期刊
IEEE SIGNAL PROCESSING LETTERS
卷 29, 期 -, 页码 877-881出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2022.3159402
关键词
Signal processing algorithms; Convergence; Estimation; Complexity theory; Estimation error; Linear regression; Prediction algorithms; Multivariate linear regression; covariate adjusted precision matrix estimation; alternating gradient descent
资金
- National Natural Science Foundation of China [61971044, 62025103]
Researchers propose a new algorithmic analysis for solving the precision matrix estimation problem in high-dimensional settings, demonstrating a time-data tradeoff in the process and providing numerical experiments to validate the theoretical results.
In this letter, we present a sharp algorithmic analysis for alternating projected gradient descent which is used to solve the covariate adjusted precision matrix estimation problem in high-dimensional settings. By introducing a new analytical tool (the generic chaining), we remove the impractical resampling assumption used in the literature. The new analysis also demonstrates that this algorithm not only enjoys a linear convergence rate in the absence of convexity, but also attains the minimax rate with optimal order of sample complexity. Our results, meanwhile, reveal a time-data tradeoff in this problem. Numerical experiments are provided to verify our theoretical results.
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