Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910132080738304 |
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| author | Liu, Jingbo |
| author_facet | Liu, Jingbo |
| contents | We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral Liu, Jingbo Information Theory Probability Machine Learning We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the rate-distortion function, up to universal multiplicative constants. The proof is based on a lifting technique, which constructs a Gaussian process indexed by a random subset of the type class of the probability distribution involved in the information-theoretic inequality, and then applying a form of the majorizing measure theorem. |
| title | Two-Sided Bounds for Entropic Optimal Transport via a Rate-Distortion Integral |
| topic | Information Theory Probability Machine Learning |
| url | https://arxiv.org/abs/2604.14061 |