### Abstract

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 |

### Fingerprint

### Cite this

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

**Sparse multiscale Gaussian process regression.** / Walder, Christian; Kim, Kwang In; Schölkopf, Bernhard .

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the.25th International Conference on Machine Learning (ICML), 2008.*Association for Computing Machinery, New York, U. S. A., pp. 1112-1119, 25th International Conference on Machine Learning (ICML), 2008, Helsinki, Finland, 5/06/08. https://doi.org/10.1145/1390156.1390296

}

TY - GEN

T1 - Sparse multiscale Gaussian process regression

AU - Walder, Christian

AU - Kim, Kwang In

AU - Schölkopf, Bernhard

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://dx.doi.org/10.1145/1390156.1390296

U2 - 10.1145/1390156.1390296

DO - 10.1145/1390156.1390296

M3 - Conference contribution

SN - 9781605582054

SP - 1112

EP - 1119

BT - Proceedings of the.25th International Conference on Machine Learning (ICML), 2008

PB - Association for Computing Machinery

CY - New York, U. S. A.

ER -