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  • 标题:A general family of trimmed estimators for robust high-dimensional data analysis
  • 本地全文:下载
  • 作者:Eunho Yang ; Aurélie C. Lozano ; Aleksandr Aravkin
  • 期刊名称:Electronic Journal of Statistics
  • 印刷版ISSN:1935-7524
  • 出版年度:2018
  • 卷号:12
  • 期号:2
  • 页码:3519-3553
  • DOI:10.1214/18-EJS1470
  • 语种:English
  • 出版社:Institute of Mathematical Statistics
  • 摘要: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.
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