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SUMMARY:A Tensor Spectral Approach to Learning Mixed Membership Community 
 Models - Anandkumar \, A (University of California\, Irvine)
DTSTART:20130813T090000Z
DTEND:20130813T094500Z
UID:TALK46607@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Rong Ge (Princeton)\, Daniel Hsu (Microsoft Resear
 ch)\, Sham Kakade (Microsoft Research) \n\nModeling community formation an
 d detecting hidden communities in networks is a well studied problem. Howe
 ver\, theoretical analysis of community detection has been mostly limited 
 to models with non-overlapping communities such as the stochastic block mo
 del. 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. 2
 008. This model allows for nodes to have fractional memberships in multipl
 e communities and assumes that the community memberships are drawn from a 
 Dirichlet distribution. We propose a unified approach to learning these mo
 dels via a tensor spectral decomposition method. Our estimator is based on
  low-order moment tensor of the observed network\, consisting of 3-star co
 unts. Our learning method is fast and is based on simple linear algebra op
 erations\, e.g. singular value decomposition and tensor power iterations. 
 We provide guaranteed recovery of community memberships and model paramete
 rs and present a careful finite sample analysis of our learning method. Ad
 ditionally\, our results match the best known scaling requirements in the 
 special case of the stochastic block model.\n\nRelated Links 	http://newpo
 rt.eecs.uci.edu/anandkumar/pubs/AnandkumarCommunity.pdf - manuscript\n\n
LOCATION:Seminar Room 1\, Newton Institute
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