Robust and sparse Gaussian graphical modeling under cell-wise contamination

2018/02/15 by Katayama, Shota, Fujisawa, Hironori, Drton, Mathias
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.1802.05475

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 γ-divergence under a cell-wise contamination model. Simulation studies demonstrate that our procedure outperforms existing methods especially for highly contaminated data.

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