Optimal transport with some directed distances

This work addresses a methodological bottleneck in optimal transport for researchers in machine learning and statistics, though it appears incremental as it builds on existing Wasserstein distance frameworks.

The authors tackled the problem of limited flexibility in optimal transport (OT) problems by introducing a toolkit of directed distances between quantile functions, which they used to solve new OT problems and significantly increase the flexibility of prominent OTs expressed through Wasserstein distances.