The Annals of Statistics

Kernel methods in machine learning

Thomas Hofmann, Bernhard Schölkopf, and Alexander J. Smola

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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.

Article information

Ann. Statist., Volume 36, Number 3 (2008), 1171-1220.

First available in Project Euclid: 26 May 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C40: Kernel functions and applications
Secondary: 68T05: Learning and adaptive systems [See also 68Q32, 91E40]

Machine learning reproducing kernels support vector machines graphical models


Hofmann, Thomas; Schölkopf, Bernhard; Smola, Alexander J. Kernel methods in machine learning. Ann. Statist. 36 (2008), no. 3, 1171--1220. doi:10.1214/009053607000000677.

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