The paper investigates the challenges of high-dimensional estimation and inference under the constraints of differential privacy in federated learning.
In the first part, the authors study scenarios involving an untrusted central server, demonstrating the inherent difficulties of accurate estimation in high-dimensional problems. They show that the tight minimax rates depend on the high-dimensionality of the data even with sparsity assumptions. This suggests that the untrusted central server setting is not suited for high-dimensional statistical problems in federated learning.
In the second part, the authors consider a scenario with a trusted central server and introduce novel federated estimation and inference algorithms. For the estimation problem, they develop an algorithm that effectively handles the slight variations among models distributed across different machines. The algorithm achieves a near-optimal rate of convergence up to logarithm factors.
For the inference problem, the authors propose methods for statistical inference, including coordinate-wise confidence intervals for individual parameters and strategies for simultaneous inference. Theoretical results show that the proposed confidence intervals are asymptotically valid, supported by simulation experiments.
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arxiv.org
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