A variational approach to learning curves

Dorthe Malzahn; Manfred Opper; Thomas G. Dietterich; Suzanna Becker; Zoubin Ghahramani

A variational approach to learning curves

Dorthe Malzahn
, Manfred Opper
, Thomas G. Dietterich (Editor)
, Suzanna Becker (Editor)
, Zoubin Ghahramani (Editor)

Aston University

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

58 Downloads (Pure)

Abstract

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

Original language	English
Journal	Advances in Neural Information Processing Systems
Volume	14
Publication status	Published - Sept 2002

Bibliographical note

Copyright of Massachusetts Institute of Technology Press (MIT Press). Available from Google Scholar.

Keywords

Gaussian process regression
generalization error
posterior variance

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Copyright of Massachusetts Institute of Technology Press (MIT Press). Available from Google Scholar.
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title = "A variational approach to learning curves",

abstract = "We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.",

keywords = "Gaussian process regression, generalization error, posterior variance",

author = "Dorthe Malzahn and Manfred Opper and Dietterich, \{Thomas G.\} and Suzanna Becker and Zoubin Ghahramani",

note = "Copyright of Massachusetts Institute of Technology Press (MIT Press). Available from Google Scholar.",

year = "2002",

month = sep,

language = "English",

volume = "14",

journal = "Advances in Neural Information Processing Systems",

issn = "1049-5258",

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T1 - A variational approach to learning curves

AU - Malzahn, Dorthe

AU - Opper, Manfred

A2 - Dietterich, Thomas G.

A2 - Becker, Suzanna

A2 - Ghahramani, Zoubin

N1 - Copyright of Massachusetts Institute of Technology Press (MIT Press). Available from Google Scholar.

PY - 2002/9

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N2 - We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

AB - We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

KW - Gaussian process regression

KW - generalization error

KW - posterior variance

UR - http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8782

M3 - Article

SN - 1049-5258

VL - 14

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

ER -

A variational approach to learning curves

Abstract

Bibliographical note

Keywords

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