[2509.20508] Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances

Statistics > Machine Learning arXiv:2509.20508 (stat) [Submitted on 24 Sep 2025 (v1), last revised 3 Mar 2026 (this version, v2)] Title:Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances Authors:Khai Nguyen, Hai Nguyen, Nhat Ho View a PDF of the paper titled Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances, by Khai Nguyen and Hai Nguyen and Nhat Ho View PDF HTML (experimental) Abstract:We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced Wasserstein (SW) distances. Specifically, we leverage both standard SW distances, which provide lower bounds, and lifted SW distances, which provide upper bounds, as predictors of the true Wasserstein distance. To ensure parsimony, we introduce two linear models: an unconstrained model with a closed-form least-squares solution, and a constrained model that uses only half as many parameters. We show that accurate models can be learned from a small number of distribution pairs. Once estimated, the model can predict the Wasserstein distance for any pair of distributions via a linear combination of SW distances, making it highly efficient. Empirically, we validate our approach on diverse tasks, including Gaussian mixtures, point-cloud classification, and Wasserstein-space visualizations ...