One-Shot Weighted Ensemble Estimation for Federated Quantile Regression: Optimal Statistical Guarantees under Heterogeneous Structured Data

Federated Quantile Regression (FQR) has emerged as a powerful modelling paradigm for estimating conditional quantiles, offering a more comprehensive understanding of response distributions than standard conditional mean regression. However, achieving communication efficiency and optimal statistical guarantees for FQR remains challenging, particularly due to the nonsmooth nature of quantile loss functions and the presence of heterogeneously structured data, where each local agent trains its conditional quantile models with distinct sets of features. In this paper, we propose a data-driven, one-shot weighted ensemble estimator for FQR that incorporates scalable weighting schemes to effectively leverage the partially observed features at each local agent, thereby enjoying both communication efficiency and estimation optimality. Theoretically, we present a unified analysis of the proposed learning procedure, establishing that the resulting estimator exhibits asymptotic normality and attains uniformly minimum variance. Furthermore, we investigate the estimator's sensitivity to perturbations introduced by local agents and derive conditions under which the estimator achieves stability and enjoys strong out-of-sample generalization. Extensive simulations and real data analysis under various scenarios validate the asymptotic normality of our estimator and demonstrate its superior estimation accuracy and uniform convergence compared to several baseline methods across a range of quantile levels.

Federated learning allows multiple agents or data holders to build a shared model without directly sharing their data. In many real-world settings, however, different data holders may collect different types of information, so each agent may observe only part of the full set of features. We study how to learn a reliable shared model in this setting, while the learned model can explain the extreme behavior of a particular feature. In this paper, we developed a data-driven, one-shot weighted ensemble method for federated quantile regression. The proposed method leverages information from local agents in a communication-efficient way, while accounting for the fact that each agent may observe only a subset of features. It is designed to improve estimation/prediction accuracy, reduce communication burden, and remain robust to local perturbations. This framework has potential applications in areas such as hydrology, social sciences, and medicine.