Efficient Distributed Estimation of High-dimensional Sparse Precision Matrix for Transelliptical Graphical Models

In this paper, distributed estimation of high-dimensional sparse precision matrix is proposed based on the debiased D-trace loss penalized lasso and the hard threshold method when samples are distributed into different machines for transelliptical graphical models. At a certain level of sparseness, this method not only achieves the correct selection of non-zero elements of sparse precision matrix, but the error rate can be comparable to the estimator in a non-distributed setting. The numerical results further prove that the proposed distributed method is more effective than the usual average method.