Tuning the Parameters for Precision Matrix Estimation Using Regression Analysis

Precision matrix, i.e., inverse covariance matrix, is widely used in signal processing, and often estimated from training samples. Regularization techniques, such as banding and rank reduction, can be applied to the covariance matrix or precision matrix estimation for improving the estimation accuracy when the training samples are limited. In this paper, exploiting regression interpretations of the precision matrix, we introduce two data-driven, distribution-free methods to tune the parameter for regularized precision matrix estimation. The numerical examples are provided to demonstrate the effectiveness of the proposed methods and example applications in the design of minimum mean squared error (MMSE) channel estimators for large-scale multiple-input multiple-output (MIMO) communication systems are demonstrated.