Regularized Ensemble Forecasting for Learning Weights from Historical and Current Forecasts

2026-02-11

AI Summary

This work addresses the challenge of effectively aggregating predictions from multiple experts when their historical performance is incomplete or dynamically evolving. The authors propose a regularized ensemble forecasting method that uniquely unifies current predictions with historical accuracy into a single modeling framework. By minimizing the variance of the combined forecast and incorporating a regularization term based on each expert’s past performance, the approach learns optimal aggregation weights. The framework admits a Bayesian interpretation, accommodates flexible distributional assumptions, and naturally handles dynamic expert entry and exit. Empirical evaluations on Walmart sales and macroeconomic forecasting tasks demonstrate that the method consistently outperforms state-of-the-art baselines, regardless of whether experts’ historical records are complete.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Combining forecasts from multiple experts often yields more accurate results than relying on a single expert. In this paper, we introduce a novel regularized ensemble method that extends the traditional linear opinion pool by leveraging both current forecasts and historical performances to set the weights. Unlike existing approaches that rely only on either the current forecasts or past accuracy, our method accounts for both sources simultaneously. It learns weights by minimizing the variance of the combined forecast (or its transformed version) while incorporating a regularization term informed by historical performances. We also show that this approach has a Bayesian interpretation. Different distributional assumptions within this Bayesian framework yield different functional forms for the variance component and the regularization term, adapting the method to various scenarios. In empirical studies on Walmart sales and macroeconomic forecasting, our ensemble outperforms leading benchmark models both when experts'full forecasting histories are available and when experts enter and exit over time, resulting in incomplete historical records. Throughout, we provide illustrative examples that show how the optimal weights are determined and, based on the empirical results, we discuss where the framework's strengths lie and when experts'past versus current forecasts are more informative.

Problem

• ensemble forecasting
• forecast combination
• weight learning
• historical performance
• regularization

Innovation

• regularized ensemble forecasting
• forecast combination
• Bayesian interpretation
• dynamic weight learning
• historical performance regularization