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

TL;DR

This paper introduces a multi-expert distributional learning framework for probabilistic time series forecasting that enhances uncertainty quantification and interpretability, outperforming traditional methods on real-world sales data.

Contribution

The paper proposes a novel Multi-Expert LDL framework with pattern-aware extensions that decompose time series into interpretable components, improving both accuracy and interpretability.

Findings

Superior performance on M5 sales data

Enhanced interpretability through component decomposition

Effective uncertainty quantification with MMD

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.