Publication: D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties
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2015-10-01
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Abstract
An accurate estimation of a precision matrix has a crucial role in the current age of high-dimensional data explosion. To deal with this problem, one of the prominent and commonly used techniques is the l1 norm (Lasso) penalization for a given loss function. This approach guarantees the sparsity of the precision matrix estimator for properly selected penalty parameters. However, the l1 norm penalization often fails to control the bias of the obtained estimator because of its overestimation behavior. In this paper, we introduce two adaptive extensions of the recently proposed l1 norm penalized D-trace loss minimization method. The proposed approaches intend to diminish the produced bias in the estimator. Extensive numerical results, using both simulated and real datasets, show the advantage of our proposed estimators.
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Adaptive lasso, D-trace loss, Gaussian Graphical Model, Gene expression data, High-dimensionality