Covariance Estimation in Decomposable Gaussian Graphical Models

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