mlsanityData to 7 Oct 2026

Local Differential Privacy Is Equivalent to Contraction of Eγ-Divergence

arXiv 2102.01258 ↗First posted 2 Feb 2021cs.IT cs.LG math.ITcited by 17

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Abstract (arXiv)

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 Eγ-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.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 13 of its 45 references that are in the map. First posted on arXiv 2 Feb 2021.

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13 of 45 references.

References · 13

  1. 2017Renyi Differential Privacycited by 643
  2. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  3. 2018Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergencescited by 237
  4. 2016Concentrated Differential Privacycited by 139
  5. 2018Protection Against Reconstruction and Its Applications in Private Federated Learningcited by 127
  6. 2016Discrete Distribution Estimation under Local Privacycited by 58
  7. 2018Inference under Information Constraints I: Lower Bounds from Chi-Square Contractioncited by 31
  8. 2017Optimal Schemes for Discrete Distribution Estimation under Locally Differential Privacycited by 28
  9. 2013Local Privacy, Data Processing Inequalities, and Statistical Minimax Ratescited by 26
  10. 2020Three Variants of Differential Privacy: Lossless Conversion and Applicationscited by 25
  11. 2020Fisher information under local differential privacycited by 22
  12. 2019Privacy Amplification by Mixing and Diffusion Mechanismscited by 21
1 more
  1. 2018Locally Private Mean Estimation: Z-test and Tight Confidence Intervalscited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 4; 2024: 4; 2025: 3; 2026: 2.

17 papers.

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  1. 2022Quantum Differential Privacy: An Information Theory Perspectivecited by 32
  2. 2022Optimal and Differentially Private Data Acquisition: Central and Local Mechanismscited by 22
  3. 2023The Sample Complexity of Approximate Rejection Sampling with Applications to Smoothed Online Learningcited by 13
  4. 2022Quantum Local Differential Privacy and Quantum Statistical Query Modelcited by 12
  5. 2023Federated Linear Contextual Bandits with User-level Differential Privacycited by 12
  6. 2022Contraction of Locally Differentially Private Mechanismscited by 8
  7. 2024Contraction of Private Quantum Channels and Private Quantum Hypothesis Testingcited by 7
  8. 2024Auditing Differential Privacy Guarantees Using Density Estimationcited by 6
  9. 2024Characterizing Dependence of Samples along the Langevin Dynamics and Algorithms via Contraction of Phi-Mutual Informationcited by 5
  10. 2023Lower Bounds on the Bayesian Risk via Information Measurescited by 2
  11. 2025Measured Hockey-Stick Divergence and its Applications to Quantum Pufferfish Privacycited by 2
  12. 2024Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognitioncited by 1
5 more
  1. 2025High-Probability Bounds For Heterogeneous Local Differential Privacycited by 1
  2. 2023Differentially Private Secure Multiplication: Hiding Information in the Rubble of Noisecited by 0
  3. 2025Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacycited by 0
  4. 2026Tighter Information-Theoretic Generalization Bounds via a Novel Class of Change of Measure Inequalitiescited by 0
  5. 2026Privacy-Utility Tradeoffs in Quantum Information Processingcited by 0