Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayes_FL

翻译：联邦学习（FL）涉及在分布在客户端的数据集上训练模型，且每个客户端的数据集具有本地化且可能异构的约束。在FL中，小规模且有噪声的数据集很常见，这凸显了对能够表示预测不确定性的良好校准模型的需求。最接近实现此类目标的FL技术是贝叶斯FL方法，这些方法从本地后验中收集参数样本，并聚合它们以近似全局后验。为了提高较大模型的可扩展性，一种常见的贝叶斯方法是通过相乘本地预测后验来近似全局预测后验。在本工作中，我们证明该方法会系统性地给出过度自信的预测，并通过提出$\beta$-预测贝叶斯（一种FL贝叶斯算法）来纠正这一问题，该算法通过可调参数$\beta$在预测后验的混合与乘积之间进行插值。该参数经过调优以改善全局集成的校准，随后将其蒸馏为单一模型。我们在多种回归和分类数据集上评估了该方法，证明即使数据异构性增加，其在校准方面也优于其他基线。代码见https://github.com/hasanmohsin/betaPredBayes_FL