Optimizing Noise for f-Differential Privacy via Anti-Concentration and Stochastic Dominance
Authors: Jordan Awan, Aishwarya Ramasethu
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we establish anti-concentration inequalities for additive noise mechanisms which achieve f-differential privacy (f-DP)... Our theoretical results shed light on the different types of privacy guarantees... In this paper, we develop an anti-concentration inequality... We prove that CNDs are sub-exponential, and establish optimality properties of log-concave CNDs. ... Our theoretical contributions |
| Researcher Affiliation | Academia | Jordan Awan EMAIL Department of Statistics Purdue University West Lafayette, IN 47907, USA Aishwarya Ramasethu EMAIL Department of Statistics Purdue University West Lafayette, IN 47907, USA |
| Pseudocode | Yes | Lemma 41 (Proposition F.6: Awan and Vadhan, 2023) Let f be a symmetric nontrivial tradeofffunction and let Ff be as in Proposition 9. Then the quantile function F 1 f : (0, 1) R for Ff can be expressed as F 1 f (u) = F 1 f (1 f(1 u)) u < cf, u 1/2 1 2cf cf u 1 cf, F 1 f (f(u)) + 1 u > 1 cf. Furthermore, for any u (0, 1), the F 1 f (u) takes a finite number of recursive steps to evaluate. Thus, if U U(0, 1) then F 1 f (U) Ff. |
| Open Source Code | Yes | Code to reproduce the numerical results of the paper is available at https://github.com/Jordan Awan/Optimizing Noise For FDP. |
| Open Datasets | No | The paper primarily focuses on theoretical contributions, including mathematical proofs and analysis of noise distributions. It does not conduct experiments on specific empirical datasets, thus no concrete access information for open datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not perform experiments requiring dataset splits. No information about training/test/validation splits is provided. |
| Hardware Specification | No | The paper primarily presents theoretical results and mathematical proofs. It does not describe any empirical experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper states 'R code for this paper includes a general method to sample from the CND...' but does not specify the version of R or any other software dependencies with their version numbers. |
| Experiment Setup | No | This paper is theoretical in nature and focuses on mathematical proofs and derivations. It does not describe an experimental setup with specific hyperparameters, training configurations, or system-level settings. |