Local Differential Privacy Is Equivalent to Contraction of E_γ-Divergence

2021/02/02 by Asoodeh, Shahab, Aliakbarpour, Maryam, Calmon, Flavio P. · 1 citation
#FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning (stat.ML)

paper · doi:10.48550/arxiv.2102.01258

Abstract

We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the E_γ-divergence. We then use this equivalent formula to express LDP guarantees of privacy mechanisms in terms of contraction coefficients of arbitrary f-divergences. When combined with standard estimation-theoretic tools (such as Le Cam's and Fano's converse methods), this result allows us to study the trade-off between privacy and utility in several testing and minimax and Bayesian estimation problems.

Cited by

• High-Probability Bounds For Heterogeneous Local Differential Privacy

Related

• Contraction of E_γ-Divergence and Its Applications to Privacy
• Contraction of Locally Differentially Private Mechanisms
• Bounds on the privacy amplification of arbitrary channels via the contraction of f_α-divergence
• A Better Bound Gives a Hundred Rounds: Enhanced Privacy Guarantees via\n f-Divergences
• Geometrizing rates of convergence under local differential privacy constraints