Research On Regularization Paths Algorithm And Efficient Distribution Algorithm For High-Dimensional Sparse Precision Matrices Estimation

This paper studies the estimation of high-dimensional sparse precision matrices under the scenario of large dimension p and small sample size n.In the first.part,we focus on computing regularization paths,or solving the opti-mization problem over the full range of regularization parameters.Benefit from a pre-cision matrix estimator which is defined as the minimizer of the lasso under a positive-definiteness constraint,we aim to compute the regularization paths of estimating the positive-definite precision matrices through a one-step approximation of the Alternating Direction Method of Multipliers(ADMM),which quickly outlines a sequence of sparse so-lutions at a fine resolution.We demonstrate the effectiveness and computational savings of our proposed algorithm through elaborative analysis of simulated examples.In the second part,distributed estimation.of high-dimensional sparse precision ma-trix is proposed based on the debiased D-trace loss penalized lasso method and the hard threshold method when samples are distributed into different machines for transelliptical graphical models.At a certain level of sparsity,this method not only achieves the correct selection of non-zero elements of sparse precision matrix,but also the error rates can be comparable with estimation in a non-distributed setting.The numerical results further demonstrate that the method is effective comparing with other methods.