Simon Hirsch: High-dimensional Energy Forecasting 27 March 2025 16:00 - 17:00

Large scale streaming data are common in many modern ML applications and especially in the energy sector, where renewable production forecasts, meteorological data and price are updated continuously. At the same time, the rise of probabilistic forecasting yields the need for effective, incremental learning of the conditional distribution of the data. Against this background, we present regularized online estimation methods for (multivariate) distributional regression. Our method builds on the penalized iteratively reweighted least squares approach for the estimation of GAMLSS models and leverages online coordinate descent methods for parameter estimation. The talk will discuss univariate and multivariate approaches. Previous work has implemented univariate online distributional regression and while the estimation principle translates seamlessly to multivariate distributions, a major complication is the quadratically growing model size. In current work in progress, we propose a possible remedy by either using regularized, Cholesky-decomposition based parameterizations or by using low-rank approximations of the covariance matrix, both in combination with path-based estimation procedures with early stopping to keep model complexity manageable. We apply our method to generate probabilistic forecasts for the 24-dimensional vector of hourly day-ahead electricity prices in Germany, modelling the conditional mean, scale, and tail behaviour of the joint distribution using the multivariate t-distribution.