Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(12)
bayesian estimator
Conditional Independence
Covariance Matrix
Estimation Error
Gaussian Graphical Model
Gaussian Random Field
Graphical Model
Minimum Mean Square Error
Noise Measurement
Random Field
Satisfiability
Maximum Likelihood
Subscribe
Academic
Publications
Optimal covariance selection for estimation using graphical models
Optimal covariance selection for estimation using graphical models,Sergey Vichik,Yaakov Oshman
Edit
Optimal covariance selection for estimation using graphical models
BibTex

RIS

RefWorks
Download
Sergey Vichik
,
Yaakov Oshman
We consider a problem encountered when trying to estimate a
Gaussian random field
using a distributed esti mation approach based on Gaussian graphical models. Because of constraints imposed by estimation tools used in Gaussian graphical models, the a priori covariance of the
random field
is constrained to embed
conditional independence
constraints among a significant number of variables. The problem is, then: given the (unconstrained) a priori covariance of the random field, and the
conditional independence
constraints, how should one select the constrained covariance, optimally representing the (given) a priori covariance, but also satisfying the constraints? In 1972, Dempster provided a solution, optimal in the
maximum likelihood
sense, to the above problem. Since then, many works have used Dempster's optimal covariance, but none has addressed the issue of suitability of this covariance for Bayesian estimation problems. We prove that Dempster's covariance is not optimal in most minimum mean squared error (MMSE) estimation problems. We also propose a method for finding the MMSE optimal covariance, and study its properties. We then illustrate the analytical results via a numerical exam ple, that demonstrates the estimation performance advantage gained by using the optimal covariance vs Dempster's covari ance. The numerical example also shows that, for the particular estimation scenario examined, Dempster's covariance violates the necessary conditions for optimality. I. INTRODUCTION
Published in 2011.
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
ieeexplore.ieee.org
)
(
ieeexplore.ieee.org
)
References
(17)
Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models
(
Citations: 151
)
A. P. Dawid
,
S. L. Lauritzen
Journal:
Annals of Statistics  ANN STATIST
, vol. 21, no. 1993, pp. 12721317, 1993
Covariance matrix selection and estimation via penalised normal likelihood
(
Citations: 67
)
Jianhua Z. Huang
,
Naiping Liu
,
Mohsen Pourahmadi
,
Linxu Liu
Journal:
Biometrika
, vol. 93, no. 1, pp. 8598, 2006
An approximation to maximum likelihood estimates in reduced models
(
Citations: 17
)
D. R. COX
,
NANNY WERMUTH
Journal:
Biometrika
, vol. 77, no. 4, pp. 747761, 1990
Maximum likelihood estimation of Gaussian graphical models: Numerical implementation and topology selection
(
Citations: 11
)
Joachim Dahl
,
Vwani Roychowdhury
,
Lieven Vandenberghe
A SINful approach to Gaussian graphical model selection
(
Citations: 14
)
Mathias Drton
,
Michael D. Perlman
Journal:
Journal of Statistical Planning and Inference  J STATIST PLAN INFER
, vol. 138, no. 4, pp. 11791200, 2008