Publication: D-Trace precision matrix estimator with eigenvalue control
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2016-07
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Abstract
The estimation of a precision matrix has an important role in several research fields. In high-dimensional settings, one of the most prominent approaches to estimate the
precision matrix is the ɭ₁ (Lasso) norm penalized convex optimization. This framework
guarantees the sparsity of the estimated precision matrix. However, it does not control
the eigenspectrum of the obtained estimator, and, moreover, it shrinks the largest
eigenvalues of the estimated precision matrix. In this paper, we focus on D-trace
precision matrix methodology. We propose imposing a negative trace penalization on
the objective function of the D-trace approach, aimed to control the eigenvalues.
Through extensive numerical analysis, using simulated and real datasets, we show the
advantageous performance of our proposed methodology.
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Gaussian Graphical Model, Hannan-Quinn Information Criterion, D-trace, Gene expression, Trace penalization