Contraction and Statistical Inference under Privacy for Uniformly Bounded Distributions
Researchers study c-interior pointwise maximal leakage for tighter privacy contraction and private statistical inference.
The paper studies c-interior pointwise maximal leakage as a disclosure constraint that generalizes local differential privacy for distributions whose densities are bounded away from zero by c. Treating the constraint algebraically, the authors give tight Dobrushin-coefficient bounds, bound Hockeystick-divergence contraction, and derive strong data-processing inequalities for f-divergences, including kernels outside pure LDP. They apply the results to minimax binary hypothesis testing and mean estimation, and note that when c is large, private inference need not increase sample complexity.
- c-interior PML generalizes local differential privacy for densities bounded below by c.
- Authors bound the Dobrushin coefficient and Hockeystick-divergence contraction.
- Data-processing inequalities cover f-divergences and kernels beyond pure LDP.
- They derive optimal hypothesis testing and mean estimation under the constraint.
From the original article
1 min read at arxiv.orgWe 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 $c>0$.
By Leonhard Grosse · arxiv.org
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