dorsal/arxiv
View SchemaDobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy
| Authors | Leonhard Grosse, Sara Saeidian, Tobias J. Oechtering, Mikael Skoglund |
|---|---|
| Categories | |
| ArXiv ID | 2601.09498vv1 |
| URL | https://arxiv.org/abs/2601.09498 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition recovers local differential privacy (LDP) for $c\to 0$. We derive achievable bounds on contraction in terms of a kernels PML guarantees, and provide mechanism constructions that achieve the presented bounds. Further, we extend the results to general $f$-divergences by an application of Binette's inequality. Our analysis yields tighter bounds for mechanisms satisfying LDP and extends beyond the LDP regime to any discrete kernel.
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"date_created": "2026-02-17T05:53:20.456000Z",
"date_modified": "2026-02-17T05:53:20.456000Z",
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"abstract": "We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c\u003e0$. This definition recovers local differential privacy (LDP) for $c\\to 0$. We derive achievable bounds on contraction in terms of a kernels PML guarantees, and provide mechanism constructions that achieve the presented bounds. Further, we extend the results to general $f$-divergences by an application of Binette\u0027s inequality. Our analysis yields tighter bounds for mechanisms satisfying LDP and extends beyond the LDP regime to any discrete kernel.",
"arxiv_id": "2601.09498",
"authors": [
"Leonhard Grosse",
"Sara Saeidian",
"Tobias J. Oechtering",
"Mikael Skoglund"
],
"categories": [
"cs.IT",
"cs.CR",
"math.IT"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Dobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy",
"url": "https://arxiv.org/abs/2601.09498",
"version": "v1"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "4683d187-3eb0-4b1f-b069-1305256a6238",
"id": "arXiv Dataset",
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"variant": "snapshot-2026-01-17",
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