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,...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 37; no. 5; pp. 689 - 706
Main Authors Wang, Guan Peng, Cui, Heng Jian
Format Journal Article
LanguageEnglish
Published Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2021
Springer Nature B.V
Subjects
Error correction
Mathematics
Mathematics and Statistics
62G05
high-dimensional
sparse precision matrix
62N02
hard threshold
Distributed estimator
efficient communication
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Summary: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-021-9553-z