Osborne, MA and Duvenaud, D and Garnett, R and Rasmussen, CE and Roberts, SJ and Ghahramani, Z (2012) *Active learning of model evidence using Bayesian quadrature.* Advances in Neural Information Processing Systems, 1. pp. 46-54. ISSN 1049-5258

## Abstract

Numerical integration is a key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a modelbased method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

Item Type: | Article |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Computational and Biological Learning |

Depositing User: | Cron Job |

Date Deposited: | 18 May 2016 18:54 |

Last Modified: | 30 May 2016 06:01 |

DOI: |