A Unifying View of Multiple Kernel Learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion’s dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

💡 Research Summary

The paper presents a comprehensive unifying framework for Multiple Kernel Learning (MKL), addressing the fragmentation in existing approaches that differ in objective formulations and regularization strategies. The authors start by observing that prior MKL methods can be broadly categorized into sparsity‑inducing ℓ₁‑regularized models, smooth ℓ₂‑regularized models, and various hybrid schemes. While each of these has demonstrated empirical success, the lack of a common mathematical foundation makes it difficult to compare their theoretical properties or to develop a single optimization algorithm that works across all variants.

To resolve this, the authors propose a generalized primal optimization problem:

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