Timezone: »

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

Wed Dec 10 05:21 PM -- 05:22 PM (PST) @
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)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors