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Marius Kloft, Ulf Brefeld, Søren Sonnenburg, and Alexander Zien (2010)
Non-Sparse Regularization and Efficient Training with Multiple Kernels
University of California, Berkeley.
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 and scalability. Unfortu-
nately, this 1 -norm MKL is rarely observed to outperform trivial baselines in practical
applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary norms.
We devise new insights on the connection between several existing MKL formulations and
develop two efficient interleaved optimization strategies for arbitrary norms, like p -norms
with p > 1. Empirically, we demonstrate that the interleaved optimization strategies are
much faster compared to the commonly used wrapper approaches. An experiment on con-
trolled artificial data experiment sheds light on the appropriateness of sparse, non-sparse
and ∞ MKL in various scenarios. Application of p -norm MKL to three hard real-world
problems from computational biology show that non-sparse MKL achieves accuracies that
go beyond the state-of-the-art. We conclude that our improvements finally made MKL fit
for deployment to practical applications: MKL now has a good chance of improving the
accuracy (over a plain sum kernel) at an affordable computational cost.
