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A Review of Latent Space Models for Social Networks
Una revisión de modelos de espacio latente para redes sociales
DOI:
https://doi.org/10.15446/rce.v44n1.89369Keywords:
Bayesian Inference, Markov chain Monte Carlo, Latent Space Models, Social Networks (en)Cadena de Makov de Monte Carlo, Inferencia Bayesiana, Modelo de espacio latente, Redes sociales (es)
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In this paper, we provide a review on both fundamentals of social networks and latent space modeling. The former discusses important topics related to network description, including vertex characteristics and network structure; whereas the latter articulates relevant advances in network modeling, including random graph models, generalized random graph models, exponential random graph models, and social space models. We discuss in detail several latent space models provided in literature, providing special attention to distance, class, and eigen models in the context of undirected, binary networks. In addition, we also examine empirically the behavior of these models in terms of prediction and goodness-of-fit using more than twenty popular datasets of the network literature.
temas importantes relacionados con la descripción de la red, incluidas las características de los vértices y la estructura de la red; mientras que la segunda articula avances relevantes en el modelado de redes, incluidos modelos de grafos aleatorios, modelos de grafos aleatorios generalizados, modelos de grafos aleatorios exponenciales y modelos de espacio social. Discutimos en detalle varios modelos de espacio latente proporcionados en la literatura, prestando especial atención a los modelos de distancia, clase y eigen, en el contexto de redes binarias no dirigidas. Además, también examinamos empíricamente el comportamiento de estos modelos en términos de predicción y bondad de ajuste utilizando más de veinte conjuntos de datos populares de la literatura de redes.
References
Airoldi, E. M., Blei, D. M., Fienberg, S. E. & Xing, E. P. (2009), Mixed membership stochastic blockmodels, in ‘Advances in Neural Information Processing Systems’, pp. 33–40.
Albert, J. H. & Chib, S. (1993), ‘Bayesian analysis of binary and polychotomous response data’, Journal of the American Statistical Association 88(422), 669–679.
Aldous, D. J. (1985), Exchangeability and related topics, Springer. Barabási, A.-L. & Albert, R. (1999), ‘Emergence of scaling in random networks’, Science 286(5439), 509–512.
Bender, E. A. & Canfield, E. R. (1978), ‘The asymptotic number of labeled graphs with given degree sequences’, Journal of Combinatorial Theory, Series A 24(3), 296–307.
Bollobás, B. (1998), Random graphs, Springer.
Borg, I. & Groenen, P. J. (2005), Modern multidimensional scaling: Theory and applications, Springer Science & Business Media.
Chung, F. & Lu, L. (2006), Complex graphs and networks, Vol. 107, American Mathematical society Providence.
Crane, H. (2018), Probabilistic foundations of statistical network analysis, CRC Press.
Durante, D., Dunson, D. B. et al. (2018), ‘Bayesian inference and testing of group differences in brain networks’, Bayesian Analysis 13(1), 29–58.
Erdös, P. & Rényi, A. (1959), ‘On random graphs’, Publicationes Mathematicae 6(290-297), 5.
Erdös, P. & Rényi, A. (1960), ‘On the evolution of random graphs’, Publ. Math. Inst. Hung. Acad. Sci 5, 17–61.
Erdös, P. & Rényi, A. (1961), ‘On the strength of connectedness of a random graph’, Acta Mathematica Hungarica 12(1-2), 261–267.
Fortunato, S. (2010), ‘Community detection in graphs’, Physics reports 486(3), 75–174.
Frank, O. & Strauss, D. (1986), ‘Markov graphs’, Journal of the American Statistical association 81(395), 832–842.
Gamerman, D. & Lopes, H. F. (2006), Markov chain Monte Carlo: stochastic simulation for Bayesian inference, CRC Press.
Gelman, A., Hwang, J. & Vehtari, A. (2014), ‘Understanding predictive information criteria for Bayesian models’, Statistics and Computing 24(6), 997–1016.
Gelman, A. & Rubin, D. (1992), ‘Inferences from iterative simulation using multiple sequences’, Statistical Science 7, 457–472.
Gilbert, E. (1959), ‘Random graphs’, The Annals of Mathematical Statistics pp. 1141–1144.
Goldenberg, A., Zheng, A., Fienberg, S. & Airoldi, E. (2010), ‘A survey of statistical network models’, Foundations and Trends in Machine Learning 2(2), 129–233.
Green, P. J. & Hastie, D. I. (2009), ‘Reversible jump MCMC, Genetics 155(3), 1391–1403.
