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 TITLE: Graphical Model Selection: Trees, Latent Trees, and Beyond
SPEAKER: Anima Anandkumar (UC Irvine)
DATE: 3:00 - 4:00 PM, Thursday, June 9, 2011
LOCATION: Eureka, 1U
ABSTRACT:
Capturing complex interactions among a large set of variables is a
challenging task. Probabilistic graphical models or Markov random
fields provide a graph-based framework for capturing such
dependencies. This interdisciplinary topic has found widespread
applications in computer vision, bioinformatics, combinatorial
optimization and machine learning. Graph estimation is an important
task, since it reveals important relationships among the variables.
In the first part of my talk, I will present a unified view of graph
estimation and propose a simple local algorithm for graph estimation
using only low-order statistics of the data. We establish that the
algorithm has consqistent graph estimation with low sample complexity
for a class of graphical models satisfying certain structural and
parameter criteria. We explicitly characterize these model classes and
point out interesting relationships between the graph structure and
the parameter regimes, required for tractable learning. Many graph
families such as the classical Erdos-Renyi random graphs, random
regular graphs, and the small-world graphs can be learnt efficiently
under our framework.
The second part of my talk is motivated by the following question: can
we discover hidden influences acting on the observed variables? We
consider latent tree models for capturing hidden relationships. We
develop novel algorithms for learning the unknown tree structure. Our
algorithm is amenable to efficient implementation of the Bayesian
Information Criterion (BIC) to tradeoff the number of hidden variables
with the accuracy of the model fitting. Experiment on the S&P 100
financial data reveals sectorization of the companies and experiment
on the newsgroups data automatically categorizes words into different
topics.
BIOGRAPHY:
Anima Anandkumar has been a faculty at the EECS Dept. at U.C.Irvine
since Aug. 2010. She was previously at the Stochastic Systems Group at
MIT as a post-doctoral researcher with Alan Willsky. She received her
B.Tech in Electrical Engineering from IIT Madras in 2004 and her PhD
from Cornell University in 2009. She is the recipient of the 2009
Best Thesis Award by the ACM Sigmetrics Society, 2008 IEEE Signal
Processing Society Young Author Best Paper Award and 2008 IBM Fran
Allen PhD fellowship. Her primary research focus is on inference and
learning of graphical models.
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