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arXiv · 2602.17525

Variational inference via radial transport

Luca Ghafourpour·Sinho Chewi·Alessio Figalli·Aram-Alexandre Pooladian
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Abstract

In variational inference (VI), the practitioner approximates a high-dimensional distribution $\pi$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions might not capture the correct radial profile of $\pi$, resulting in poor coverage. In this work, we approach the VI problem from the perspective of optimizing over these radial profiles. Our algorithm radVI is a cheap, effective add-on to many existing VI schemes, such as Gaussian (mean-field) VI and Laplace approximation. We provide theoretical convergence guarantees for our algorithm, owing to recent developments in optimization over the Wasserstein space--the space of probability distributions endowed with the Wasserstein distance--and new regularity properties of radial transport maps in the style of Caffarelli (2000).

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Luca Ghafourpour, Sinho Chewi, Alessio Figalli, Aram-Alexandre Pooladian. 2026-02-19. Variational inference via radial transport. https://arxiv.org/abs/2602.17525

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