Slicing / Wasserstein

[Matthijspals]

• Intuitive description, of what these metrics try to measure, and how, and for what they are used
• Thorough description of the metric in supplementary
• Common variants and hyper parameters choices
• Scaling with dimensionality
• Scaling with number of samples
• Computational complexity
• Induced geometry
• Failure modes

[gmoss13]

TODOs:

• make a notebook +figure explaining slicing (@jsvetter)
• compare behaviour of SWD and Sinkhorn approximation as dimensionality goes up when GT distance is known (@gmoss13 and comparisons team)
• make a notebook + figure explaining Wasserstein Distance in 1D (@gmoss13)
• (Optional) implement GSWD (@gmoss13) and make a notebook comparing with SWD
• Consider examples where choice of p matters, and/or failure modes (@gmoss13)
• Writing (@gmoss13 and @jsvetter)