Kernel learning with nonconvex ramp loss

Abstract

We study the kernel learning problems with ramp loss, a nonconvex but noise‐resistant loss function. In this work, we justify the validity of ramp loss under the classical kernel learning framework. In particular, we show that the generalization bound for empirical ramp risk minimizer is similar to that of convex surrogate losses, which implies kernel learning with such loss function is not only noise‐resistant but, more importantly, statistically consistent. For adapting to real‐time data streams, we introduce PA‐ramp, a heuristic online algorithm based on the passive‐aggressive framework, to solve this learning problem. Empirically, with fewer support vectors, this algorithm achieves robust empirical performances on tested noisy scenarios.