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Sparse Multiscale Gaussian Process Regression

MPS-Authors
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Walder,  C
Max Planck Institute for Biological Cybernetics, Max Planck Society;
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Kim,  KI
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Fulltext (public)

MPIK-TR-162.pdf
(Publisher version), 330KB

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Citation

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


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CC4F-6
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. 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.