Online Distributional Regression
To address online probabilistic forecasting for large-scale streaming data, this paper proposes an incremental learning method that integrates online LASSO with the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework—enabling, for the first time, real-time updating of regularized conditional distribution models capturing heteroscedasticity and higher-order moments. The method leverages online gradient optimization coupled with sparse regularization, achieving both statistical interpretability and substantial computational efficiency gains. Evaluated on day-ahead electricity price forecasting, it achieves state-of-the-art probabilistic forecast accuracy while reducing training time by over 80%, supporting millisecond-level dynamic calibration and industrial-grade real-time deployment. Key contributions include: (1) the first scalable online GAMLSS framework; (2) joint sparse estimation and progressive updating of distribution parameters; and (3) an open-source, high-performance Python implementation balancing modeling flexibility with engineering practicality.