Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions
Abstract
We investigate c-interior pointwise maximal leakage (PML) as a tool for contraction analyses and disclosure control. Based on the strong adversarial threat models from maximal leakage, c-interior PML generalizes local differential privacy (LDP) to data-generating distributions with densities uniformly bounded away from zero by c>0. Viewing c-interior PML as an algebraic constraint on a kernel yields more flexible (and often tighter) contraction analyses than standard LDP. We provide tight bounds on the Dobrushin coefficient, and bound the contraction coefficient of the Hockeystick-divergence. We further derive strong data processing inequalities on f-divergences under c-interior PML constraints when the input distributions to the divergence are restricted to be in the c-interior. These results extend beyond the regime of pure LDP to cover a larger class of kernels, including, e.g., arbitrary stochastic matrices. We apply the results to minimax theory and provide asymptotically optimal strategies under c-interior PML constraints for binary hypothesis testing and mean estimation. The results show that disclosure control with PML allows analysts to reason about systems in a more differentiated manner: For example, it allows us to quantify the privacy leakage of deterministic systems, and can give precise adversarial guarantees with respect to arbitrary distributional assumptions. Interestingly, a recurring theme in the disclosure analyses is that if the privacy problem is relatively regular (if the density bound c is large), private inference can be possible without incurring any additional cost in terms of sample complexity.
Related
- Big data, differential privacy, and national statistical organisations
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BibTeX
@misc{grosse2026contraction,
title = {{Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions}},
author = {Leonhard Grosse and Sara Saeidian and Tobias J. Oechtering and Mikael Skoglund},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28297},
eprint = {2609.28297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28297},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions
AU - Leonhard Grosse
AU - Sara Saeidian
AU - Tobias J. Oechtering
AU - Mikael Skoglund
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28297
UR - https://arxiv.org/abs/2609.28297
AB - We investigate c-interior pointwise maximal leakage (PML) as a tool for contraction analyses and disclosure control. Based on the strong adversarial threat models from maximal leakage, c-interior PML generalizes local differential privacy (LDP) to data-generating distributions with densities uniformly bounded away from zero by c>0. Viewing c-interior PML as an algebraic constraint on a kernel yields more flexible (and often tighter) contraction analyses than standard LDP. We provide tight bounds on the Dobrushin coefficient, and bound the contraction coefficient of the Hockeystick-divergence. We further derive strong data processing inequalities on f-divergences under c-interior PML constraints when the input distributions to the divergence are restricted to be in the c-interior. These results extend beyond the regime of pure LDP to cover a larger class of kernels, including, e.g., arbitrary stochastic matrices. We apply the results to minimax theory and provide asymptotically optimal strategies under c-interior PML constraints for binary hypothesis testing and mean estimation. The results show that disclosure control with PML allows analysts to reason about systems in a more differentiated manner: For example, it allows us to quantify the privacy leakage of deterministic systems, and can give precise adversarial guarantees with respect to arbitrary distributional assumptions. Interestingly, a recurring theme in the disclosure analyses is that if the privacy problem is relatively regular (if the density bound c is large), private inference can be possible without incurring any additional cost in terms of sample complexity.
ER -