A User's Guide to Sampling Strategies for Sliced Optimal Transport

TL;DR

This paper reviews and compares various sampling strategies for sliced optimal transport, providing theoretical insights, complexity analysis, and practical recommendations based on extensive experiments.

Contribution

It offers a comprehensive guide with new regularity results, detailed construction methods, and practical insights for sampling strategies in sliced optimal transport.

Findings

Different strategies have varying suitability depending on data and application.

Theoretical guarantees help in choosing appropriate sampling methods.

Experimental results guide practical implementation choices.

Abstract

This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance. We detail the construction methods, generation time complexity, theoretical guarantees, and conditions for each strategy. Additionally, we provide insights into their suitability for sliced optimal transport in theory. Extensive experiments on both simulated and real-world data offer a representative comparison of the strategies, culminating in practical recommendations for their best usage.