FTP outperforms PTF in differential privacy for functional data
Original title: On the Order of Privacy and Smoothing in Functional Mean Estimation
Fit-Then-Protect yields smaller mean squared error than Protect-Then-Fit under Gaussian differential privacy in functional mean estimation
The paper compares two pipelines for differential privacy in functional mean estimation: Fit-Then-Protect, which smooths before privatizing, and Protect-Then-Fit, which privatizes first. FTP achieves strictly smaller asymptotic mean squared error than PTF under the same μ-Gaussian differential privacy budget in Hilbert and RKHS spaces. Simulations confirm the result under noise, with PTF better in high-noise cases. A novel Gaussian differential privacy guarantee for Banach spaces is also provided.
- FTP has strictly smaller MSE than PTF asymptotically
- Theory holds in finite and infinite-dimensional spaces
- FTP outperforms in low observation noise
- PTF preferable in high-noise settings
From the original article
1 min read at arxiv.orgDifferential privacy (DP) is a leading framework for privacy protection, yet privacy mechanisms tailored to functional data analysis (FDA) remain relatively underexplored.
By Haotian Chen · arxiv.org
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