Bayesian optimal experimental design with Wasserstein information criteria
For researchers in Bayesian experimental design, this work offers new criteria with theoretical guarantees and computational advantages over existing methods.
This paper introduces Wasserstein information criteria for Bayesian optimal experimental design, which use the expected Wasserstein distance between prior and posterior as an alternative to the Kullback-Leibler divergence. The Wasserstein-2 criterion admits closed-form solutions in linear-Gaussian settings, and stability analysis provides error rates for empirical approximations.
Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-$p$ distance between the prior and posterior distributions, termed Wasserstein information criteria. These criteria have many parallels with the widely used expected information gain (EIG) criterion, which instead relies on the Kullback--Leibler divergence. We show that the Wasserstein-$2$ criterion admits a closed-form solution in the linear-Gaussian setting, a property which can be used for more general approximation schemes, and contrast this solution with classical notions of Bayesian alphabetic optimality. Then we develop a stability analysis of the Wasserstein-$1$ criterion, wherein we bound errors induced by perturbations of the prior or likelihood. We partially extend this analysis to the Wasserstein-$2$ criterion. In particular, these results yield error rates for empirical approximations of the prior. We then illustrate the computability of the Wasserstein-$2$ criterion and demonstrate our approximation rates through simulations.