Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI).

Under label corruptions, we prove that this simple estimator achieves minimax near-optimal riskonawiderange ofgeneralized linear models, including Gaussian regression, Poisson regression and Binomial regression.