### 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.

Original language | English |
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Title of host publication | Proceedings of the.25th International Conference on Machine Learning (ICML), 2008 |

Place of Publication | New York, U. S. A. |

Publisher | Association for Computing Machinery |

Pages | 1112-1119 |

Number of pages | 8 |

ISBN (Print) | 9781605582054 |

DOIs | |

Publication status | Published - 2008 |

Event | 25th International Conference on Machine Learning (ICML), 2008 - Helsinki, Finland Duration: 5 Jun 2008 → 9 Jun 2008 |

### Conference

Conference | 25th International Conference on Machine Learning (ICML), 2008 |
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Country | Finland |

City | Helsinki |

Period | 5/06/08 → 9/06/08 |

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## Cite this

Walder, C., Kim, K. I., & Schölkopf, B. (2008). Sparse multiscale Gaussian process regression. In

*Proceedings of the.25th International Conference on Machine Learning (ICML), 2008*(pp. 1112-1119). Association for Computing Machinery. https://doi.org/10.1145/1390156.1390296