Efficient Bayesian Experimental Design for Implicit Models

Steven Kleinegesse, Michael U. Gutmann
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:476-485, 2019.

Abstract

Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search or sampling-based methods. We find that this increases efficiency and allows us to consider higher design dimensions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-kleinegesse19a, title = {Efficient Bayesian Experimental Design for Implicit Models}, author = {Kleinegesse, Steven and Gutmann, Michael U.}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {476--485}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/kleinegesse19a/kleinegesse19a.pdf}, url = {https://proceedings.mlr.press/v89/kleinegesse19a.html}, abstract = {Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search or sampling-based methods. We find that this increases efficiency and allows us to consider higher design dimensions.} }
Endnote
%0 Conference Paper %T Efficient Bayesian Experimental Design for Implicit Models %A Steven Kleinegesse %A Michael U. Gutmann %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-kleinegesse19a %I PMLR %P 476--485 %U https://proceedings.mlr.press/v89/kleinegesse19a.html %V 89 %X Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible, this task is particularly difficult and therefore largely unexplored. This is mainly due to technical difficulties associated with approximating posterior distributions and utility functions. We devise a novel experimental design framework for implicit models that improves upon previous work in two ways. First, we use the mutual information between parameters and data as the utility function, which has previously not been feasible. We achieve this by utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate posterior distributions, instead of the traditional approximate Bayesian computation or synthetic likelihood methods. Secondly, we use Bayesian optimisation in order to solve the optimal design problem, as opposed to the typically used grid search or sampling-based methods. We find that this increases efficiency and allows us to consider higher design dimensions.
APA
Kleinegesse, S. & Gutmann, M.U.. (2019). Efficient Bayesian Experimental Design for Implicit Models. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:476-485 Available from https://proceedings.mlr.press/v89/kleinegesse19a.html.

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