Online Multi-Task Learning Framework for Ensemble Forecasting

Ensemble forecasting is a widely-used numerical prediction method for modeling the evolution of nonlinear dynamic systems. To predict the future state of such systems, a set of ensemble member forecasts is generated from multiple runs of computer models, where each run is obtained by perturbing the starting condition or using a different model representation of the system. The ensemble mean or median is typically chosen as a point estimate for the ensemble member forecasts. These approaches are limited in that they assume each ensemble member is equally skillful and may not preserve the temporal autocorrelation of the predicted time series. To overcome these limitations, we present an online multi-task learning framework called ORION to estimate the optimal weights for combining the ensemble member forecasts. Unlike other existing formulations, the proposed framework is novel in that its learning algorithm must backtrack and revise its previous forecasts before making future predictions if the earlier forecasts were incorrect when verified against new observation data. We termed this strategy as online learning with restart. Our proposed framework employs a graph Laplacian regularizer to ensure consistency of the predicted time series. It can also accommodate different types of loss functions, including ϵ-insensitive and quantile loss functions, the latter of which is particularly useful for extreme value prediction. A theoretical proof demonstrating the convergence of our algorithm is also given. Experimental results on seasonal soil moisture forecasts from 12 major river basins in North America demonstrate the superiority of ORION compared to other baseline algorithms.