A User's Guide to Sampling Strategies for Sliced Optimal Transport
It addresses the problem of selecting effective sampling strategies for practitioners in machine learning and statistics, offering incremental insights based on existing methods.
The paper provides a comprehensive guide to sampling strategies for sliced optimal transport, detailing methods, complexity, and theoretical guarantees, with experiments on simulated and real-world data leading to practical recommendations.
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.