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A New Discriminative Kernel from Probabilistic Models

koji.tsuda{at}aist.go.jp, AIST Computational Biology Research Center, Koto-ku, Tokyo, 135-0064, Japan, and Fraunhofer FIRST, 12489 Berlin, Germany

Motoaki Kawanabe

nabe{at}first.fraunhofer.de, Fraunhofer FIRST, 12489 Berlin, Germany

Gunnar Rätsch

Gunnar.Raetsch{at}anu.edu.au, Australian National University, Research School for Information Sciences and Engineering, Canberra, ACT 0200, Australia, and Fraunhofer FIRST, 12489 Berlin, Germany

Sören Sonnenburg

sonne{at}first.fraunhofer.de, Fraunhofer FIRST, 12489 Berlin, Germany

Klaus-Robert Müller

klaus{at}first.fraunhofer.de, Fraunhofer FIRST, 12489 Berlin, Germany, and University of Potsdam, 14469 Potsdam, Germany

Recently, Jaakkola and Haussler (1999) proposed a method for constructing kernel functions from probabilistic models. Their so-called Fisher kernel has been combined with discriminative classifiers such as support vector machines and applied successfully in, for example, DNA and protein analysis. Whereas the Fisher kernel is calculated from the marginal log-likelihood, we propose the TOP kernel derived from tangent vectors of posterior log-odds. Furthermore, we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing the TOP kernel. In experiments, our new discriminative TOP kernel compares favorably to the Fisher kernel.

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