Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data, while existing probabilistic approaches struggle to balance computational efficiency with interpretability. We propose a novel Multi-Expert Learning Distributional Labels (LDL) framework that addresses these challenges through mixture-of-experts architectures with distributional learning capabilities. Our approach introduces two complementary methods: (1) Multi-Expert LDL, which employs multiple experts with different learned parameters to capture diverse temporal patterns, and (2) Pattern-Aware LDL-MoE, which explicitly decomposes time series into interpretable components (trend, seasonality, changepoints, volatility) through specialized sub-experts. Both frameworks extend traditional point prediction to distributional learning, enabling rich uncertainty quantification through Maximum Mean Discrepancy (MMD). We evaluate our methods on aggregated sales data derived from the M5 dataset, demonstrating superior performance compared to baseline approaches. The continuous Multi-Expert LDL achieves the best overall performance, while the Pattern-Aware LDL-MoE provides enhanced interpretability through component-wise analysis. Our frameworks successfully balance predictive accuracy with interpretability, making them suitable for real-world forecasting applications where both performance and actionable insights are crucial.

翻译：现实应用中的时间序列预测既需要高预测精度，也需要可解释的不确定性量化。传统点预测方法往往无法捕捉时间序列数据固有的不确定性，而现有概率方法难以在计算效率与可解释性之间取得平衡。我们提出了一种新颖的多专家学习分布标签框架，该框架通过具备分布学习能力的专家混合架构应对这些挑战。我们的方法引入了两种互补技术：（1）多专家LDL，采用具有不同学习参数的多个专家来捕捉多样化的时序模式；（2）模式感知LDL-MoE，通过专用子专家将时间序列显式分解为可解释的组成部分（趋势、季节性、变点、波动性）。两种框架都将传统点预测扩展至分布学习，通过最大平均差异实现丰富的不确定性量化。我们在基于M5数据集构建的聚合销售数据上评估了所提方法，结果表明其性能优于基线方法。连续型多专家LDL取得了最佳综合性能，而模式感知LDL-MoE通过分量分析提供了更强的可解释性。我们的框架成功实现了预测精度与可解释性的平衡，适用于同时需要高性能和可操作洞察的现实世界预测应用场景。