Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions
Researchers have developed a method to describe Wasserstein gradient flows for maximum mean discrepancy (MMD) functionals using a negative distance kernel. This approach characterizes these flows through solving an associated Cauchy problem on quantile functions, which are embeddings of the Wasserstein-2 space. The study provides a solution for this Cauchy problem, offering a piecewise linear formula for discrete target measures and demonstrating invariance and smoothing properties of the flow. AI