Fast inference for the latent space network model using a case-control approximate likelihood

Adrian E. Raftery, Xiaoyue Niu, Peter D. Hoff, Ka Yee Yeung

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


Network models are widely used in social sciences and genome sciences. The latent space model proposed by Hoff et al. (2002), and extended by Handcock et al. (2007) 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(N2), whereNis 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 loglikelihood, 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(N2) 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.

Original languageEnglish (US)
Pages (from-to)901-919
Number of pages19
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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