Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems

Published: 21 Jul 2023, Last Modified: 21 Jul 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Changes are highlighted in blue.
Assigned Action Editor: ~Alp_Kucukelbir1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1050