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

2025/02/04 by Sisouk, Keanu, Delon, Julie, Tierny, Julien · 3 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.02275

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.

Cited by

• Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances
• Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimization
• Repulsive Monte Carlo on the sphere for the sliced Wasserstein distance

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