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About this paper
Jen Ning Lim, Adam M. Johansen
Researchers at the University of Warwick developed Particle Variational Inference (PVI), a method that leverages Euclidean-Wasserstein gradient flows and particle approximations to directly optimize the Evidence Lower Bound (ELBO) for semi-implicit variational inference. PVI accurately approximates complex posterior distributions, achieving lower Wasserstein distances on toy examples and competitive RMSE on Bayesian neural networks compared to existing semi-implicit variational inference methods.
Key insights
- Direct optimization of the mixing distribution, especially when combined with appropriately designed kernels, is crucial for capturing complex, multimodal target distributions.
- Formulating the variational inference problem as a gradient flow in Euclidean-Wasserstein space enables principled and direct optimization of the Evidence Lower Bound.
- Theoretical analysis demonstrates the existence and uniqueness of solutions for the mollified PVI flow and justifies particle approximations through propagation of chaos results.
Summary by alphaXiv.
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