High dimensional sparse covariance estimation via directed acyclic graphs

TL;DR

This paper introduces a graph-based method for estimating sparse covariance matrices in high-dimensional data by learning a DAG structure and using Cholesky decomposition, with proven consistency and comparisons to Glasso.

Contribution

It proposes a novel DAG-based approach for covariance estimation that ensures positive semi-definite estimates and demonstrates theoretical consistency in high-dimensional settings.

Findings

Method outperforms Glasso in simulations and real data

Provides consistent estimates in high-dimensional regimes

Ensures positive semi-definite sparse covariance matrices

Abstract

We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian distribution based on a DAG. For inferring the underlying DAG we use the PC-algorithm and for estimating the DAG-based covariance matrix and its inverse, we use a Cholesky decomposition approach which provides a positive (semi-)definite sparse estimate. We present a consistency result in the high-dimensional framework and we compare our method with the Glasso for simulated and real data.