Robust and sparse Gaussian graphical modeling under cell-wise contamination

TL;DR

This paper introduces a robust method for sparse Gaussian graphical modeling that effectively handles high-dimensional data with cell-wise contamination, outperforming existing techniques in simulations.

Contribution

It proposes a novel sparse precision matrix estimation method based on the γ-divergence, tailored for cell-wise contaminated data, improving robustness in high-dimensional settings.

Findings

Outperforms existing methods in highly contaminated data scenarios

Effective in high-dimensional settings with partial contamination

Demonstrated through comprehensive simulation studies

Abstract

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision matrix. Many modern applications feature high-dimensional and contaminated data that complicate this task. In particular, traditional robust methods that down-weight entire observation vectors are often inappropriate as high-dimensional data may feature partial contamination in many observations. We tackle this problem by giving a robust method for sparse precision matrix estimation based on the $\gamma$-divergence under a cell-wise contamination model. Simulation studies demonstrate that our procedure outperforms existing methods especially for highly contaminated data.