The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning

Abstract

We derive an upper bound on the local Rademacher complexity of ${\ell }_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while our analysis covers all cases $1\le p\le \infty$, assuming the different feature mappings corresponding to the different kernels to be uncorrelated. We also show a lower bound that shows that the bound is tight, and derive consequences regarding excess loss, namely fast convergence rates of the order $O(n^{-\frac{\alpha }{1+\alpha }})$, where $\alpha$ is the minimum eigenvalue decay rate of the individual kernels.