Covariate Adjusted Precision Matrix Estimation via Nonconvex Optimization


Jinghui Chen, Pan Xu, Lingxiao Wang, Jian Ma, Quanquan Gu ;
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:922-931, 2018.


We propose a nonconvex estimator for the covariate adjusted precision matrix estimation problem in the high dimensional regime, under sparsity constraints. To solve this estimator, we propose an alternating gradient descent algorithm with hard thresholding. Compared with existing methods along this line of research, which lack theoretical guarantees in optimization error and/or statistical error, the proposed algorithm not only is computationally much more efficient with a linear rate of convergence, but also attains the optimal statistical rate up to a logarithmic factor. Thorough experiments on both synthetic and real data support our theory.

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