Fast and adaptive sparse precision matrix estimation in high dimensions

Weidong Liu and Xi Luo

Journal of Multivariate Analysis, 2015, vol. 135, issue C, 153-162

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.

Keywords: Adaptivity; Coordinate descent; Cross validation; Gaussian graphical models; Lasso; Convergence rates (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1016/j.jmva.2014.11.005

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