Consistent Optimal Transport with Empirical Conditional Measures

arXiv:2305.15901v5 Announce Type: replace
Abstract: Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the marginals of this variable in the two joint distributions may not be the same. In such settings, standard OT variants cannot be employed, and novel estimation techniques are necessary. Since the main challenge is that the conditional distributions …

abstract arxiv consistent continuous cs.lg focus general samples them transport transportation type