Variational inference via radial transport
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915902374543360 |
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| author | Ghafourpour, Luca Chewi, Sinho Figalli, Alessio Pooladian, Aram-Alexandre |
| author_facet | Ghafourpour, Luca Chewi, Sinho Figalli, Alessio Pooladian, Aram-Alexandre |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_17525 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variational inference via radial transport Ghafourpour, Luca Chewi, Sinho Figalli, Alessio Pooladian, Aram-Alexandre Machine Learning Statistics Theory 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). |
| title | Variational inference via radial transport |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2602.17525 |