Sharp bounds for max-sliced Wasserstein distances

2024-03-01 · March T. Boedihardjo

We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from $n$ samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure $\mu$ on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of $\mu$ and the diameter of the support of $\mu$.

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Max-sliced 2-Wasserstein distance

2024-03-04 · March T. Boedihardjo

This note is a continuation of the author's previous work on "Sharp bounds for the max-sliced Wasserstein distance." We use the same technique to obtain an upper bound for the expected max-sliced 2-Wasserstein distance b…

Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances

2022-06-07 · Ruben Ohana, Kimia Nadjahi, Alain Rakotomamonjy, Liva Ralaivola

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its genera…

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Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distances

2025-09-24 · Khai Nguyen, Hai Nguyen, Nhat Ho arxiv

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 d…

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Orthogonal Estimation of Wasserstein Distances

2019-03-09 · Mark Rowland, Jiri Hron, Yunhao Tang, Krzysztof Choromanski 외

Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sortin…

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Generalized Sliced Wasserstein Distances

2019-02-01 · NeurIPS 2019 12 · Soheil Kolouri, Kimia Nadjahi, Umut Simsekli, Roland Badeau 외

The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar propert…