Unbalanced Optimal Transport, from Theory to Numerics

Understand

Optimal Transport (OT) has recently emerged as a central tool in data sciences to compare in a geometrically faithful way point clouds and more generally probability distributions.

• The wide adoption of OT into existing data analysis and machine learning pipelines is however plagued by several shortcomings.
• This includes its lack of robustness to outliers, its high computational costs, the need for a large number of samples in high dimension and the difficulty to handle data in distinct spaces.
• In this review, we detail several recently proposed approaches to mitigate these issues.