## Frontmatter | | | | --- | --- | | Authors | [[Luca Ambrogioni]], [[Umut Güçlü]], [[Yağmur Güçlütürk]], [[Marcel van Gerven]] | | Date | 2018/11 | | Source | [[arXiv]] | | URL | https://doi.org/10.48550/arXiv.1811.02827 | | Citation | Ambrogioni, L., Güçlü, U., Güçlütürk, Y., & van Gerven, M. (2018). [[Wasserstein variational gradient descent - From semi-discrete optimal transport to ensemble variational inference]]. _arXiv_. [[URL](https://doi.org/10.48550/arXiv.1811.02827)]. #Preprint | ## Abstract 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. ## PDF ![[Wasserstein variational gradient descent - From semi-discrete optimal transport to ensemble variational inference.pdf]]