Bayesian Uncertainty Calibration for Federated Time Series Analysis

Deep learning models for time series analysis often require large-scale labeled datasets for training. However, acquiring such datasets is cost-intensive and challenging, particularly for individual institutions. To overcome this challenge and concern about data confidentiality among different institutions, federated learning (FL) servers as a viable solution to this dilemma by offering a decentralized learning framework. However, the datasets collected by each institution often suffer from imbalance and may not adhere to uniform protocols, leading to diverse data distributions. To address this problem, we design a global model to approximate the global data distribution of all participant clients, then transfer it to local clients as an induction in the training phase. While discrepancies between the approximate distribution and the actual distribution result in uncertainty in the predicted results. Moreover, the diverse data distributions among various clients within the FL framework, combined with the inherent lack of reliability and interpretability in deep learning models, further amplify the uncertainty of the prediction results. To address these issues, we propose an uncertainty calibration method based on Bayesian deep learning techniques, which captures uncertainty by learning a fidelity transformation to reconstruct the output of time series regression and classification tasks, utilizing deterministic pre-trained models. Extensive experiments on the regression dataset (C-MAPSS) and classification datasets (ESR, Sleep-EDF, HAR, and FD) in the Independent and Identically Distributed (IID) and non-IID settings show that our approach effectively calibrates uncertainty within the FL framework and facilitates better generalization performance in both the regression and classification tasks, achieving state-of-the-art performance.