arXiv:2608.28116cs.LGstat.ML2026-08

用概率方法动态加权多个预测模型,提升组合预测效果。

Generalized Gibbs Ensemble Weighting for Forecast Combination

  • 将模型视为专家,基于损失值的指数变换分配权重
  • 在多个数据集上优于均值、中位数等传统方法
  • 适合需要自适应调整的实时预测场景

当有多个预测模型可用时,组合预测是提升性能的可靠方式。简单聚合规则如均值、中位数、截尾均值、逆损失加权和指数加权常作为强基线,但其表现随数据集、预测期限、部署环境和模型间分歧程度而异。本文提出广义吉布斯集成加权(GGEW),一种概率框架,将预测模型视为专家,通过归一化预测损失的吉布斯式指数变换分配集成权重。该框架通过数值稳定、多样性感知得分修正及在线超参数自适应扩展基础规则。GGEW生成一系列相关方法,包括稳定吉布斯加权、方向性吉布斯-NCL和对称吉布斯-NCL,它们共享核心算法,仅在指数权重中的得分定义上不同。对于序列部署,采用类似UCB的带兵机制——在线局部UCB,无需每步遍历完整超参数网格即可自适应学习率、多样性强度和吉布斯变体。在官方M4竞赛提交结果及外部滚动起源实验中评估,涵盖Monash Traffic Hourly、Electricity Hourly和Solar Weekly数据集。结果显示,吉布斯式自适应加权在多个基准设置中表现优异且具竞争力,但相对表现随数据集、预测期限、部署协议和模型分歧程度变化。贡献不在于宣称普适优势,而是提供一个框架与实证研究,推动对自适应吉布斯式组合预测适用场景的进一步探索。

原文摘要 · Abstract (English)

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.

预测组合加权方法自适应时间序列

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