Derives a federated van Trees lower bound under total clientwise sample-level zCDP for parameter estimation with squared l2 loss in federated learning protocols with arbitrary public-transcript interactions.
Privacy and statistical risk: Formalisms and minimax bounds
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We explore and compare a variety of definitions for privacy and disclosure limitation in statistical estimation and data analysis, including (approximate) differential privacy, testing-based definitions of privacy, and posterior guarantees on disclosure risk. We give equivalence results between the definitions, shedding light on the relationships between different formalisms for privacy. We also take an inferential perspective, where---building off of these definitions---we provide minimax risk bounds for several estimation problems, including mean estimation, estimation of the support of a distribution, and nonparametric density estimation. These bounds highlight the statistical consequences of different definitions of privacy and provide a second lens for evaluating the advantages and disadvantages of different techniques for disclosure limitation.
representative citing papers
The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.
Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.
DP-GD achieves minimax optimal non-asymptotic risk O(γ + γ²/ρ²) for well-conditioned high-dimensional data and power-law scaling for ill-conditioned power-law spectra, with the exponent depending on the privacy parameter ρ.
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General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions
Derives a federated van Trees lower bound under total clientwise sample-level zCDP for parameter estimation with squared l2 loss in federated learning protocols with arbitrary public-transcript interactions.
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Optimal Rates for Pure $\varepsilon$-Differentially Private Stochastic Convex Optimization with Heavy Tails
The minimax optimal excess-risk rate for pure ε-DP heavy-tailed SCO is characterized up to logarithmic factors, with a polynomial-time algorithm based on Lipschitz extensions of the empirical loss and a nearly matching lower bound.
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Robust Statistical Estimators with Bounded Empirical Sensitivity
Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.
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High-Dimensional Private Linear Regression with Optimal Rates
DP-GD achieves minimax optimal non-asymptotic risk O(γ + γ²/ρ²) for well-conditioned high-dimensional data and power-law scaling for ill-conditioned power-law spectra, with the exponent depending on the privacy parameter ρ.