The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning

We derive an upper bound on the local Rademacher complexity of lp-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches analyzed the case p = 1 only while our analysis covers all cases 1 ≤ p ≤ ∞, 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 α is the minimum eigenvalue decay rate of the individual kernels.