Unified Enhancement of Privacy Bounds for Mixture Mechanisms via $f$-Differential Privacy
Authors: Chendi Wang, Buxin Su, Jiayuan Ye, Reza Shokri, Weijie Su
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical computations of the trade-off function indicate that random initialization can enhance the privacy of DP-GD. Our analysis of f-DP guarantees for these mixture mechanisms relies on an inequality for trade-off functions introduced in this paper. This inequality implies the joint convexity of F-divergences. Finally, we study an f-DP analog of the advanced joint convexity of the hockey-stick divergence related to ( , δ)-DP and apply it to analyze the privacy of mixture mechanisms. To the best of our understanding, the leading privacy analysis for shuffled mechanisms is given in [23]. In this section, we compare the privacy bounds from our Theorem 4.2 and Corollary 4.3 with those found in Theorem 3.2 of [23]. Additionally, we assess the tightness of our bound against the empirical lower bounds obtained through binary search. Specifically, Figure 1 presents a comparison of the trade-off function derived from our Theorem 4.2 to that of [23]. This comparison clearly illustrates that f-DP offers tighter privacy bounds, given that its trade-off function aligns closer to the identity trade-off function. In our Table 1, we compare the values of δf-DP( ), as derived from Corollary 4.3 with δ( ) in [23]. The results indicate that δf-DP( ) is significantly smaller than δ( ). In Table 2, we present f-DP alongside the numerical upper bound of from [23] and the numerical lower bound determined by binary search. |
| Researcher Affiliation | Academia | Chendi Wang University of Pennsylvania Philadelphia, PA, USA, 19104 & Shenzhen Research Institute of Big data Shenzhen, Guangdong, China, 518000 chendi@wharton.upenn.edu Buxin Su Department of Mathematics University of Pennsylvania Philadelphia, PA, USA, 19104 subuxin@sas.upenn.edu Jiayuan Ye Department of Computer Science National University of Singapore Singapore jiayuan@comp.nus.edu.sg Reza Shokri Department of Computer Science National University of Singapore Singapore reza@comp.nus.edu.sg Weijie J. Su Wharton Statistics and Data Science Department University of Pennsylvania Philadelphia, PA, USA, 19104 suw@wharton.upenn.edu |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about open-sourcing code for the methodology described, nor does it include links to a code repository. |
| Open Datasets | No | The paper discusses theoretical analysis and numerical computations for privacy bounds. It describes considering an 'example D0 = {(xi, yi)}n i=1 with yi = axi and x2 i = 1 for some constant a' and 'D1 by removing an arbitrary element in D0'. This refers to a synthetic setup for numerical evaluation rather than an external, publicly available dataset with concrete access information. |
| Dataset Splits | No | The paper performs numerical evaluations of privacy bounds and trade-off functions rather than training machine learning models on datasets with explicit splits. Therefore, it does not provide training/test/validation dataset splits. |
| Hardware Specification | No | The paper does not mention any specific hardware used for its numerical computations or experiments. |
| Software Dependencies | No | The paper does not mention any specific software dependencies with version numbers used for its numerical computations or experiments. |
| Experiment Setup | No | The paper focuses on theoretical analysis and numerical evaluation of trade-off functions for privacy. While it describes the setup for numerical evaluation (e.g., 'consider an example D0 = {(xi, yi)}n i=1 with yi = axi and x2 i = 1 for some constant a... assume that σ = 1'), this does not constitute explicit experimental setup details like hyperparameters, optimizers, or training schedules for a machine learning model. |