# Measure Transport with Kernel Stein Discrepancy

arXiv: https://arxiv.org/abs/2010.11779 · HTML: https://mlsanity.com/paper/2010.11779/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Stein Variational Gradient Descent: many-particle and long-time asymptotics](https://mlsanity.com/paper/2102.12956/) (2021)
- [Stein transport for Bayesian inference](https://mlsanity.com/paper/2409.01464/) (2024)
- [Interpreting diffusion score matching using normalizing flow](https://mlsanity.com/paper/2107.10072/) (2021)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces](https://mlsanity.com/paper/2206.04552/) (2022)
- [Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis](https://mlsanity.com/paper/2502.06525/) (2025)
- [Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transport](https://mlsanity.com/paper/2308.13815/) (2023)

## Abstract (arXiv)

Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback--Leibler divergence (KLD) from the posterior to the approximation. The KLD is a strong mode of convergence, requiring absolute continuity of measures and placing restrictions on which transport maps can be permitted. Here we propose to minimise a kernel Stein discrepancy (KSD) instead, requiring only that the set of transport maps is dense in an L2 sense and demonstrating how this condition can be validated. The consistency of the associated posterior approximation is established and empirical results suggest that KSD is competitive and more flexible alternative to KLD for measure transport.