Feature uncertainty bounds for explicit feature maps and large robust nonlinear SVM classifiers

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We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to random approximate features in low dimensional spaces. The proposed bound calculations are based on Random Fourier Features and the Nystrom methods. Numerical experiments are conducted to illustrate the benefit of the technique. We also emphasize the decomposable structure of the proposed robust nonlinear formulation that allows the use of efficient stochastic approximation techniques when datasets are large.