Generalized Gibbs Ensemble Weighting for Forecast Combination

Prasen R. Nuthanakaluva; Nava K. Gaddam

cs.LGAug 28, 2026

Generalized Gibbs Ensemble Weighting for Forecast Combination

Authors: Prasen R. Nuthanakaluva, Nava K. Gaddam

Organizations: Independent Researcher Oxford, United Kingdom · Department of Physics Utrecht University Utrecht, Netherlands

Abstract

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.

Figures & tables

g_{m}=\sum_{t}\frac{G_{t,m}^{(v)}(S_{t}-A_{t,m})}{(M-1)S_{t}+\varepsilon}

Algorithm 1 Generalized Gibbs Ensemble Weighting

Base forecast	Description
last value	repeats most recent value
daily seasonal naive	repeats value from 24 hours ago
weekly seasonal naive	repeats value from 168 hours ago
24-hour mean	repeats recent 24-hour mean
168-hour mean	repeats recent weekly mean
168-hour drift	linear drift over recent week

Table 4: Deterministic rolling baseline forecast pool.

Explore similar work

Jun 1, 2026cs.LG

AdaWeather: Adaptively Mixing Probabilistic Weather Forecasts with Logarithmic Regret

Recent advances in machine learning have produced probabilistic weather forecasting models comparable to state-of-the-art numerical weather predictors. But no model consistently dominates spatio-temporally, and relative performance is highly context-dependent. This motivates adaptive methods for combining multiple forecasts to obtain improvements and robustness. While combined forecasts have been proposed in the literature, these are achieved either through supervised learning or through prediction with expert advice methods. We introduce AdaWeather, an adaptive framework that combines many probabilistic forecasts using both machine learning as well as mixture of experts to arrive at a unified improved probabilistic forecast. While traditional expert methods develop the regret bounds with respect to the best single expert in hindsight, we extend the algorithm and analysis to show our method has logarithmic regret compared to the best static mixture of experts in hindsight. Empirically, we focus on forecasting temperature, and observe improvements over existing methods.

Saptarishi Dhanuka, Sarvesh Iyer, Manmeet Singh +5

Ashoka University · Ashoka University, India · Western Kentucky University

Probabilistic Forecasting Mixture-of-Experts Models Online Learning

Ask PDF

Sep 14, 2026cs.LG

Ensemble Complexity in Photovoltaic Forecasting

An ensemble can improve photovoltaic forecasts while adding components that contribute little or increase computation. We assess these effects through matched comparisons and ablations of a fixed heterogeneous predictor bank. Hourly experiments use GEFCom2014 and three additional public datasets, with chronological partitions and three seeds. Under retrospective ERA5 assistance, static fusion reduces scaled mean absolute error against matched boosting by 1.11%, 4.41%, and 1.63% on PVDAQ, OPSD, and Ausgrid; only OPSD remains supported after multiple-comparison correction. Weather gating offers no consistent incremental benefit. Exploratory member removals show group-level dependence alongside individual redundancy. A separate, previously inspected fifteen-minute case replaces one neural member with a tree predictor: normalized error falls by 1.72%, but measured inference is slower. These findings support component-wise evaluation with explicit limits on weather availability and test-set reuse.

Sun Ze, Zhou Liguo, Xu Yuqing +2

aSchool of Computer Science and Technology, Huaibei Normal University, China

Ensemble Learning Solar Power Forecasting

Ask PDF

Sep 14, 2026cs.AI

Horizon-specific Expert Fusion for Photovoltaic Power Forecasting

Short-term photovoltaic power forecasting requires models to represent regular solar cycles and weather-driven fluctuations whose importance changes with the forecast horizon. This study develops a hierarchical ensemble that combines temporal neural models, historical analogs, state climatology, and gradient-boosted trees. Solar geometry and numerical weather forecasts describe the expected generation conditions, while horizon-specific convex weights combine complementary predictions. A separate calibration step uses available historical forecast errors to account for recent bias. The framework is evaluated on public PVDAQ data at 15--240-minute horizons and on three GEFCom2014 solar zones at hourly horizons up to four hours. On PVDAQ, the ensemble achieves a daylight capacity-normalized mean absolute error of 4.315%, reducing error by 4.11% relative to full-feature LightGBM and by 6.03% relative to fine-tuned Chronos-2 under identical calibration. Expert-removal experiments identify redundancy within the ensemble. Across three training seeds on GEFCom2014, learned fusion improves upon equal weighting but performs comparably to LightGBM. The results support horizon-specific combination as a useful forecasting strategy while showing that its advantage over strong individual models depends on the dataset and evaluation period.

Xu Yuqing, Zhou Liguo, Sun Ze +2

School of Computer Science and Technology, Huaibei Normal University, China

Ensemble Learning Solar Power Forecasting Mixture-of-Experts Models

Ask PDF