Numerical approximations for speeding up MCMC inference in the infinite relational model

The infinite relational model (IRM) is a powerful model for discovering clusters in complex networks; however, the computational speed of Markov chain Monte Carlo inference in the model can be a limiting factor when analyzing large networks. We investigate how using numerical approximations of the log-Gamma function in evaluating the likelihood of the IRM can improve the computational speed of MCMC inference, and how it affects the performance of the model. Using an ensemble of networks generated from the IRM, we compare three approximations in terms of their generalization performance measured on test data. We demonstrate that the computational time for MCMC inference can be reduced by a factor of two without affecting the performance, making it worthwhile in practical situations when on a computational budget.