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Robust Regression and Lasso
Huan Xu · Constantine Caramanis · Shie Mannor

Wed Dec 10 05:21 PM -- 05:22 PM (PST) @ None
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 $\ell_1$ 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.

Author Information

Huan Xu (National University of Singapore)
Constantine Caramanis (The Univ. of Texas at Austin)
Shie Mannor (McGill University)

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