Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
About the Cost of Central Privacy in Density Estimation
Authors: Clément Lalanne, Aurélien Garivier, Rémi Gribonval
TMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study non-parametric density estimation for densities in Lipschitz and Sobolev spaces, and under central privacy. In particular, we investigate regimes where the privacy budget is not supposed to be constant. We consider the classical definition of central differential privacy, but also the more recent notion of central concentrated differential privacy. We recover the result of Barber & Duchi (2014) stating that histogram estimators are optimal against Lipschitz distributions for the L2 risk and, under regular differential privacy, we extend it to other norms and notions of privacy. Then, we investigate higher degrees of smoothness, drawing two conclusions: First, and contrary to what happens with constant privacy budget (Wasserman & Zhou, 2010), there are regimes where imposing privacy degrades the regular minimax risk of estimation on Sobolev densities. Second, so-called projection estimators are near-optimal against the same classes of densities in this new setup with pure differential privacy, but contrary to the constant privacy budget case, it comes at the cost of relaxation. With zero concentrated differential privacy, there is no need for relaxation, and we prove that the estimation is optimal. |
| 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 | No | The paper describes histogram estimators and projection estimators using mathematical definitions (e.g., 'ˆπhist(X)(x) := Xb bins 1b(x) 1i=1 1b(Xi) + Zb' for histogram estimators in Section 3 and 'ˆπproj(X) = i=1 N ˆθiϕi where ˆθi := 1n Pn j=1 ϕi(Xj)' for projection estimators in Section 4), but it does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about making source code publicly available, nor does it provide links to code repositories. The mention of 'Reviewed on Open Review: https://openreview.net/forum?id=uq29MIWv IV' refers to the review platform, not a code repository. |
| Open Datasets | No | The paper focuses on theoretical aspects of non-parametric density estimation, discussing 'densities in Lipschitz and Sobolev spaces' and abstract 'probability densities'. It does not mention or use any specific datasets for empirical evaluation, nor does it provide access information for any open datasets. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments involving datasets. Therefore, it does not provide any information regarding training/test/validation dataset splits. |
| Hardware Specification | No | The paper is purely theoretical and does not report on any experiments that would require specific hardware. Consequently, no hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe implementation details or experimental procedures that would necessitate mentioning specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical, focusing on mathematical derivations and proofs related to density estimation under privacy constraints. It does not include any experimental setup details, hyperparameters, or training configurations. |