Sliced Orlicz-Wasserstein

TL;DR

The paper introduces the sliced Orlicz-Wasserstein distance, a generalization of the sliced Wasserstein distance. It proves the metric properties and derives topological properties of the distance. The authors demonstrate its superiority over Orlicz-Wasserstein distance in computational efficiency.

Why It Matters

The sliced Orlicz-Wasserstein distance has practical significance in detecting differences between distributions and evaluating generative models. It offers favorable flexibility over existing methods. This can lead to improved performance in various applications such as image datasets analysis.

Key Findings

• sliced Orlicz-Wasserstein distance is a metric
• convergence under SOW implies weak convergence
• superior computational efficiency over Orlicz-Wasserstein distance