Inference on social graphs

Heterogeneous media and controls


Fun keywords: Egocentric sampling, graph sampling, friendship paradox, majority illusion, and the analysis of projectivity. πŸ—

Majority Illusions and filter bubbles

In homophilic networks (0.5 ≀ h ≀ 1), the minority overestimates their own size (filter bubble) and the majority underestimates the size of the minority. The insets show the same information on log scale to make the amount of underestimation and overestimation comparable. As group sizes become more disproportionate, perception bias increases. (Lerman, Yan, and Wu 2016)

This insight is one of those ones that seems trivial in hindsight, but people are terrible at articulating in advance. Related, perhaps a consequence of this, is pluralistic ignorance

Confounding on graphs

Cosma Shalizi, Return of β€œHomophily, Contagion, Confounding: Pick Any Three”, or, The Adventures of Irene and Joey Along the Back-Door Paths and sequel. and Experiments on Social Networks. See also his Neutral cultural networks stuff.

My colleague at UNSW, Pavel Krivitsky is highly productive in this area, especially with the exponential family random graph (pronounced β€œergum”.) model, and I will list the articles he wrote so that I can pester him for details: (Hunter, Krivitsky, and Schweinberger 2012; Kolaczyk and Krivitsky 2015; Krivitsky and Morris 2017; Krivitsky et al. 2009; Krivitsky and Handcock 2014)


Michele Coscia. Michele Coscia’s new paper uses a graph Laplacian to calculate an approximate Earth mover distance over a graph topology. (buzzword use case: inferring graph transmission rate of a disease interpretably). This looks simple; surely it must be a known result in optimal transport metric studies?

For models, specifically, of actual disease contagion, see Shalizi’s review of Kiss, Miller, and Simon (2017).


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Aral, Sinan, Lev Muchnik, and Arun Sundararajan. 2009. β€œDistinguishing Influence-Based Contagion from Homophily-Driven Diffusion in Dynamic Networks.” Proceedings of the National Academy of Sciences 106 (51): 21544–49.
Baker, Antoine, Indaco Biazzo, Alfredo Braunstein, Giovanni Catania, Luca Dall’Asta, Alessandro Ingrosso, Florent Krzakala, et al. 2021. β€œEpidemic Mitigation by Statistical Inference from Contact Tracing Data.” Proceedings of the National Academy of Sciences 118 (32).
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Coscia, Michele. 2017. β€œPopularity Spikes Hurt Future Chances for Viral Propagation of Protomemes.” Communications of the ACM 61 (1): 70–77.
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Gomez-Rodriguez, Manuel, Jure Leskovec, and Andreas Krause. 2012. β€œInferring Networks of Diffusion and Influence.” ACM Trans. Knowl. Discov. Data 5 (4): 21:1–37.
Gonzalez-Bailon, Sandra. 2009. β€œOpening the Black Box of Link Formation: Social Factors Underlying the Structure of the Web.” Social Networks 31 (4): 271–80.
Goyal, Amit, Francesco Bonchi, and Laks V. S. Lakshmanan. 2011. β€œA Data-Based Approach to Social Influence Maximization.” In Proc. VLDB Endow., 5:73–84.
Goyal, Amit, Francesco Bonchi, and Laks V.S. Lakshmanan. 2010. β€œLearning Influence Probabilities in Social Networks.” In Proceedings of the Third ACM International Conference on Web Search and Data Mining, 241–50. WSDM ’10. New York, NY, USA: ACM.
Green, Alden, and Cosma Rohilla Shalizi. 2017. β€œBootstrapping Exchangeable Random Graphs.” arXiv:1711.00813 [Stat], November.
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Harris, Jenine K. 2013. An Introduction to Exponential Random Graph Modeling. SAGE Publications.
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β€”β€”β€”. 2014. β€œNetworks in the Understanding of Economic Behaviors.” Journal of Economic Perspectives 28 (4): 3–22.
β€”β€”β€”. 2018. β€œThe Friendship Paradox and Systematic Biases in Perceptions and Social Norms.” Journal of Political Economy 127 (2): 777–818.
Jaeger, Manfred, and Oliver Schulte. 2021. β€œA Complete Characterization of Projectivity for Statistical Relational Models.” In Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, 4283–90. IJCAI’20. Yokohama, Yokohama, Japan.
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Krivitsky, Pavel N., and Mark S. Handcock. 2014. β€œA Separable Model for Dynamic Networks.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76 (1): 29–46.
Krivitsky, Pavel N., Mark S. Handcock, Adrian E. Raftery, and Peter D. Hoff. 2009. β€œRepresenting Degree Distributions, Clustering, and Homophily in Social Networks with Latent Cluster Random Effects Models.” Social Networks 31 (3): 204–13.
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