L0 sparse graphical modeling

Graphical models are well established in providing compact conditional probability descriptions of complex multivariable interactions. In the Gaussian case, graphical models are determined by zeros in the precision or concentration matrix, i.e. the inverse of the covariance matrix. Hence, there has been much recent interest in sparse precision matrices in areas such as statistics, machine learning, computer vision, pattern recognition and signal processing. In this paper we propose a simple new algorithm for constructing a sparse estimator for the precision matrix from multivariate data where the sparsity is enforced by an l₀ penalty. We compare and test the quality of our method on a synthetic graphical model.