用于预测组合的广义吉布斯集成加权方法
Generalized Gibbs Ensemble Weighting for Forecast Combination
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- Utrecht University（乌得勒支大学）
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中文总结 AI 辅助
本文提出广义吉布斯集成加权（GGEW）框架，结合在线Local-UCB机制，在多基准数据集上验证其作为预测组合工具的竞争力，为自适应吉布斯型预测组合的应用提供实证依据。
中文摘要 AI 辅助
当存在多个预测模型时，预测组合是提升预测性能的可靠方法。均值、中位数、截尾均值、逆损失加权、指数加权等简单聚合规则通常是强基准方法，但其相对性能会随数据集、预测时域、部署场景以及基础预测器间的分歧程度而变化。本文提出广义吉布斯集成加权（Generalized Gibbs Ensemble Weighting, GGEW），这一概率框架将预测模型视为专家，通过归一化预测损失的吉布斯型指数变换分配集成权重。该框架通过数值稳定性处理、感知多样性的得分修正以及在线超参数自适应扩展了基础加权规则。GGEW衍生出一系列相关方法，包括稳定吉布斯加权、方向吉布斯-NCL和对称吉布斯-NCL，这些变体共享同一核心算法，仅在指数加权规则内部使用的得分上存在差异。对于序列部署，本文采用一种名为在线局部上置信界（online Local-UCB）的上置信界（UCB）型多臂老虎机机制，以在不于每个预测步骤评估完整超参数网格的情况下，自适应调整学习率、多样性强度和吉布斯变体。本文在官方M4竞赛预测提交结果，以及使用莫纳什交通小时级、电力小时级和太阳能周级数据集开展的外部滚动原点部署实验中对GGEW进行评估。结果表明，吉布斯型自适应加权是在多个基准场景中有用且具有竞争力的工具，尽管其相对性能会随数据集、预测时域、部署协议和预测分歧组而变化。本文的贡献并非声称具有普遍优势，而是提供了一个框架和实证研究，以推动进一步探究自适应吉布斯型预测组合何时有用。
英文摘要
Forecast combination is a reliable way to improve predictive performance when several forecasting models are available. Simple aggregation rules such as the mean, median, trimmed mean, inverse-loss weighting, and exponential weighting are often strong baselines, but their relative performance can vary across datasets, forecast horizons, deployment settings, and levels of disagreement among base forecasters. We develop Generalized Gibbs Ensemble Weighting (GGEW), a probabilistic framework that treats forecasting models as experts and assigns ensemble weights using a Gibbs-style exponential transformation of normalized predictive loss. The framework extends this basic weighting rule through numerical stabilization, diversity-aware score corrections, and online hyperparameter adaptation. GGEW produces a family of related methods, including Stable Gibbs weighting, Directional Gibbs-NCL, and Symmetric Gibbs-NCL. These variants share one core algorithm and differ only in the score used inside the exponential weighting rule. For sequential deployment, we adopt a UCB-style bandit mechanism, called online Local-UCB, to adapt the learning rate, diversity strength, and Gibbs variant without evaluating the full hyperparameter grid at every prediction step. We evaluate GGEW on official M4 competition forecast submissions and external rolling-origin deployment experiments using Monash Traffic Hourly, Electricity Hourly, and Solar Weekly datasets. Results suggest that Gibbs-style adaptive weighting is a useful and competitive tool across several benchmark settings, although its relative performance varies across datasets, forecast horizons, deployment protocols, and forecast disagreement groups. The contribution is not a universal dominance claim, but a framework and empirical study motivating further investigation of when adaptive Gibbs-style forecast combination is useful.
