ADMM-Based Differential Privacy Learning for Penalized Quantile Regression on Distributed Functional Data

Abstract

Alternating Direction Method of Multipliers (ADMM) is a widely used machine learning tool in distributed environments. In the paper, we propose an ADMM-based differential privacy learning algorithm (FDP-ADMM) on penalized quantile regression for distributed functional data. The FDP-ADMM algorithm can resist adversary attacks to avoid the possible privacy leakage in distributed networks, which is designed by functional principal analysis, an approximate augmented Lagrange function, ADMM algorithm, and privacy policy via Gaussian mechanism with time-varying variance. It is also a noise-resilient, convergent, and computationally effective distributed learning algorithm, even if for high privacy protection. The theoretical analysis on privacy and convergence guarantees is derived and offers a privacy–utility trade-off: a weaker privacy guarantee would result in better utility. The evaluations on simulation-distributed functional datasets have demonstrated the effectiveness of the FDP-ADMM algorithm even if under high privacy guarantee.