Fast Inference for the Latent Space Network Model Using a Case-Control Approximate Likelihood

摘要

Network models are widely used in social sciences and genome sciences. The latent space model proposed by Hoff et al. (200217. Hoff , P. D. , Raftery , A. E. and Handcock , M. S. 2002 . “Latent Space Approaches to Social Network Analysis,” . Journal of the American Statistical Association , 97 : 1090 - 1098 . View all references), and extended by Handcock et al. (200715. Handcock , M. S. , Raftery , A. E. and Tantrum , J. M. 2007 . “Model-Based Clustering for Social Networks” (with discussion), . Journal of the Royal Statistical Society, Series A , 170 : 301 - 354 . View all references) to incorporate clustering, provides a visually interpretable model-based spatial representation of relational data and takes account of several intrinsic network properties. Due to the structure of the likelihood function of the latent space model, the computational cost is of order O(N 2), where N is the number of nodes. This makes it infeasible for large networks. In this article, we propose an approximation of the log-likelihood function. We adapt the case-control idea from epidemiology and construct a case-control log-likelihood, which is an unbiased estimator of the log-full likelihood. Replacing the full likelihood by the case-control likelihood in the Markov chain Monte Carlo estimation of the latent space model reduces the computational time from O(N 2) to O(N), making it feasible for large networks. We evaluate its performance using simulated and real data. We fit the model to a large protein-protein interaction data using the case-control likelihood and use the model fitted link probabilities to identify false positive links. Supplemental materials are available online.View full textDownload full textKey WordsClustering, Genome science, Graph, Markov chain Monte Carlo, Protein-protein interaction, Social networkRelated var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/10618600.2012.679240