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arXiv · 1605.08299

A General Family of Trimmed Estimators for Robust High-dimensional Data Analysis

Eunho Yang·Aurelie Lozano·Aleksandr Aravkin
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Abstract

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 possibly 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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Eunho Yang, Aurelie Lozano, Aleksandr Aravkin. 2016-05-26. A General Family of Trimmed Estimators for Robust High-dimensional Data Analysis. https://arxiv.org/abs/1605.08299

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