  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.
