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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.16845 |
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| _version_ | 1866914275635757056 |
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| author | Nuradha, Theshani George, Ian Hirche, Christoph |
| author_facet | Nuradha, Theshani George, Ian Hirche, Christoph |
| contents | The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard data-processing inequalities and strong data-processing inequalities (SDPI) are employed. Most of the previously known and even tight characterizations of contraction of information measures, including total variation distance, hockey-stick divergences, and $f$-divergences, are applicable for $(\varepsilon,0)$-local differential private (LDP) mechanisms. In this work, we derive both linear and non-linear strong data-processing inequalities for hockey-stick divergence and $f$-divergences that are valid for all $(\varepsilon,δ)$-LDP mechanisms even when $δ\neq 0$. Our results either generalize or improve the previously known bounds on the contraction of these distinguishability measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information Contraction under $(\varepsilon,δ)$-Differentially Private Mechanisms Nuradha, Theshani George, Ian Hirche, Christoph Information Theory The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard data-processing inequalities and strong data-processing inequalities (SDPI) are employed. Most of the previously known and even tight characterizations of contraction of information measures, including total variation distance, hockey-stick divergences, and $f$-divergences, are applicable for $(\varepsilon,0)$-local differential private (LDP) mechanisms. In this work, we derive both linear and non-linear strong data-processing inequalities for hockey-stick divergence and $f$-divergences that are valid for all $(\varepsilon,δ)$-LDP mechanisms even when $δ\neq 0$. Our results either generalize or improve the previously known bounds on the contraction of these distinguishability measures. |
| title | Information Contraction under $(\varepsilon,δ)$-Differentially Private Mechanisms |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.16845 |