Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions.
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.
Department of Mathematics and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, CHINA.
Weidong
W
Liu
Department of Biostatistics and Center for Statistical Sciences, Brown University, Providence, Rhode Island, USA ; Brown Institute for Brain Science, Brown University, Providence, Rhode Island, USA ; Initiative for Computation in Brain and Mind, Brown University, Providence, Rhode Island, USA.
Xi
X
Luo
Adaptivity; Convergence rates; Coordinate descent; Cross validation; Gaussian graphical models; Lasso