On the convergence rate of lp-norm multiple kernel learning

Authors:
Marius Kloft;Gilles Blanchard
Affiliations:
Machine Learning Laboratory, Technische Universität Berlin, Berlin, Germany;Department of Mathematics, University of Potsdam, Potsdam, Germany
Venue:
The Journal of Machine Learning Research
Year:
2012

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Abstract

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-α/1+a), where α is the minimum eigenvalue decay rate of the individual kernels.