Private and Efficient Federated Statistical Learning

Federated Learning (FL) enables collaborative model training across multiple sites while preserving data privacy and differential privacy (DP) provides a probabilistic framework to safeguard sensitive information when sharing output derived from data. While numerous DP-FL methods exist for large-scale prediction models, achieving DP, efficiency, and robustness in federated statistical learning remains a significant challenge. In this work, we propose a novel federated statistical learning framework that ensures efficient, robust, and privacy-preserving estimation. We introduce a new noising mechanism that encodes Fisher information along with the maximum likelihood estimate (MLE) by leveraging multiple noisy copies of the MLE. To calibrate noise effectively, we extend the smooth sensitivity to account for data-dependent correlations, ensuring strong DP guarantees while maintaining utility. Additionally, we develop INFEMBLER, an information-assembling algorithm that efficiently de-noises multiple noisy MLE copies using a hierarchical Bayesian model and an expectation-maximization (EM) algorithm. INFEMBLER significantly enhances estimation efficiency over existing methods and is inherently robust, providing estimates at least as reliable as those derived from local data alone, thereby preserving the benefits of FL. We establish its asymptotic properties and validate its effectiveness through experiments on both simulated and real datasets, demonstrating its superior statistical efficiency and robustness.