A note on the radiant formula and its relations to the sliced Wasserstein distance (Q6614068)

The author explaines the concept of the Wasserstein distance between two probability measures over the \(d\)-dimensional Euclidean space and gives a survey of its applications. He points out that for many other fields using Wasserstein distance is inefficient in comparison with other metrics and there were proposed cheap-to-compute alternatives to it. Special attention is devoted in the paper to Slice Wasserstein distance (SWD). The author proposes in the paper a general methodology to relate the original Wasserstein distance to the SWD. An upper bound on the absolute error between SWD and the Wasserstein distance is provided.