A general family of trimmed estimators for robust high-dimensional data

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We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized M-estimators in the high-dimensional setting, including the popular Least Trimmed Squares estimator, as well as analogous estimators for generalized linear models and graphical models, using convex and non-convex loss functions. We present a general analysis of their statistical convergence rates and consistency, and then take a closer look at the trimmed versions of the Lasso and Graphical Lasso estimators as special cases. On the optimization side, we show how to extend algorithms for M-estimators to fit trimmed variants and provide guarantees on their numerical convergence. The generality and competitive performance of high-dimensional trimmed estimators are illustrated numerically on both simulated and real-world genomics data.
Publisher
INST MATHEMATICAL STATISTICS
Issue Date
2018-10
Language
English
Article Type
Article
Citation

ELECTRONIC JOURNAL OF STATISTICS, v.12, no.2, pp.3519 - 3553

ISSN
1935-7524
DOI
10.1214/18-EJS1470
URI
http://hdl.handle.net/10203/248758
Appears in Collection
AI-Journal Papers(저널논문)
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