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Communication-Efficient Large Precision Matrix Estimation by Distributed Refitted Cross-Validation
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AI
DOI：10.1007/s11424-026-4547-7.png)
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Abstract
En 中文
The precision matrix is an essential tool for studying the conditional relationships among large groups of variables. This paper develops a Distributed Refitted Cross-Validation (DRCV) procedure to estimate a large precision matrix in distributed settings, whose communication complexity is proportional to the number of non-zero entries in the precision matrix. The proposed method designs two rounds of communication. The first round selects non-zero positions of the precision matrix via node-wise regressions, while the second round constructs a global-debiased estimation for the precision matrix. To address the overfitting issue regarding this inference-after-selection strategy, the proposed method splits observations at each machine into two parts, one for position selection and the other for parameter estimation. DRCV achieves the global estimation consistency with respect to the total sample size under certain conditions and allows the number of machines in distributed settings to increase as the total sample size increases. Numerical studies on simulated datasets and a real high-frequency stock dataset show that DRCV has good estimation performance and a low communication cost.
Keywords:
Data splitting
distributed setting
high dimensionality
sparse precision matrix
Journal
J
IF:
2.8
Papers:
23
Citations:
0
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