Projection Robust Optimal Transport Between Unbalanced Distributions
Published in preprint, 2022
Recommended citation: Yu, T., Wan, Y., Ma, S. (2022). Projection Robust Optimal Transport Between Unbalanced Distributions. preprint (In progress) https://YistYU.github.io/files/PRUOT.pdf
Tingyang Yu*, Yuxuan Wan*, Shiqian Ma
We propose a novel unbalanced optimal transport (UOT) formulation that has the potential to alleviate the curse of dimensionality. The key idea is borrowed from recent developments of the projection robust Wasserstein distance, which projects the sampled data onto lowerdimensional subspace and computes the Wasserstein distance between the projected data. Using the same idea, we propose the projection robust UOT, which is a max-min problem over Stiefel manifold. We propose two algorithms for solving this problem and analyze their complexity for obtaining an ϵ-stationary point. Numerical experiments on both synthetic and real datasets are conducted to demonstrate the advantages of our new UOT formulation in high-dimensional cases.’