Efficient and accurate ℓ_p-norm multiple kernel learning

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability. Unfortunately, ℓ₁-norm MKL is hardly observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary ℓ_p-norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary p > 1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the traditionally used wrapper approaches. Finally, we apply ℓp-norm MKL to real-world problems from computational biology, showing that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.