Variational Inference via Radial Transport

Luca Ghafourpour, Sinho Chewi, Alessio Figalli, Aram-Alexandre Pooladian
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1945-1953, 2026.

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 $\texttt{radVI}$ 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).

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-ghafourpour26a, title = { Variational Inference via Radial Transport }, author = {Ghafourpour, Luca and Chewi, Sinho and Figalli, Alessio and Pooladian, Aram-Alexandre}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1945--1953}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/ghafourpour26a/ghafourpour26a.pdf}, url = {https://proceedings.mlr.press/v300/ghafourpour26a.html}, 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 $\texttt{radVI}$ 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). } }
Endnote
%0 Conference Paper %T Variational Inference via Radial Transport %A Luca Ghafourpour %A Sinho Chewi %A Alessio Figalli %A Aram-Alexandre Pooladian %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-ghafourpour26a %I PMLR %P 1945--1953 %U https://proceedings.mlr.press/v300/ghafourpour26a.html %V 300 %X 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 $\texttt{radVI}$ 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).
APA
Ghafourpour, L., Chewi, S., Figalli, A. & Pooladian, A.. (2026). Variational Inference via Radial Transport . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1945-1953 Available from https://proceedings.mlr.press/v300/ghafourpour26a.html.

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