Balancing Simulation-based Inference for Conservative Posteriors

Conservative inference is a major concern in simulation-based inference. It
has been shown that commonly used algorithms can produce overconfident
posterior approximations. Balancing has empirically proven to be an effective
way to mitigate this issue. However, its application remains limited to neural
ratio estimation. In this work, we extend balancing to any algorithm that
provides a posterior density. In particular, we introduce a balanced version of
both neural posterior estimation and contrastive neural ratio estimation. We
show empirically that the balanced versions tend to produce conservative
posterior approximations on a wide variety of benchmarks. In addition, we
provide an alternative interpretation of the balancing condition in terms of
the $\chi^2$ divergence.