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IEEE 2010 - - Covariance Estimation in Decomposable Gaussian Graphical Models by ncctrtp


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									NCCT                                   IEEE PROJECTS 2010-11
Promise for the Best Projects             JAVA & .NET
VOL. 58, NO. 3, MARCH 2010


Graphical models are a framework for representing and exploiting prior
conditional independence structures within distributions using graphs. In
the Gaussian case, these models are directly related to the sparsity of
the inverse covariance (concentration) matrix and allow for improved
covariance estimation with lower computational complexity.
We consider concentration estimation with the mean-squared error
(MSE) as the objective, in a special type of model known as
decomposable. This model includes, for example, the well known
banded structure and other cases encountered in practice.
Our first contribution is the derivation and analysis of the minimum
variance unbiased estimator (MVUE) in decomposable graphical models.
We provide a simple closed form solution to the MVUE and compare it
with the classical maximum likelihood estimator (MLE) in terms of
performance and complexity. Next, we extend the celebrated Stein’s
unbiased risk estimate (SURE) to graphical models.
Using SURE, we prove that the MSE of the MVUE is always smaller or
equal to that of the biased MLE, and that the MVUE itself is dominated
by other approaches. In addition, we propose the use of SURE as a
constructive mechanism for deriving new covariance estimators.
Similarly to the classical MLE, all of our proposed estimators have
simple closed form solutions but result in a significant reduction in MSE.

Covariance estimation, graphical models, minimum variance unbiased

      NCCT, 28235816, 93801 02891, 98411 93224,, ncctchennai@g

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