Error Bounds for l p -Norm Multiple Kernel Learning with Least Square Loss

Abstract

The problem of learning the kernel function with linear combinations of multiple kernels has attracted considerable attention recently in machine learning. Specially, by imposing an $l^p$-norm penalty on the kernel combination coefficient, multiple kernel learning (MKL) was proved useful and effective for theoretical analysis and practical applications (Kloft et al., 2009, 2011). In this paper, we present a theoretical analysis on the approximation error and learning ability of the $l^p$-norm MKL. Our analysis shows explicit learning rates for $l^p$-norm MKL and demonstrates some notable advantages compared with traditional kernel-based learning algorithms where the kernel is fixed.