Non-asymptotic error controlled sparse high dimensional precision matrix estimation

Abstract

Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose a novel methodology for estimating such matrices while controlling the false positive rate, percentage of matrix entries incorrectly chosen to be non-zero. We specifically focus on false positive rates tending towards zero with finite sample guarantees. In the context of large scale hypothesis testing, control of the false discovery rate is also considered. This methodology is distribution free, but is particularly applicable to the problem of Gaussian network recovery. We also consider applications to constructing gene networks in genomics data.