Measure transfer via stochastic slicing and matching

Understand

This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure.

• Similar to the sliced Wasserstein distance, these schemes benefit from the availability of closed-form solutions for the one-dimensional optimal transport problem and the associated computational advantages.
• While such schemes have already been successfully utilized in data science applications, not too many results on their convergence are available.
• The main contribution of this paper is an almost sure convergence proof for stochastic slicing-and-matching schemes.