Modeling community formation and detecting hidden
communities in networks is a well studied problem. However,
theoretical analysis of community detection has been mostly limited
to models with non-overlapping communities such as the stochastic
block model. In this paper, we remove this restriction, and consider a
family of probabilistic network models with overlapping communities,
termed as the mixed membership Dirichlet model, first introduced in
Aioroldi et. al. 2008. This model allows for nodes to have fractional
memberships in multiple communities and assumes that the community
memberships are drawn from a Dirichlet distribution. We propose a
unified approach to learning these models via a tensor spectral
decomposition method. Our estimator is based on low-order moment
tensor of the observed network, consisting of 3-star counts. Our
learning method is fast and is based on simple linear algebra
operations, e.g. singular value decomposition and tensor power
iterations. We provide guaranteed recovery of community memberships
and model parameters and present a careful finite sample analysis of
our learning method. Additionally, our results match the best known
scaling requirements in the special case of the stochastic block
model. This is joint work with Rong Ge, Daniel Hsu and Sham Kakade and will appear at COLT 2013.
Anima Anandkumar has been a faculty at the EECS Dept. at U.C.Irvine since Aug. 2010. Her current research interests are in the area of high-dimensional statistics and machine learning with a focus on learning probabilistic graphical models and latent variable models. She was recently a visiting faculty at Microsoft Research New England (April-Dec. 2012). She was a post-doctoral researcher at the Stochastic Systems Group at MIT (2009-2010). She received her B.Tech in Electrical Engineering from IIT Madras (2004) and her PhD from Cornell University (2009). She is the recipient of the Microsoft Faculty Fellowship (2013), ARO Young Investigator Award (2013), NSF CAREER Award (2013), and Paper awards from Sigmetrics and Signal Processing Societies.
