Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

Journal of Multivariate Analysis
Weidong Liu, Xi Luo

Abstract

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.

References

Dec 15, 2007·Biostatistics·Jerome FriedmanRobert Tibshirani
Aug 27, 2010·Biological Psychiatry·Daniel P DicksteinMichael P Milham
Jan 1, 2009·Annals of Statistics·Clifford Lam, Jianqing Fan

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Citations

May 30, 2019·Biometrics·Wenjing WangLexin Li
Jan 21, 2017·BMC Bioinformatics·Otte HeinävaaraAntti Honkela
Jan 31, 2017·Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·Tuo Zhao, Han Liu

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