The Local Rademacher Complexity of Lp-Norm Multiple Kernel Learning

TL;DR

This paper provides a comprehensive analysis of the local Rademacher complexity for $ ext{Lp}$-norm multiple kernel learning, offering tighter bounds and insights into convergence rates across all $p$ values.

Contribution

It extends local Rademacher complexity analysis to all $p$ in $ ext{Lp}$-norm multiple kernel learning, including tight bounds and convergence rate implications.

Findings

Derived a tighter excess risk bound than global approaches.

Established a lower bound demonstrating the bound's tightness.

Showed fast convergence rates of order $O(n^{-rac{eta}{1+eta}})$ depending on kernel eigenvalue decay.

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