Reweighted information inequalities

Jonathan Niles-Weed

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arXiv · 2603.13135

Reweighted information inequalities

Jonathan Niles-Weed

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Abstract

We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $\pi$ can be decomposed into components that individually satisfy such inequalities, then any measure $\mu$ close to $\pi$ in relative Fisher information is close in relative entropy or transport distance to a reweighted version of $\pi$ 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.

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Jonathan Niles-Weed. 2026-03-13. Reweighted information inequalities. https://arxiv.org/abs/2603.13135

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