Wasserstein distance and applications to Bayesian nonparametrics

Bayesian nonparametric models are able to learn complex distributional patterns in the data by leveraging on infinite-dimensional parameters, typically consisting in vectors of random measures. To perform a principled BNP model comparison one thus needs a measure of discrepancy between vectors of random measures. In recent works the authors have proposed two different metrics based on the Wasserstein distance. We here provide new perspectives to our findings, highlighting a universal relation between the two metrics.