p-norm multiple kernel learning

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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. Unfortunately, this ℓ1norm MKL is rarely observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures that generalize well, we extend 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, that is ℓp -norms with p ≥ 1. This interleaved optimization is much faster than the commonly used wrapper approaches, as demonstrated on several data sets. A theoretical analysis and an experiment on controlled artificial data shed light on the appropriateness of sparse, non-sparse and ℓ-norm MKL in various scenarios. Importantly, empirical applications of ℓp-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that surpass the state-of-the-art. Data sets, source code to reproduce the experiments, implementations of the algorithms, and further information are available at http://doc.ml.tu-berlin.de/nonsparse-mkl/.

Original languageEnglish
JournalJournal of Machine Learning Research
Volume12
Pages (from-to)953-997
Number of pages45
ISSN1532-4435
Publication statusPublished - 03.2011
Externally publishedYes

    Research areas

  • Bioinformatics, Block coordinate descent, Convex conjugate, Generalization bounds, Large scale optimization, Learning kernels, Multiple kernel learning, Non-sparse, Rademacher complexity, Support vector machine
  • Informatics

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