Federated learning (FL) enables collaborative machine learning across distributed data owners, but data heterogeneity poses a challenge for model calibration. While prior work focused on improving accuracy for non-iid data, calibration remains under-explored. This study reveals existing FL aggregation approaches lead to sub-optimal calibration, and theoretical analysis shows despite constraining variance in clients' label distributions, global calibration error is still asymptotically lower bounded. To address this, we propose a novel Federated Calibration (FedCal) approach, emphasizing both local and global calibration. It leverages client-specific scalers for local calibration to effectively correct output misalignment without sacrificing prediction accuracy. These scalers are then aggregated via weight averaging to generate a global scaler, minimizing the global calibration error. Extensive experiments demonstrate FedCal significantly outperforms the best-performing baseline, reducing global calibration error by 47.66% on average.

翻译：联邦学习（FL）使得分布式数据所有者能够协作进行机器学习，但数据异质性给模型校准带来了挑战。尽管先前的研究侧重于提高非独立同分布数据的准确性，但校准问题仍未得到充分探索。本研究揭示了现有的FL聚合方法会导致次优校准，并且理论分析表明，即使约束客户端标签分布的方差，全局校准误差仍然存在渐近下界。为解决这一问题，我们提出了一种新颖的联邦校准（FedCal）方法，同时强调局部和全局校准。该方法利用客户端特定的缩放器进行局部校准，以有效校正输出偏差而不牺牲预测准确性。这些缩放器随后通过权重平均进行聚合，生成一个全局缩放器，从而最小化全局校准误差。大量实验表明，FedCal显著优于性能最佳的基线方法，平均将全局校准误差降低了47.66%。