A Variational Bayes Approach to Clustered Latent Preference Models for Directed Network Data
Date
2016
Authors
Lee, Jaron Jia Rong
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Abstract
Variational Bayes (VB) refers to a framework used to
make fast deterministic approximations to the posterior density
for Bayesian statistical inference. Traditionally, it has
competed with Markov Chain Monte Carlo (MCMC) methods, a
stochastic method which is asymptotically correct but
computationally expensive. We derive the VB approximation to the
Directed Clustered Latent Preference Network Model, which is
inspired by ideas from Hoff et al. (2002); Handcock et al.
(2007); Ward and Hoff (2007); Salter-Townshend and Murphy (2013);
Krivitsky and Handcock (2008). The model handles binary-valued or
continuous directed network data, and incorporates Gaussian
mixture models over the separate latent sending and receiving
preference spaces of each actor. We apply the model to simulated
and real datasets to evaluate its performance against ex- isting
MCMC methods such as the Gibbs sampler. We discover new insights
in the well-studied Sampson’s Monks dataset (Sampson, 1968), as
well as confirm existing results with the Correlates of War
International Trade dataset (Barbieri and Keshk, 2012). We
conclude by discussing unresolved issues, potential solutions,
and areas of future work.
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