2024/04/25 by Zhe Zhang, Zhang, Zhe, Ryumei Nakada +3 · 2 citations
Computer Science · #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Privacy-Preserving Technologies in Data #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2404.16287
openalex publication_date 2024/04/25 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28
Differentially private federated learning is crucial for maintaining privacy in distributed environments. This paper investigates the challenges of high-dimensional estimation and inference under the constraints of differential privacy. First, we study scenarios involving an untrusted central server, demonstrating the inherent difficulties of accurate estimation in high-dimensional problems. Our findings indicate that the tight minimax rates depends on the high-dimensionality of the data even with sparsity assumptions. Second, we consider a scenario with a trusted central server and introduce a novel federated estimation algorithm tailored for linear regression models. This algorithm effectively handles the slight variations among models distributed across different machines. We also propose methods for statistical inference, including coordinate-wise confidence intervals for individual parameters and strategies for simultaneous inference. Extensive simulation experiments support our theoretical advances, underscoring the efficacy and reliability of our approaches.