Title: Small-Variance Asymptotics for Nonparametric Bayesian Overlapping Stochastic Blockmodels,
Abstract: The latent feature relational model (LFRM) is a generative model for
graph-structured data to learn a binary vector representation for each node in
the graph. The binary vector denotes the node's membership in one or more
communities. At its core, the LFRM miller2009nonparametric is an overlapping
stochastic blockmodel, which defines the link probability between any pair of
nodes as a bilinear function of their community membership vectors. Moreover,
using a nonparametric Bayesian prior (Indian Buffet Process) enables learning
the number of communities automatically from the data. However, despite its
appealing properties, inference in LFRM remains a challenge and is typically
done via MCMC methods. This can be slow and may take a long time to converge.
In this work, we develop a small-variance asymptotics based framework for the
non-parametric Bayesian LFRM. This leads to an objective function that retains
the nonparametric Bayesian flavor of LFRM, while enabling us to design
deterministic inference algorithms for this model, that are easy to implement
(using generic or specialized optimization routines) and are fast in practice.
Our results on several benchmark datasets demonstrate that our algorithm is
competitive to methods such as MCMC, while being much faster.