024/Identifying_Influential_Spreaders_by_Graph_Sampling.
Zhang, L.-C., and M. Patone. 2017. “Graph Sampling.” METRON 75 (3): 277–99. https://doi.org/10.1007/s40300-017-0126-y.
Zhang, Li-Chun, and Nancy Nguyen. 2020. “An Appraisal of Common Reweighting Methods for Nonresponse in Household Surveys Based on Norwegian Labour Force Survey and Statistics on Income and Living Conditions Survey.” Journal of Official Statistics 36 (1, 1): 151–72. https://doi.org/10.2478/JOS-2020-0008.
Zhang, Li-Chun, and Melike Oguz-Alper. 2020. BIG Sampling.” March 20, 2020. http://arxiv.org/abs/2003.09467.

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