Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

TL;DR

This paper introduces a novel sparse precision matrix estimation method that is both computationally efficient and adaptively tuned, with proven convergence rates and demonstrated effectiveness on real high-dimensional datasets.

Contribution

A new Sparse Column-wise Inverse Operator method for fast, adaptive sparse precision matrix estimation with theoretical convergence guarantees.

Findings

Achieves fast computation via coordinate descent.

Converges under Frobenius and other matrix norms.

Performs well on real high-dimensional datasets.

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.