Conditional-Risk Optimization and KKT Geometry of a Regime- and Horizon-Adaptive Probabilistic Ensemble for Local Weather Forecasting
4 affiliations
- 1Department of Electrotechnical Complexes, Novosibirsk State Technical University, 630073 Novosibirsk, Russia
- 2Department of Information Technology, Tomsk Polytechnic University, 634050 Tomsk, Russia
- 3Yurga Technological Institute (Branch), Tomsk Polytechnic University, 652055 Yurga, Russia
- 4Department of Mechanical Engineering, Tomsk Polytechnic University, 634050 Tomsk, Russia
Abstract
A regime- and horizon-adaptive probabilistic ensemble is proposed for local multi-horizon weather forecasting. The theoretical formulation links conditional second-moment error matrices to posterior probabilities of latent atmospheric-state components, while the Soft_Final scheme combines horizon adaptation, regime-dependent weighting, stabilization, and soft posterior mixing. For the posterior-weighted quadratic model, we derive an exact excess-risk decomposition, a Karush–Kuhn–Tucker (KKT) optimality certificate, an active-boundary decomposition on the probability simplex, and deterministic spectral stability bounds. The experimental dataset comprises 5184 hourly meteorological observations and 1296 forecast records across nine lead times; confirmatory inference is based on six station–season blocks. After Holm correction, statistically significant superiority of Soft_Final over the globally fixed static ensemble is not established, whereas ablation analysis indicates that horizon adaptation contributes more consistently than additional regime conditioning. Probabilistic performance exhibits a substantive trade-off among coverage, interval width, and the continuous ranked probability score (CRPS). The main contribution is a rigorous separation of model optimality, operational approximation, and out-of-sample predictive error. Same-protocol comparisons with ensemble model output statistics (EMOS), Bayesian model averaging (BMA), quantile regression forests (QRFs), and residual conformal post-processing demonstrate competitive but non-uniform performance rather than universal dominance.
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BibTeX
@article{malozyomov2026conditionalrisk,
title = {{Conditional-Risk Optimization and KKT Geometry of a Regime- and Horizon-Adaptive Probabilistic Ensemble for Local Weather Forecasting}},
author = {Boris V. Malozyomov and Nikita V. Martyushev and Denis V. Valuev and Svetlana N. Sorokova and Egor A. Efremenkov and Anton Y. Demin and Alexander V. Pogrebnoy},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203711},
url = {https://www.mdpi.com/2227-7390/14/20/3711},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Conditional-Risk Optimization and KKT Geometry of a Regime- and Horizon-Adaptive Probabilistic Ensemble for Local Weather Forecasting
AU - Boris V. Malozyomov
AU - Nikita V. Martyushev
AU - Denis V. Valuev
AU - Svetlana N. Sorokova
AU - Egor A. Efremenkov
AU - Anton Y. Demin
AU - Alexander V. Pogrebnoy
PY - 2026
DA - 2026/10/13
JO - Mathematics
DO - 10.3390/math14203711
UR - https://www.mdpi.com/2227-7390/14/20/3711
AB - A regime- and horizon-adaptive probabilistic ensemble is proposed for local multi-horizon weather forecasting. The theoretical formulation links conditional second-moment error matrices to posterior probabilities of latent atmospheric-state components, while the Soft_Final scheme combines horizon adaptation, regime-dependent weighting, stabilization, and soft posterior mixing. For the posterior-weighted quadratic model, we derive an exact excess-risk decomposition, a Karush–Kuhn–Tucker (KKT) optimality certificate, an active-boundary decomposition on the probability simplex, and deterministic spectral stability bounds. The experimental dataset comprises 5184 hourly meteorological observations and 1296 forecast records across nine lead times; confirmatory inference is based on six station–season blocks. After Holm correction, statistically significant superiority of Soft_Final over the globally fixed static ensemble is not established, whereas ablation analysis indicates that horizon adaptation contributes more consistently than additional regime conditioning. Probabilistic performance exhibits a substantive trade-off among coverage, interval width, and the continuous ranked probability score (CRPS). The main contribution is a rigorous separation of model optimality, operational approximation, and out-of-sample predictive error. Same-protocol comparisons with ensemble model output statistics (EMOS), Bayesian model averaging (BMA), quantile regression forests (QRFs), and residual conformal post-processing demonstrate competitive but non-uniform performance rather than universal dominance.
SN - 2227-7390
ER -