Efficient Inference in the Infinite Multiple Membership Relational Model

The Indian Buffet Process (IBP) is a stochastic process on binary features that has been applied to modeling communities in complex networks [4, 5, 6]. Inference in the IBP is challenging as the potential number of possible configurations grows as 2 where K is the number of latent features and N the number of nodes in the network. We presently consider the performance of three MCMC sampling approaches for the IBP; standard Gibbs sampling, joint Gibbs sampling and non-conjugate split/merge sampling. Our results indicate that including joint sampling significantly improves on parameter inference over standard Gibbs sampling while split-merge sampling appears useful for improving the inference as measured by burn-in-time of the sampler. Introduction: Recently the Indian Buffet Process (IBP) [1] has been applied to modeling overlapping communities in networks[4, 5, 6]. We currently focus on the model proposed in [6] that is given by the following generative process Z ∼ IBP (α), σ ∼ Beta(β c , β− c ), ηlk ∼ Beta(β c , β− c ) ηlk ∼ Beta(β o , β− o ) (for l 6= k) Yij ∼ Bernoulli(1− (1− σ) ∏