Reweighted information inequalities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917338999160832 |
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| author | Niles-Weed, Jonathan |
| author_facet | Niles-Weed, Jonathan |
| contents | We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $π$ can be decomposed into components that individually satisfy such inequalities, then any measure $μ$ close to $π$ in relative Fisher information is close in relative entropy or transport distance to a reweighted version of $π$ with the same mixture components but possibly different weights. This provides a user-friendly interpretation of Fisher information bounds for non-log-concave measures and explains phenomena observed in the analysis of Langevin Monte Carlo for multimodal distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reweighted information inequalities Niles-Weed, Jonathan Information Theory Probability 60E15, 47D07 We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $π$ can be decomposed into components that individually satisfy such inequalities, then any measure $μ$ close to $π$ in relative Fisher information is close in relative entropy or transport distance to a reweighted version of $π$ with the same mixture components but possibly different weights. This provides a user-friendly interpretation of Fisher information bounds for non-log-concave measures and explains phenomena observed in the analysis of Langevin Monte Carlo for multimodal distributions. |
| title | Reweighted information inequalities |
| topic | Information Theory Probability 60E15, 47D07 |
| url | https://arxiv.org/abs/2603.13135 |