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Summary
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Differential privacy protects data by adding noise. This study links privacy guarantees to robust statistics, showing convergence rates depend on Gross Error Sensitivity (GES) for accurate estimation.

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Area of Science:

  • Computer Science
  • Statistics
  • Cryptography

Background:

  • Differential privacy is a robust privacy definition using noise addition.
  • Designing differentially private algorithms requires balancing privacy, accuracy, and sample size.
  • Statistical estimation under differential privacy is a key research area.

Purpose of the Study:

  • To analyze convergence rates of differentially private statistical estimators.
  • To establish a formal connection between differential privacy and robust statistics concepts.
  • To derive bounds for differentially private estimation with bounded range and Gross Error Sensitivity (GES).

Main Methods:

  • Deriving upper and lower bounds on convergence rates for differentially private approximations.
  • Investigating the relationship between differential privacy and Gross Error Sensitivity (GES).
  • Analyzing the necessity of bounded range for strict differential privacy.

Main Results:

  • Established that convergence rates of differentially private estimators grow with their GES.
  • Provided an upper bound on convergence rates for estimators with bounded range and GES.
  • Demonstrated that bounded range is essential for ensuring strict differential privacy.

Conclusions:

  • The study formally connects differential privacy with robust statistics, specifically GES.
  • Achieving accurate differentially private estimation is fundamentally linked to the estimator's sensitivity.
  • Bounded range is a necessary condition for strict differential privacy in statistical estimation.