In many data-driven applications, collecting data from different sources is increasingly desirable for enhancing performance. In this paper, we are interested in the problem of probabilistic forecasting with multi-source time series. We propose a neural mixture structure-based probability model for learning different predictive relations and their adaptive combinations from multi-source time series. We present the prediction and uncertainty quantification methods that apply to different distributions of target variables. Additionally, given the imbalanced and unstable behaviors observed during the direct training of the proposed mixture model, we develop a phased learning method and provide a theoretical analysis. In experimental evaluations, the mixture model trained by the phased learning exhibits competitive performance on both point and probabilistic prediction metrics. Meanwhile, the proposed uncertainty conditioned error suggests the potential of the mixture model's uncertainty score as a reliability indicator of predictions.

翻译：在众多数据驱动应用中，为提升性能，从不同来源收集数据的需求日益增长。本文关注多源时间序列的概率预测问题。我们提出一种基于神经混合结构的概率模型，用于从多源时间序列中学习不同的预测关系及其自适应组合。我们提出了适用于不同目标变量分布的预测与不确定性量化方法。此外，针对直接训练所提混合模型时观察到的行为不平衡与不稳定现象，我们开发了一种分阶段学习方法并提供了理论分析。实验评估表明，经分阶段学习训练的混合模型在点预测与概率预测指标上均展现出竞争性表现。同时，所提出的基于条件误差的不确定性度量，揭示了混合模型的不确定性分数作为预测可靠性指标的潜力。