Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections. (arXiv:2106.15427v2 [stat.ML] UPDATED)

The Sliced-Wasserstein distance (SW) is being increasingly used in machine
learning applications as an alternative to the Wasserstein distance and offers
significant computational and statistical benefits. Since it is defined as an
expectation over random projections, SW is commonly approximated by Monte
Carlo. We adopt a new perspective to approximate SW by making use of the
concentration of measure phenomenon: under mild assumptions, one-dimensional
projections of a high-dimensional random vector are approximately Gaussian.
Based on this observation, we develop a …

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