Learning rates of multi-kernel regularized regression

Learning the kernel function has recently received considerable attention in machine learning. In this paper, we consider the multi-kernel regularized regression (MKRR) algorithm associated with least square loss over reproducing kernel Hilbert spaces. We provide an error analysis for the MKRR algorithm based on the Rademacher chaos complexity and iteration techniques. The main result is an explicit learning rate for the MKRR algorithm. Two examples are given to illustrate that the learning rates are much improved compared to those in the literature.