Bayesian Quadrature for Ratios

Michael Osborne, Roman Garnett, Stephen Roberts, Christopher Hart, Suzanne Aigrain, Neale Gibson
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:832-840, 2012.

Abstract

We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. It offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the non-negativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate, as is commonplace in exoplanets research; we demonstrate the efficacy of our method on data from the Kepler spacecraft.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-osborne12, title = {Bayesian Quadrature for Ratios}, author = {Osborne, Michael and Garnett, Roman and Roberts, Stephen and Hart, Christopher and Aigrain, Suzanne and Gibson, Neale}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {832--840}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/osborne12/osborne12.pdf}, url = {https://proceedings.mlr.press/v22/osborne12.html}, abstract = {We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. It offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the non-negativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate, as is commonplace in exoplanets research; we demonstrate the efficacy of our method on data from the Kepler spacecraft.} }
Endnote
%0 Conference Paper %T Bayesian Quadrature for Ratios %A Michael Osborne %A Roman Garnett %A Stephen Roberts %A Christopher Hart %A Suzanne Aigrain %A Neale Gibson %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-osborne12 %I PMLR %P 832--840 %U https://proceedings.mlr.press/v22/osborne12.html %V 22 %X We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. It offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the non-negativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate, as is commonplace in exoplanets research; we demonstrate the efficacy of our method on data from the Kepler spacecraft.
RIS
TY - CPAPER TI - Bayesian Quadrature for Ratios AU - Michael Osborne AU - Roman Garnett AU - Stephen Roberts AU - Christopher Hart AU - Suzanne Aigrain AU - Neale Gibson BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-osborne12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 832 EP - 840 L1 - http://proceedings.mlr.press/v22/osborne12/osborne12.pdf UR - https://proceedings.mlr.press/v22/osborne12.html AB - We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. It offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the non-negativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate, as is commonplace in exoplanets research; we demonstrate the efficacy of our method on data from the Kepler spacecraft. ER -
APA
Osborne, M., Garnett, R., Roberts, S., Hart, C., Aigrain, S. & Gibson, N.. (2012). Bayesian Quadrature for Ratios. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:832-840 Available from https://proceedings.mlr.press/v22/osborne12.html.

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