Approximating Functions with Approximate Privacy for Applications in Signal Estimation and Learning

Area of Science:

• Computer Science
• Data Privacy
• Algorithm Design

Background:

• Organizations collect sensitive personal data, necessitating privacy-preserving algorithms.
• Differential privacy (DP) offers rigorous privacy but often compromises data utility.
• Existing functional mechanisms (FM) face a utility-cost trade-off under DP.

Purpose of the Study:

• To develop an improved functional mechanism (FM) offering enhanced utility with approximate differential privacy (DP).
• To reduce the noise in DP algorithms, thereby improving the privacy-utility balance.
• To extend the proposed mechanism to decentralized data settings.

Main Methods:

• Proposed Gaussian FM, an enhancement to the functional mechanism (FM) using Gaussian noise.
• Developed capeFM by integrating Gaussian FM with the CAPE protocol for decentralized data.
• Analyzed noise reduction and utility improvements analytically and empirically.

Main Results:

• Gaussian FM offers orders of magnitude less noise compared to existing FM algorithms.
• capeFM achieves utility comparable to centralized methods in decentralized settings.
• Empirical results demonstrate superior performance over state-of-the-art methods on various datasets.

Conclusions:

• Gaussian FM provides a superior privacy-utility trade-off for data analysis.
• The proposed methods enhance data utility while preserving individual privacy.
• These algorithms represent a significant advancement in privacy-preserving data analysis techniques.