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

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Yitong Sun, Anna Gilbert, Ambuj Tewari


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 feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set.