Variational inference via radial transport

• URL: http://arxiv.org/abs/2602.17525v1
• Date: Thu, 19 Feb 2026 16:36:52 GMT
• Title: Variational inference via radial transport
• Authors: Luca Ghafourpour, Sinho Chewi, Alessio Figalli, Aram-Alexandre Pooladian,
• Abstract summary: In variational inference (VI), the practitioner approximates a high-dimensional distribution $$ with a simple surrogate one, often a (product) Gaussian distribution.<n>In this work, we approach the VI problem from the perspective of optimizing over these radial profiles.<n>Our algorithm radVI is a cheap, effective add-on to many existing VI schemes, such as Gaussian (mean-field) VI and Laplace approximation.
• Score: 13.100339469711466
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In variational inference (VI), the practitioner approximates a high-dimensional distribution $π$ 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 $π$, 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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