# A greedy algorithm for sparse precision matrix approximation

## TL;DR

This paper presents GISS$^{{
ho}}$, a fast greedy algorithm for sparse precision matrix estimation that combines $l_1$ minimization with computational efficiency, outperforming existing methods in accuracy and speed.

## Contribution

The paper introduces GISS$^{{
ho}}$, a novel greedy algorithm for sparse precision matrix estimation, with proven convergence and superior numerical performance.

## Key findings

- GISS$^{{
ho}}$ outperforms ADMM and HTP in accuracy.
- The algorithm has favorable convergence properties.
- Numerical experiments demonstrate efficiency and advantages over existing methods.

## Abstract

Precision matrix estimation is an important problem in statistical data analysis. This paper introduces a fast sparse precision matrix estimation algorithm, namely GISS$^{{\rho}}$, which is originally introduced for compressive sensing. The algorithm GISS$^{{\rho}}$ is derived based on $l_1$ minimization while with the computation advantage of greedy algorithms. We analyze the asymptotic convergence rate of the proposed GISS$^{{\rho}}$ for sparse precision matrix estimation and sparsity recovery properties with respect to the stopping criteria. Finally, we numerically compare GISS$^{\rho}$ to other sparse recovery algorithms, such as ADMM and HTP in three settings of precision matrix estimation. The numerical results show the advantages of the proposed algorithm.