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

Xingcai Zhou () and Yu Xiang
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Xingcai Zhou: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, China
Yu Xiang: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, China

Mathematics, 2022, vol. 10, issue 16, 1-28

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.

Keywords: distributed machine learning; ADMM; quantile regression; functional principal component analysis; differential privacy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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