Entropic continuity bounds for conditional covariances with applications to Schr\" odinger and Sinkhorn bridges
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912348985360384 |
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| author | Del Moral, Pierre |
| author_facet | Del Moral, Pierre |
| contents | The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices.
These bounds are expressed in terms of the relative entropy between different coupling distributions.
Our approach combines Wasserstein coupling with quadratic transportation cost inequalities. We illustrate the impact of these results in the context of entropic optimal transport problems.
The entropic continuity theorem presented in the article allows to estimate
the conditional expectations and the conditional covariances of Schr\" odinger and Sinkhorn transitions in terms of the relative
entropy between the corresponding bridges. These entropic continuity bounds turns out to be a very useful tool for obtaining remarkably simple proofs of the exponential decays of the gradient and the Hessian of Schrödinger and Sinkhorn bridge potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18822 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entropic continuity bounds for conditional covariances with applications to Schr\" odinger and Sinkhorn bridges Del Moral, Pierre Probability Optimization and Control 49N05, 49Q22, 94A17, 62J99, 60J20 The article presents new entropic continuity bounds for conditional expectations and conditional covariance matrices. These bounds are expressed in terms of the relative entropy between different coupling distributions. Our approach combines Wasserstein coupling with quadratic transportation cost inequalities. We illustrate the impact of these results in the context of entropic optimal transport problems. The entropic continuity theorem presented in the article allows to estimate the conditional expectations and the conditional covariances of Schr\" odinger and Sinkhorn transitions in terms of the relative entropy between the corresponding bridges. These entropic continuity bounds turns out to be a very useful tool for obtaining remarkably simple proofs of the exponential decays of the gradient and the Hessian of Schrödinger and Sinkhorn bridge potentials. |
| title | Entropic continuity bounds for conditional covariances with applications to Schr\" odinger and Sinkhorn bridges |
| topic | Probability Optimization and Control 49N05, 49Q22, 94A17, 62J99, 60J20 |
| url | https://arxiv.org/abs/2504.18822 |