# Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

arXiv: https://arxiv.org/abs/1811.02827 · HTML: https://mlsanity.com/paper/1811.02827/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Stein Variational Gradient Descent: many-particle and long-time asymptotics](https://mlsanity.com/paper/2102.12956/) (2021)
- [Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution](https://mlsanity.com/paper/2103.06263/) (2021)
- [Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selection](https://mlsanity.com/paper/2407.18707/) (2024)

## Abstract (arXiv)

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the posterior and the variational approximation, we minimize a semi-discrete optimal transport divergence. The solution of the resulting optimal transport problem provides both a particle approximation and a set of optimal transportation densities that map each particle to a segment of the posterior distribution. We approximate these transportation densities by minimizing the KL divergence between a truncated distribution and the optimal transport solution. The resulting algorithm can be interpreted as a form of ensemble variational inference where each particle is associated with a local variational approximation.