Robust expected information gain for optimal Bayesian experimental design using ambiguity sets

Jinwoo Go, Tobin Isaac
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:728-737, 2022.

Abstract

The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model’s prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of a perturbed prior. We define and analyze Robust Expected Information Gain(REIG), a modification of the objective in EIG maximization by minimizing an affine relaxation of EIG over an ambiguity set of distributions that are close to the original prior in KL-divergence. We show that, when combined with a sampling-based approach to estimating EIG, REIG corresponds to a "log-sum-exp" stabilization of the samples used to estimate EIG, meaning that it can be efficiently implemented in practice. Numerical tests combining REIG with variational nested Monte Carlo (VNMC), adaptive contrastive estimation (ACE) and mutual information neural estimation (MINE) suggest that in practice REIG also compensates for the variability of under-sampled estimators.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-go22a, title = {Robust expected information gain for optimal Bayesian experimental design using ambiguity sets}, author = {Go, Jinwoo and Isaac, Tobin}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {728--737}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/go22a/go22a.pdf}, url = {https://proceedings.mlr.press/v180/go22a.html}, abstract = {The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model’s prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of a perturbed prior. We define and analyze Robust Expected Information Gain(REIG), a modification of the objective in EIG maximization by minimizing an affine relaxation of EIG over an ambiguity set of distributions that are close to the original prior in KL-divergence. We show that, when combined with a sampling-based approach to estimating EIG, REIG corresponds to a "log-sum-exp" stabilization of the samples used to estimate EIG, meaning that it can be efficiently implemented in practice. Numerical tests combining REIG with variational nested Monte Carlo (VNMC), adaptive contrastive estimation (ACE) and mutual information neural estimation (MINE) suggest that in practice REIG also compensates for the variability of under-sampled estimators.} }
Endnote
%0 Conference Paper %T Robust expected information gain for optimal Bayesian experimental design using ambiguity sets %A Jinwoo Go %A Tobin Isaac %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-go22a %I PMLR %P 728--737 %U https://proceedings.mlr.press/v180/go22a.html %V 180 %X The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model’s prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of a perturbed prior. We define and analyze Robust Expected Information Gain(REIG), a modification of the objective in EIG maximization by minimizing an affine relaxation of EIG over an ambiguity set of distributions that are close to the original prior in KL-divergence. We show that, when combined with a sampling-based approach to estimating EIG, REIG corresponds to a "log-sum-exp" stabilization of the samples used to estimate EIG, meaning that it can be efficiently implemented in practice. Numerical tests combining REIG with variational nested Monte Carlo (VNMC), adaptive contrastive estimation (ACE) and mutual information neural estimation (MINE) suggest that in practice REIG also compensates for the variability of under-sampled estimators.
APA
Go, J. & Isaac, T.. (2022). Robust expected information gain for optimal Bayesian experimental design using ambiguity sets. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:728-737 Available from https://proceedings.mlr.press/v180/go22a.html.

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