A General Family of Trimmed Estimators for Robust High-dimensional Data Analysis
This work addresses robust data analysis for high-dimensional applications like genomics, but it is incremental as it extends existing trimmed estimators to structured settings.
The authors tackled the problem of robust high-dimensional structured estimation by introducing a general family of trimmed estimators, including variants for Lasso and Graphical Lasso, and demonstrated their competitive performance on simulated and real-world genomics data.
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.