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  Sparse Multiscale Gaussian Process Regression

Walder, C., Kim, K., & Schölkopf, B.(2007). Sparse Multiscale Gaussian Process Regression (162). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.

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 Urheber:
Walder, C1, 2, Autor           
Kim, KI1, 2, Autor           
Schölkopf, B1, 2, Autor           
Affiliations:
1Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              
2Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Zusammenfassung: 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. Although we focus on g.p. regression, the central idea is applicable to all kernel
based algorithms, such as the support vector machine. 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. 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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 Datum: 2007-08
 Publikationsstatus: Erschienen
 Seiten: 14
 Ort, Verlag, Ausgabe: Tübingen, Germany : Max Planck Institute for Biological Cybernetics
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 Identifikatoren: Reportnr.: 162
BibTex Citekey: 5102
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Titel: Technical Report of the Max Planck Institute for Biological Cybernetics
Genre der Quelle: Reihe
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