Robustness, Risk, and Regularization in Support Vector Machines Export

@misc{citeulike:2620063, abstract = {We consider two new formulations for classification problems in the spirit of support vector machines based on robust optimization. Our formulations are designed to build in protection to noise and control overfitting, but without being overly conservative. Our first formulation allows the noise between different samples to be correlated. We show that the standard norm-regularized support vector machine classifier is a solution to a special case of our first formulation, thus providing an explicit link between regularization and robustness in pattern classification. Our second formulation is based on a softer version of robust optimization called comprehensive robustness. We show that this formulation is equivalent to regularization by any arbitrary convex regularizer, thus extending our first equivalence result. Moreover, we explain how the connection of comprehensive robustness to convex risk-measures can be used to design risk-measure constrained classifiers with robustness to the input distribution. Our formulations result in convex optimization problems that can be easily solved. Finally, we provide some empirical results that show the promise of comprehensive robust classifiers.}, archivePrefix = {arXiv}, author = {Xu, Huan and Mannor, Shie and Caramanis, Constantine}, citeulike-article-id = {2620063}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.3490}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.3490}, day = {25}, eprint = {0803.3490}, keywords = {mathematics}, month = {Mar}, posted-at = {2008-04-01 15:15:44}, priority = {2}, title = {Robustness, Risk, and Regularization in Support Vector Machines}, url = {http://arxiv.org/abs/0803.3490}, year = {2008} }

TY - ELEC ID - citeulike:2620063 L3 - citeulike-article-id:2620063 N2 - We consider two new formulations for classification problems in the spirit of support vector machines based on robust optimization. Our formulations are designed to build in protection to noise and control overfitting, but without being overly conservative. Our first formulation allows the noise between different samples to be correlated. We show that the standard norm-regularized support vector machine classifier is a solution to a special case of our first formulation, thus providing an explicit link between regularization and robustness in pattern classification. Our second formulation is based on a softer version of robust optimization called comprehensive robustness. We show that this formulation is equivalent to regularization by any arbitrary convex regularizer, thus extending our first equivalence result. Moreover, we explain how the connection of comprehensive robustness to convex risk-measures can be used to design risk-measure constrained classifiers with robustness to the input distribution. Our formulations result in convex optimization problems that can be easily solved. Finally, we provide some empirical results that show the promise of comprehensive robust classifiers. TI - Robustness, Risk, and Regularization in Support Vector Machines KW - mathematics AU - Xu, Huan AU - Mannor, Shie AU - Caramanis, Constantine PY - 2008/Mar/25/ UR - http://arxiv.org/abs/0803.3490 ER -