On the Statistical Complexity of Estimation and Testing under Privacy Constraints

Authors: Clément Lalanne, Aurélien Garivier, Rémi Gribonval

TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We study minimax lower bounds for classes of differentially private estimators. In particular, we show how to characterize the power of a statistical test under differential privacy in a plug-and-play fashion by solving an appropriate transport problem. With specific coupling constructions, this observation allows us to derive Le Cam-type and Fano-type inequalities not only for regular definitions of differential privacy but also for those based on Renyi divergence. We then proceed to illustrate our results on three simple, fully worked out examples.
Researcher Affiliation Academia Clément Lalanne EMAIL Univ. Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France Aurélien Garivier EMAIL Univ. Lyon, ENS Lyon, UMPA UMR 5669, 46 allée d Italie, F-69364, Lyon cedex 07 Rémi Gribonval EMAIL Univ. Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France
Pseudocode Yes Algorithm 1: DP-SGML: Differentially Private Stochastic Gradient Maximum Likelihood
Open Source Code No The paper does not provide any explicit statements about code availability, specific repository links, or mention of code in supplementary materials.
Open Datasets No The paper focuses on theoretical models (Bernoulli, Gaussian, Uniform) and minimax lower bounds. It does not conduct experiments on specific datasets or provide access information for any datasets.
Dataset Splits No The paper is theoretical and does not involve experiments with datasets, therefore, no dataset splits are mentioned.
Hardware Specification No The paper is theoretical and does not report any experimental results that would require specific hardware specifications.
Software Dependencies No The paper is theoretical and does not mention any specific software names with version numbers for implementation.
Experiment Setup No The paper describes theoretical algorithms and their properties (e.g., Fact 5 for DP-SGML), which include abstract parameters like 'step sizes (ηk)k 0, batch size m, noise variance σ2, initial parameter θ0, stopping time K'. However, it does not provide concrete hyperparameter values or system-level settings for any actual experiments.