Exact Jensen-Shannon Divergence for the Continuous Gaussian Shuffle Model
Abstract
We derive the exact asymptotic expansion for Jensen-Shannon divergence in the Gaussian Shuffle Model of differential privacy: JSD = SNR/(8n) − SNR²/(64n²) + O(n⁻³) where SNR = μ²/σ² is the signal-to-noise ratio and n is the number of users. The negative second-order coefficient −1/64 contrasts with +3/64 for discrete Randomized Response, revealing a fundamental sign reversal between continuous and discrete local randomizers. Both cases unify under JSD = χ²/(8n) + O(n⁻²).
Fields of Study & Subjects
Random Matrices and Applications
Privacy-Preserving Technologies in Data
Survey Sampling and Estimation Techniques
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 9 January 2026
- Language
- EN
- Document type
- Preprint