Speaker
Description
The sliced Wasserstein distance was introduced as an analogue of the Wasserstein distance, based solely on one-dimensional transports. This makes it computationally efficient and well suited to applications.
We prove that the squared sliced Wasserstein distance from a fixed target measure is (\lambda)-geodesically convex, provided that the target satisfies a geometric condition controlling its one-dimensional projections. This is in contrast with the usual Wasserstein distance, for which such geodesic convexity is not expected in general.
We then apply this result to the study of the sliced Wasserstein flow: this is an isotropic and continuous-in-time counterpart of the IDT algorithm. In particular, we establish uniqueness of the flow and investigate its long-time behavior.