Sparse multiscale Gaussian process regression

Christian Walder, Kwang In Kim, Bernhard Schölkopf

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

40 Citations (SciVal)


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.
Original languageEnglish
Title of host publicationProceedings of the.25th International Conference on Machine Learning (ICML), 2008
Place of PublicationNew York, U. S. A.
PublisherAssociation for Computing Machinery
Number of pages8
ISBN (Print)9781605582054
Publication statusPublished - 2008
Event25th International Conference on Machine Learning (ICML), 2008 - Helsinki, Finland
Duration: 5 Jun 20089 Jun 2008


Conference25th International Conference on Machine Learning (ICML), 2008


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