# Non-asymptotic error controlled sparse high dimensional precision matrix estimation

## TL;DR

This paper introduces a new method for estimating sparse high-dimensional precision matrices that controls false positive rates with finite sample guarantees, applicable to Gaussian networks and genomics.

## Contribution

A novel distribution-free methodology for precision matrix estimation that explicitly controls false positive rates in high-dimensional settings.

## Key findings

- Method achieves finite sample guarantees for false positive control.
- Applicable to Gaussian graphical models and gene network inference.
- Performs well in high-dimensional, sparse settings.

## 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. 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.