  This contribution presents substantial computational advancements to compare
measures even with varying masses. Specifically, we utilize the nonequispaced
fast Fourier transform to accelerate the radial kernel convolution in
unbalanced optimal transport approximation, built upon the Sinkhorn algorithm.
We also present accelerated schemes for maximum mean discrepancies involving
kernels. Our approaches reduce the arithmetic operations needed to compute
distances from $\mathcal O(n^2)$ to $\mathcal O(n\log n)$, opening the door to
handle large and high-dimensional datasets efficiently. Furthermore, we
establish robust connections between transportation problems, encompassing
Wasserstein distance and unbalanced optimal transport, and maximum mean
discrepancies. This empowers practitioners with compelling rationale to opt for
adaptable distances.
