Small-Variance Asymptotics for Nonparametric Bayesian Overlapping\n Stochastic Blockmodels

The latent feature relational model (LFRM) is a generative model for\ngraph-structured data to learn a binary vector representation for each node in\nthe graph. The binary vector denotes the node's membership in one or more\ncommunities. At its core, the LFRM miller2009nonparametric is an overlapping\nstochastic blockmodel, which defines the link probability between any pair of\nnodes as a bilinear function of their community membership vectors. Moreover,\nusing a nonparametric Bayesian prior (Indian Buffet Process) enables learning\nthe number of communities automatically from the data. However, despite its\nappealing properties, inference in LFRM remains a challenge and is typically\ndone via MCMC methods. This can be slow and may take a long time to converge.\nIn this work, we develop a small-variance asymptotics based framework for the\nnon-parametric Bayesian LFRM. This leads to an objective function that retains\nthe nonparametric Bayesian flavor of LFRM, while enabling us to design\ndeterministic inference algorithms for this model, that are easy to implement\n(using generic or specialized optimization routines) and are fast in practice.\nOur results on several benchmark datasets demonstrate that our algorithm is\ncompetitive to methods such as MCMC, while being much faster.\n