Conditional Bayesian Quadrature

Zonghao Chen, Masha Naslidnyk, Arthur Gretton, Francois-Xavier Briol
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:648-684, 2024.

Abstract

We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-chen24b, title = {Conditional Bayesian Quadrature}, author = {Chen, Zonghao and Naslidnyk, Masha and Gretton, Arthur and Briol, Francois-Xavier}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {648--684}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/chen24b/chen24b.pdf}, url = {https://proceedings.mlr.press/v244/chen24b.html}, abstract = {We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.} }
Endnote
%0 Conference Paper %T Conditional Bayesian Quadrature %A Zonghao Chen %A Masha Naslidnyk %A Arthur Gretton %A Francois-Xavier Briol %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-chen24b %I PMLR %P 648--684 %U https://proceedings.mlr.press/v244/chen24b.html %V 244 %X We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.
APA
Chen, Z., Naslidnyk, M., Gretton, A. & Briol, F.. (2024). Conditional Bayesian Quadrature. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:648-684 Available from https://proceedings.mlr.press/v244/chen24b.html.

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