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Robust and sparse Gaussian graphical modelling under cell‐wise contamination
Author(s) -
Katayama Shota,
Fujisawa Hironori,
Drton Mathias
Publication year - 2018
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.181
Subject(s) - computer science , pairwise comparison , graphical model , gaussian , data mining , contamination , feature (linguistics) , graph , sparse matrix , conditional dependence , pattern recognition (psychology) , artificial intelligence , algorithm , theoretical computer science , mathematics , statistics , ecology , linguistics , philosophy , physics , quantum mechanics , biology
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. Copyright © 2018 John Wiley & Sons, Ltd.