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.

本文研究了多源时序下的概率预测问题，提出了一种基于混合结构的神经概率模型用于学习不同的预测关系和它们的自适应组合，并给出了适用于不同目标变量分布的预测和不确定性量化方法，同时提出了分段学习方法，并提供了理论分析和实验评估。

多源时间序列概率预测中的混合结构学习