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

Understand

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.