Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap
Charita Dellaporta, Jeremias Knoblauch, Theodoros Damoulas, Francois-Xavier Briol
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.
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. }
}