Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap
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
@article{arxiv.2202.04744,
title = {Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap},
author = {Charita Dellaporta and Jeremias Knoblauch and Theodoros Damoulas and François-Xavier Briol},
journal= {arXiv preprint arXiv:2202.04744},
year = {2022}
}
Comments
Accepted for publication (with an oral presentation) at AISTATS 2022. A preliminary version of this paper was accepted in the NeurIPS 2021 workshop "Your Model is Wrong: Robustness and misspecification in probabilistic modeling". v2: added some references. v3: corrected small error in theorem 3