Open Access
June 2008 Kernel methods in machine learning
Thomas Hofmann, Bernhard Schölkopf, Alexander J. Smola
Ann. Statist. 36(3): 1171-1220 (June 2008). DOI: 10.1214/009053607000000677


We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data.

We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.


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Thomas Hofmann. Bernhard Schölkopf. Alexander J. Smola. "Kernel methods in machine learning." Ann. Statist. 36 (3) 1171 - 1220, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1151.30007
MathSciNet: MR2418654
Digital Object Identifier: 10.1214/009053607000000677

Primary: 30C40
Secondary: 68T05

Keywords: graphical models , machine learning , reproducing kernels , Support vector machines

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 3 • June 2008
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