Robust Estimation of Sparse Precision Matrix using Adaptive Weighted Graphical Lasso Approach

TL;DR

This paper introduces a robust method for estimating sparse precision matrices that effectively handles abnormal observations in high-dimensional data using an adaptive weighted graphical lasso approach.

Contribution

It proposes a novel robust estimation technique based on a weighted sample covariance and an efficient algorithm to address non-convexity, with proven consistency and practical validation.

Findings

Outperforms existing methods in simulations.

Demonstrates robustness in genetic network inference.

Establishes asymptotic consistency of the estimator.

Abstract

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the dimensionality increases. In this work, we propose robust estimation of the inverse covariance matrix based on an $l_1$ regularized objective function with a weighted sample covariance matrix. The robustness of the proposed objective function can be justified by a nonparametric technique of the integrated squared error criterion. To address the non-convexity of the objective function, we develop an efficient algorithm in a similar spirit of majorization-minimization. Asymptotic consistency of the proposed estimator is also established. The performance of the proposed method is compared with several existing approaches via numerical simulations. We further demonstrate the merits of the proposed method with application in genetic network inference.