Abstract
Understanding edge formation represents a key question in network analysis. Various approaches have been postulated across disciplines ranging from network growth models to statistical (regression) methods. In this work, we extend this existing arsenal of methods with a hypotheses-driven Bayesian approach that allows to intuitively compare hypotheses about edge formation on attributed multigraphs. We model the multiplicity of edges using a simple categorical model and propose to express hypotheses as priors encoding our belief about parameters. Using Bayesian model comparison techniques, we compare the relative plausibility of hypotheses which might be motivated by previous theories about edge formation based on popularity or similarity. We demonstrate the utility of our approach on synthetic and empirical data. This work is relevant for researchers interested in studying mechanisms explaining edge formation in networks.
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References
Adamic, L.A., Glance, N.: The political blogosphere and the 2004 us election: divided they blog. In: Proceedings of the 3rd int. workshop on Link discovery, pp. 36–43. ACM (2005)
Casiraghi, G., Nanumyan, V., Scholtes, I., Schweitzer, F.: Generalized hypergeometric ensembles: Statistical hypothesis testing in complex networks. arXiv:1607.02441 (2016)
Goldenberg, A., Zheng, A.X., Fienberg, S.E., Airoldi, E.M.: A survey of statistical network models. Foundations and TrendsR in Machine Learning 2(2), 129–233 (2010)
Holland, P.W., Leinhardt, S.: An exponential family of probability distributions for directed graphs. Journal of the american Statistical association 76(373), 33–50 (1981)
Hubert, L., Schultz, J.: Quadratic assignment as a general data analysis strategy. British journal of mathematical and statistical psychology 29(2), 190–241 (1976)
Karrer, B., Newman, M.E.: Stochastic blockmodels and community structure in networks. Physical Review E 83(1), 016,107 (2011)
Kass, R.E., Raftery, A.E.: Bayes factors. Journal of the American Statistical Association 90(430), 773–795 (1995)
Kim, M., Leskovec, J.: Modeling social networks with node attributes using the multiplicative attribute graph model. In: UAI 2011, Barcelona, Spain, July 14-17, 2011, pp. 400–409 (2011)
Kiti, M.C., Tizzoni, M., Kinyanjui, T.M., Koech, D.C., Munywoki, P.K., Meriac, M., Cappa, L., Panisson, A., Barrat, A., Cattuto, C., et al.: Quantifying social contacts in a household setting of rural kenya using wearable proximity sensors. EPJ Data Science 5(1), 1 (2016)
Krackhardt, D.: Predicting with networks: Nonparametric multiple regression analysis of dyadic data. Social networks 10(4), 359–381 (1988)
Kruschke, J.: Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press (2014)
Martin, T., Ball, B., Karrer, B., Newman, M.: Coauthorship and citation patterns in the physical review. Physical Review E 88(1), 012,814 (2013)
Moreno, S., Neville, J.: Network hypothesis testing using mixed kronecker product graph models. In: Data Mining (ICDM), pp. 1163–1168. IEEE (2013)
Nguyen, H.T.: Multiple hypothesis testing on edges of graph: a case study of bayesian networks
Papadopoulos, F., Kitsak, M., Serrano, M.Á ., Boguná, M., Krioukov, D.: Popularity versus similarity in growing networks. Nature 489(7417), 537–540 (2012)
Pfeiffer III, J.J., Moreno, S., La Fond, T., Neville, J., Gallagher, B.: Attributed graph models: Modeling network structure with correlated attributes. In: WWW, pp. 831–842. ACM (2014)
Robins, G., Pattison, P., Kalish, Y., Lusher, D.: An introduction to exponential random graph (p*) models for social networks. Social networks 29(2), 173–191 (2007)
Sampson, S.F.: A novitiate in a period of change: An experimental and case study of social relationships. Cornell University (1968)
Schwiebert, L., Gupta, S.K., Weinmann, J.: Research challenges in wireless networks of biomedical sensors. In: Proceedings of the 7th annual international conference on Mobile computing and networking, pp. 151–165. ACM (2001)
Shah, K.R., Sinha, B.K.: Mixed Effects Models, pp. 85–96. Springer New York (1989)
Singer, P., Helic, D., Hotho, A., Strohmaier, M.: Hyptrails: A bayesian approach for comparing hypotheses about human trails on the web. WWW, pp. 1003–1013. ACM (2015)
Singer, P., Helic, D., Taraghi, B., Strohmaier, M.: Detecting memory and structure in human navigation patterns using markov chain models of varying order. PloS one 9(7), e102,070 (2014)
Snijders, T., Spreen, M., Zwaagstra, R.: The use of multilevel modeling for analysing personal networks: Networks of cocaine users in an urban area. Journal of quantitative anthropology 5(2), 85–105 (1995)
Snijders, T.A.: Statistical models for social networks. Review of Sociology 37, 131–153 (2011)
Tu, S.: The dirichlet-multinomial and dirichlet-categorical models for bayesian inference. Computer Science Division, UC Berkeley (2014)
Winter, B.: Linear models and linear mixed effects models in r with linguistic applications. arXiv:1308.5499 (2013)
Xiang, R., Neville, J., Rogati, M.: Modeling relationship strength in online social networks. In: WWW, pp. 981–990. ACM (2010)
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Espín-Noboa, L., Lemmerich, F., Strohmaier, M., Singer, P. (2017). A Hypotheses-driven Bayesian Approach for Understanding Edge Formation in Attributed Multigraphs. In: Cherifi, H., Gaito, S., Quattrociocchi, W., Sala, A. (eds) Complex Networks & Their Applications V. COMPLEX NETWORKS 2016 2016. Studies in Computational Intelligence, vol 693. Springer, Cham. https://doi.org/10.1007/978-3-319-50901-3_1
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DOI: https://doi.org/10.1007/978-3-319-50901-3_1
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