Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inference
This addresses privacy-preserving statistical analysis in distributed settings, with incremental contributions to federated learning methods.
The paper tackles high-dimensional estimation and inference in differentially private federated learning, showing that minimax rates depend on data dimensionality even with sparsity, and introduces a novel algorithm for linear regression with a trusted server, supported by simulations.
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.