Robust and sparse Gaussian graphical modelling under cell-wise contamination

Graphical modelling 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.     «

Graphical modelling 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 con...     »