Bayesian model-averaged regularization for Gaussian graphical models

ABSTRACT

The graphical lasso has now become a useful tool to estimate high-dimensional Gaussian graphical models, but its practical applications suffer from the problem of choosing regularization parameters in a data-dependent way. In this article, we propose a model-averaged method for estimating sparse inverse covariance matrices for Gaussian graphical models. We consider the graphical lasso regularization path as the model space for Bayesian model averaging and use Markov chain Monte Carlo techniques for the regularization path point selection. Numerical performance of our method is investigated using both simulated and real datasets, in comparison with some state-of-art model selection procedures.

KEYWORDS:

• Bayesian model averaging
• Gaussian graphical model
• Graphical lasso
• Markov chain Monte Carlo
• Regularization

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H12
• Secondary 62F15