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arXiv · 1811.02827

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

Luca Ambrogioni·Umut Guclu·Marcel van Gerven
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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.

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Luca Ambrogioni, Umut Guclu, Marcel van Gerven. 2018-11-07. Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference. https://arxiv.org/abs/1811.02827

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