Abstract
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.
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We would like to thank the Editor and the anonymous referees for their critical comments and thoughtful suggestions, which lead to a much improved version of this paper.
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This work is partly supported by National Natural Science Foundation of China (Grant Nos. 12031016, 11971324, 11471223); Foundations of Science and Technology Innovation Service Capacity Building, Interdisciplinary Construction of Bioinformatics and Statistics, and Academy for Multidisciplinary Studies, Capital Normal University, Beijing
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Wang, G.P., Cui, H.J. Efficient Distributed Estimation of High-dimensional Sparse Precision Matrix for Transelliptical Graphical Models. Acta. Math. Sin.-English Ser. 37, 689–706 (2021). https://doi.org/10.1007/s10114-021-9553-z
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DOI: https://doi.org/10.1007/s10114-021-9553-z