## Using sparse kernels to design computer experiments with tunable precision

Please always quote using this URN: urn:nbn:de:0297-zib-59605

- Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate. In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples). We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave. On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.

Author: | Guillaume Sagnol, Hans-Christian Hege, Martin Weiser |
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Document Type: | ZIB-Report |

Tag: | Gaussian Process; Optimal design of computer experiments; Sparse kernels |

MSC-Classification: | 62-XX STATISTICS / 62Kxx Design of experiments [See also 05Bxx] / 62K05 Optimal designs |

Date of first Publication: | 2016/06/03 |

Series (Serial Number): | ZIB-Report (16-33) |

ISSN: | 1438-0064 |

Published in: | Appeared in: Ana Colubi, Angela Blanco and Cristian Gatu (eds.) 22nd Intern. Conf. on Computational Statistics - COMSTAT 2016, Oviedo, Spain, 23-26 August 2016, Proceedings ISBN 978-90-73592-36-0. Pp. 397-408 |