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 Nyström 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.

中文翻译：

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显式特征图和大型鲁棒非线性 SVM 分类器的特征不确定性界限

当数据很大并且受到未知但有界不确定性的影响时，我们考虑二元分类问题。我们通过制定具有鲁棒优化的非线性支持向量机训练问题来解决该问题。为此，我们分析并提出了两种与低维空间中随机近似特征相关的不确定性的边界方案。建议的边界计算基于随机傅立叶特征和 Nyström 方法。进行了数值实验以说明该技术的好处。我们还强调了所提出的鲁棒非线性公式的可分解结构，当数据集很大时，它允许使用有效的随机近似技术。