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We prove that, under low noise assumptions, the support vector machine with$N\ll m$ random features (RFSVM) can achieve the learning rate faster than$O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized featuremap is used. Our work extends the previous fast rate analysis of randomfeatures method from least square loss to 0-1 loss. We also show that thereweighted feature selection method, which approximates the optimized featuremap, helps improve the performance of RFSVM in experiments on a synthetic dataset.

But How Does It Work in Theory? Linear SVM with Random Features