# Covariance Estimation in Decomposable Gaussian Graphical Models

@article{Wiesel2010CovarianceEI, title={Covariance Estimation in Decomposable Gaussian Graphical Models}, author={Ami Wiesel and Yonina C. Eldar and Alfred O. Hero}, journal={IEEE Transactions on Signal Processing}, year={2010}, volume={58}, pages={1482-1492} }

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…

## 46 Citations

Distributed Covariance Estimation in Gaussian Graphical Models

- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 2012

This work proposes to improve the MSE performance by introducing additional symmetry constraints using averaging and pseudolikelihood estimation approaches, and compute the proposed estimates using message passing protocols, which can be efficiently implemented in large scale graphical models with many nodes.

Distributed Covariance Estimation in

- Computer Science, Mathematics
- 2012

This work proposes to improve the MSE performance by introducing additionalsymmetry constraints using averaging and pseudolikelihood estimation approaches, and compute the proposed estimates using message passing protocols, which can be efficiently implemented in large scale graphical models with many nodes.

Distributed Learning of Gaussian Graphical Models via Marginal Likelihoods

- Computer Science, MathematicsAISTATS
- 2013

This paper proposes a general framework for distributed estimation based on a maximum marginal likelihood (MML) approach, and derives and considers solving a convex relaxation of the MML problem, and proves that this relaxed MML estimator is asymptotically consistent.

Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

- MathematicsIEEE Transactions on Signal Processing
- 2013

This work considers covariance estimation in the multivariate generalized Gaussian distribution and shows that the optimizations can be formulated as convex minimization as long the MGGD shape parameter is larger than half and the sparsity pattern is chordal.

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

- MathematicsOper. Res.
- 2022

Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depend…

Joint Learning of Multiple Sparse Matrix Gaussian Graphical Models

- Computer ScienceIEEE Transactions on Neural Networks and Learning Systems
- 2015

The proposed approach borrows strength across the different graphical models and is based on the maximum likelihood with penalized row and column precision matrices, respectively, and is more parsimonious and flexible than the joint vector graphical models.

Iterative Reconstruction of High-Dimensional Gaussian Graphical Models Based on a New Method to Estimate Partial Correlations under Constraints

- MathematicsPloS one
- 2013

This work presents a simple procedure, called PACOSE, to estimate partial correlations under the constraint that some of them are strictly zero, and shows on simulated and real data that iPACOSE shows very interesting properties with regards to sensitivity, positive predictive value and stability.

Regularized Estimation of High-dimensional Covariance Matrices.

- Computer Science, Mathematics
- 2011

This dissertation attempts to develop necessary components for covariance estimation in the high-dimensional setting by introducing a state-of-the-art sampling system, the Modulated Wideband Converter (MWC), which is capable of achieving sub-Nyquist sampling for multiband signals with arbitrary carrier frequency over a wide bandwidth.

Multiple Gaussian graphical estimation with jointly sparse penalty

- Computer ScienceSignal Process.
- 2016

Approximate least squares parameter estimation with structured observations

- Mathematics, Computer Science2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2014

This work considers the situation where it is not appropriate to assume a structure for the parameter, but the observations on which the estimate are based are structured; specifically, when the observations are parametrized by a decomposable graphical model.

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