Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap

Charita Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, Francois-Xavier Briol
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:943-970, 2022.

Abstract

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-dellaporta22a, title = { Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap }, author = {Dellaporta, Charita and Knoblauch, Jeremias and Damoulas, Theodoros and Briol, Francois-Xavier}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {943--970}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/dellaporta22a/dellaporta22a.pdf}, url = {https://proceedings.mlr.press/v151/dellaporta22a.html}, abstract = { Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model. } }
Endnote
%0 Conference Paper %T Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap %A Charita Dellaporta %A Jeremias Knoblauch %A Theodoros Damoulas %A Francois-Xavier Briol %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-dellaporta22a %I PMLR %P 943--970 %U https://proceedings.mlr.press/v151/dellaporta22a.html %V 151 %X Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.
APA
Dellaporta, C., Knoblauch, J., Damoulas, T. & Briol, F.. (2022). Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:943-970 Available from https://proceedings.mlr.press/v151/dellaporta22a.html.

Related Material