Robust and sparse Gaussian graphical modeling under cell-wise contamination
Shota Katayama, Hironori Fujisawa and Mathias Drton
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.
Preprint
http://arxiv.org/abs/1802.05475
Print
https://doi.org/10.1002/sta4.181
Code
https://github.com/shkatayama/robust_graphical_model
