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Sparse multiscale Gaussian process regression

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Publication date2008
Host publicationProc. International Conference on Machine Learning (ICML) 2008
Place of PublicationTuebingen, Germany
PublisherMax Planck Institute for Biological Cybernetics
Pages1112-1119
Number of pages8
ISBN (Print)9781605582054
Original languageEnglish

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.