# Unbalanced Optimal Transport and Maximum Mean Discrepancies: Interconnections and Rapid Evaluation

arXiv: https://arxiv.org/abs/2306.13618 · HTML: https://mlsanity.com/paper/2306.13618/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Computing the Distance between unbalanced Distributions -- The flat Metric](https://mlsanity.com/paper/2308.01039/) (2023)
- [Soft Quantization using Entropic Regularization](https://mlsanity.com/paper/2309.04428/) (2023)

## Abstract (arXiv)

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(n2) to mathcal O(nlog 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.