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  Sparse Multiscale Gaussian Process Regression

Walder, C., Kim, K., & Schölkopf, B. (2008). Sparse Multiscale Gaussian Process Regression. In W. Cohen, A. McCallum, & S. Roweis (Eds.), ICML '08: Proceedings of the 25th international conference on Machine learning (pp. 1112-1119). New York, NY, USA: ACM Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-C841-F Version Permalink: http://hdl.handle.net/21.11116/0000-0003-431E-1
Genre: Conference Paper

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 Creators:
Walder, C1, 2, 3, Author              
Kim, KI2, 4, Author              
Schölkopf, B2, 4, Author              
Affiliations:
1Department Human Perception, Cognition and Action, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497797              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
3Project group: Cognitive Engineering, Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_2528702              
4Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Abstract: Most existing sparse Gaussian process (g.p.) models seek computational advantages by basing their computations on a set of m basis functions that are the covariance function of the g.p. with one of its two inputs fixed. We generalise this for the case of Gaussian covariance function, by basing our computations on m Gaussian basis functions with arbitrary diagonal covariance matrices (or length scales). For a fixed number of basis functions and any given criteria, this additional flexibility permits approximations no worse and typically better than was previously possible. We perform gradient based optimisation of the marginal likelihood, which costs O(m2n) time where n is the number of data points, and compare the method to various other sparse g.p. methods. Although we focus on g.p. regression, the central idea is applicable to all kernel based algorithms, and we also provide some results for the support vector machine (s.v.m.) and kernel ridge regression (k.r.r.). Our approach outperforms the other methods, particularly for the case of very few basis functions, i.e. a very high sparsity ratio.

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Language(s):
 Dates: 2008-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1145/1390156.1390296
BibTex Citekey: 5121
 Degree: -

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Title: 25th International Conference on Machine Learning (ICML 2008)
Place of Event: Helsinki, Finland
Start-/End Date: 2008-07-05 - 2008-07-09

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Title: ICML '08: Proceedings of the 25th international conference on Machine learning
Source Genre: Proceedings
 Creator(s):
Cohen, WW, Editor
McCallum, A, Editor
Roweis, ST, Editor
Affiliations:
-
Publ. Info: New York, NY, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1112 - 1119 Identifier: ISBN: 978-1-60558-205-4