Learning Observation-Guided Probabilistic Forecast Mixtures with Online Regret Guarantees

Data-driven weather models have achieved similar overall performance to physics-based methods, but no single model wins benchmarks. A common next step is blending them, but existing methods are usually simple averages over coarse boxes with less online adaptation and no theoretical relative error guarantees. We look at historical forecast ground station pairs and learn the best mixed model through supervised learning. We then adapt online to streamed observations with expert advice algorithms, and develop novel relative error bounds in terms of probabilistic ensemble metrics. We get 30% + improvements in evaluation metrics relative to standard methods and lower error relative to estimates of the best possible forecast in hindsight, in evaluations over multiple variables and regions. This is extensible to any observation set which can help create bespoke forecasts customized to different uses with formal guarantees.