Let Experts Feel Uncertainty: A Multi-Expert Label Distribution Approach to Probabilistic Time Series Forecasting

2026-02-04

AI Summary

This work addresses the challenge of achieving both high predictive accuracy and interpretable uncertainty quantification in real-world time series forecasting, a balance that existing methods often fail to strike. The authors propose a multi-expert label distribution learning (LDL) framework that extends point predictions to full predictive distributions through a mixture-of-experts (MoE) architecture. By integrating time series component decomposition—capturing trend, seasonality, changepoints, and volatility—and leveraging the Maximum Mean Discrepancy (MMD) as a distributional metric, the method enables fine-grained uncertainty modeling with component-level interpretability. Experiments on the M5 hierarchical sales dataset demonstrate that the continuous variant of the multi-expert LDL achieves superior overall performance, while the pattern-aware LDL-MoE excels in providing interpretable insights into the underlying forecasting uncertainty.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• time series forecasting
• uncertainty quantification
• probabilistic forecasting
• interpretability
• predictive accuracy

Innovation

• Label Distribution Learning
• Mixture-of-Experts
• Probabilistic Time Series Forecasting
• Uncertainty Quantification
• Interpretable Forecasting