Probabilistic energy forecasting through quantile regression in reproducing kernel Hilbert spaces

Accurate energy demand forecasting is crucial for sustainable and resilient energy development. To meet the Net Zero Representative Concentration Pathways (RCP) $4.5$ scenario in the DACH countries, increased renewable energy production, energy storage, and reduced commercial building consumption are needed. This scenario's success depends on hydroelectric capacity and climatic factors. Informed decisions require quantifying uncertainty in forecasts. This study explores a non-parametric method based on \emph{reproducing kernel Hilbert spaces (RKHS)}, known as kernel quantile regression, for energy prediction. Our experiments demonstrate its reliability and sharpness, and we benchmark it against state-of-the-art methods in load and price forecasting for the DACH region. We offer our implementation in conjunction with additional scripts to ensure the reproducibility of our research.

Samplet basis pursuit

We consider kernel-based learning in samplet coordinates with l1-regularization. The application of an l1-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Therefore, we call this approach samplet basis pursuit. Samplets are wavelet-type signed measures, which are tailored to scattered data. They provide similar properties as wavelets in terms of localization, multiresolution analysis, and data compression. The class of signals that can sparsely be represented in a samplet basis is considerably larger than the class of signals which exhibit a sparse representation in the single-scale basis. In particular, every signal that can be represented by the superposition of only a few features of the canonical feature map is also sparse in samplet coordinates. We propose the efficient solution of the problem under consideration by combining soft-shrinkage with the semi-smooth Newton method and compare the approach to the fast iterative shrinkage thresholding algorithm. We present numerical benchmarks as well as applications to surface reconstruction from noisy data and to the reconstruction of temperature data using a dictionary of multiple kernels.