Robust Regression and Lasso

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Robust Regression and Lasso
We consider robust least-squares regression with feature-wise disturbance. We show that this formulation leads to tractable convex optimization problems, and we exhibit a particular uncertainty set for which the robust problem is equivalent to 1 regularized regression (Lasso). This provides an interpretation of Lasso from a robust optimization perspective. We generalize this robust formulation to consider more general uncertainty sets, which all lead to tractable convex optimization problems. Therefore, we provide a new methodology for designing regression algorithms, which generalize known formulations. The advantage is that robustness to disturbance is a physical property that can be exploited: in addition to obtaining new formulations, we use it directly to show sparsity properties of Lasso, as well as to prove a general consistency result for robust regression problems, including Lasso, from a unified robustness perspective.
Huan Xu, Constantine Caramanis, Shie Mannor
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Huan Xu, Constantine Caramanis, Shie Mannor
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