The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning

Part of Advances in Neural Information Processing Systems 24 (NIPS 2011)

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Marius Kloft, Gilles Blanchard


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 $1\leq p\leq\infty$, 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.