Advanced Computation of a Sparse Precision Matrix HADAP: A Hadamard-Dantzig Estimation of a Sparse Precision Matrix

Estimating large sparse precision matrices is an interesting and challenging problem in many fields of sciences, engineering, and humanities, thanks to advances in computing technologies. Recent applications often encounter high dimensionality with a limited number of data points leading to a number of covariance parameters that greatly exceeds the number of observations. Several methods have been proposed to deal with this problem, but there is no guarantee that the obtained estimator is positive definite. Furthermore, in many cases, one needs to capture some additional information on the setting of the problem. In this work, we propose an innovative approach named HADAP for estimating the precision matrix by minimizing a criterion combining a relaxation of the gradient-log likelihood and a penalization of lasso type. We derive an efficient Alternating Direction Method of multipliers algorithm to obtain the optimal solution.