Guhaniyogi, R. & Rodriguez, A. (2020), ‘Joint modeling of longitudinal relational data and exogenous variables’, Bayesian Analysis.
Han, Q., Xu, K. & Airoldi, E. (2015), Consistent estimation of dynamic and multi-layer block models, in ‘International Conference on Machine Learning’, pp. 1511–1520.
Handcock, M. S., Raftery, A. E. & Tantrum, J. M. (2007), ‘Model-based clustering for social networks’, Journal of the Royal Statistical Society: Series A (Statistics in Society) 170(2), 301–354.
Handcock, M. S., Robins, G., Snijders, T., Moody, J. & Besag, J. (2003), Assessing degeneracy in statistical models of social networks, Technical report, Citeseer.
Hoff, P. D. (2005), ‘Bilinear mixed-effects models for dyadic data’, Journal of the American Statistical Association 100(469), 286–295.
Hoff, P. D. (2008), Modeling homophily and stochastic equivalence in symmetric relational data, in ‘Advances in Neural Information Processing Systems’, pp. 657–664.
Hoff, P. D. (2009), ‘Multiplicative latent factor models for description and prediction of social networks’, Computational and Mathematical Organization Theory 15(4), 261–272.
Hoff, P. D. (2015), ‘Multilinear tensor regression for longitudinal relational data’, The annals of applied statistics 9(3), 1169.
Hoff, P. D., Raftery, A. E. & Handcock, M. S. (2002), ‘Latent space approaches to social network analysis’, Journal of the American Statistical association 97(460), 1090–1098.
Hoover, D. N. (1982), ‘Row-column exchangeability and a generalized model for probability’, Exchangeability in probability and statistics (Rome, 1981) pp. 281–291.
Ishwaran, H. & Zarepour, M. (2000), ‘Markov chain monte Carlo in approximate dirichlet and beta two-parameter process hierarchical models’, Biometrika 87(2), 371–390.
Kemp, C., Tenenbaum, J. B., Griffiths, T. L., Yamada, T. & Ueda, N. (2006), Learning systems of concepts with an infinite relational model, in ‘AAAI’, Vol. 3, p. 5.
Kim, B., Lee, K. H., Xue, L. & Niu, X. (2018), ‘A review of dynamic network models with latent variables’, Statistics surveys 12, 105.
Kolaczyk, E. D. (2009), Statistical Analysis of Network Data: Methods and Models, Springer Series in Statistics, Springer.
Kolaczyk, E. D. & Csárdi, G. (2020), Statistical analysis of network data with R, 2nd edn, Springer.
Krivitsky, P. N. & Handcock, M. S. (2008), ‘Fitting latent cluster models for networks with latentnet’, Journal of Statistical Software 24(5).
Krivitsky, P. N., Handcock, M. S., Raftery, A. E. & Hoff, P. D. (2009), ‘Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models’, Social networks 31(3), 204–213.
Lau, J. W. & Green, P. J. (2007), ‘Bayesian model-based clustering procedures’, Journal of Computational and Graphical Statistics 16(3), 526–558.
Li, W.-J., Yeung, D.-Y. & Zhang, Z. (2011), Generalized latent factor models for social network analysis, in ‘Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), Barcelona, Spain’.
Linkletter, C. D. (2007), Spatial process models for social network analysis, PhD thesis, Simon Fraser University.
Lusher, D., Koskinen, J. & Robins, G. (2012), Exponential random graph models for social networks: Theory, methods, and applications, Cambridge University Press.
Minhas, S., Hoff, P. D. & Ward, M. D. (2019), ‘Inferential approaches for network analysis: Amen for latent factor models’, Political Analysis 27(2), 208–222.
Newman, M. (2010), Networks: An Introduction, Oxford University Press.
Newman, M. & Watts, D. J. (1999), ‘Scaling and percolation in the small-world network model’, Physical Review E 60(6), 7332.
Nowicki, K. & Snijders, T. (2001), ‘Estimation and prediction for stochastic blockstructures’, Journal of the American Statistical Association 96(455), 1077–1087.
Paez, M. S., Amini, A. A. & Lin, L. (2019), ‘Hierarchical stochastic block model for community detection in multiplex networks’, arXiv preprint arXiv:1904.05330 .
Polson, N. G., Scott, J. G. & Windle, J. (2013), ‘Bayesian inference for logistic models using Pólya-Gamma latent variables’, Journal of the American Statistical Association 108(504), 1339–1349.
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