[Ml-stat-talks] Wed: Anima Anandkumar on spectral methods

David Mimno mimno at CS.Princeton.EDU
Mon Apr 22 14:16:40 EDT 2013


Spectral methods have recently become popular in machine learning for two
reasons that should please everybody: they allow us to prove bounds on
performance, and they can be extremely efficient. This week we welcome
Anima Anandkumar from UC Irvine, who will discuss recent work in community
detection.

Anima Anandkumar, UC Irvine
Wed, Apr 23, 12:30, CS402

Title: A Tensor Spectral Approach to Learning Mixed
Membership Community Models

Abstract: 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.

Bio: 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.
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