Partial Correlation Estimation by Joint Sparse Regression Models

TL;DR

This paper introduces space, a computationally efficient sparse regression method for estimating partial correlations in high-dimensional data, outperforming existing methods and revealing key genetic interactions.

Contribution

The paper proposes a novel sparse regression approach, space, for partial correlation estimation that is computationally efficient and asymptotically consistent in high-dimensional settings.

Findings

space outperforms existing methods in simulations

successfully identifies hub variables in gene networks

proves asymptotic consistency of the method

Abstract

In this paper, we propose a computationally efficient approach -- space(Sparse PArtial Correlation Estimation)-- for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial correlation selection and the identification of hub variables, and also outperforms two existing methods. We then apply space to a microarray breast cancer data set and identify a set of hub genes which may provide important insights on genetic regulatory networks. Finally, we prove that, under a set of suitable assumptions, the proposed procedure is asymptotically consistent in terms of model selection and parameter estimation.