Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems
This addresses the robustness issue in conditional generative models for Bayesian inverse problems, which is incremental as it extends known robustness properties from classical Bayesian literature to these models.
The paper tackles the problem of robustness in conditional generative models for Bayesian inverse problems, proving for the first time that these models can provide robust results for single observations with respect to perturbations.
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.