Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions

arXiv:2404.15378v1 Announce Type: cross
Abstract: Sliced Wasserstein (SW) and Generalized Sliced Wasserstein (GSW) have been widely used in applications due to their computational and statistical scalability. However, the SW and the GSW are only defined between distributions supported on a homogeneous domain. This limitation prevents their usage in applications with heterogeneous joint distributions with marginal distributions supported on multiple different domains. Using SW and GSW directly on the joint domains cannot make a meaningful comparison since their homogeneous slicing operator …

abstract applications arxiv computational cs.ai cs.cv cs.gr cs.lg domain generalized hierarchical however hybrid scalability scalable statistical stat.ml type usage