Robust and sparse Gaussian graphical modeling under cell-wise contamination

Shota Katayama; Hironori Fujisawa; Mathias Drton

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arXiv · 1802.05475

Robust and sparse Gaussian graphical modeling under cell-wise contamination

Shota Katayama·Hironori Fujisawa·Mathias Drton

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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.

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Shota Katayama, Hironori Fujisawa, Mathias Drton. 2018-02-15. Robust and sparse Gaussian graphical modeling under cell-wise contamination. https://arxiv.org/abs/1802.05475

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