# Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting

arXiv: https://arxiv.org/abs/2504.02518 · HTML: https://mlsanity.com/paper/2504.02518/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 92 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 30 of 31)

- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Semi-Structured Distributional Regression -- Extending Structured Additive Models by Arbitrary Deep Neural Networks and Data Modalities](https://mlsanity.com/paper/2002.05777/) (2020)
- [Distributional neural networks for electricity price forecasting](https://mlsanity.com/paper/2207.02832/) (2022)
- [Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks](https://mlsanity.com/paper/1805.06649/) (2018)
- [Conformal Prediction Interval Estimations with an Application to Day-Ahead and Intraday Power Markets](https://mlsanity.com/paper/1905.07886/) (2019)
- [Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories](https://mlsanity.com/paper/2005.01365/) (2020)
- [Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices](https://mlsanity.com/paper/2010.01844/) (2020)
- [M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond](https://mlsanity.com/paper/2107.06675/) (2021)
- [Evaluating the Discrimination Ability of Proper Multivariate Scoring Rules](https://mlsanity.com/paper/2101.12693/) (2021)
- [Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules](https://mlsanity.com/paper/1910.07325/) (2019)
- [Cholesky-based multivariate Gaussian regression](https://mlsanity.com/paper/2102.13518/) (2021)
- [Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts](https://mlsanity.com/paper/2304.09836/) (2023)
- [Postprocessing of point predictions for probabilistic forecasting of day-ahead electricity prices: The benefits of using isotonic distributional regression](https://mlsanity.com/paper/2404.02270/) (2024)
- [Marginally-calibrated deep distributional regression](https://mlsanity.com/paper/1908.09482/) (2019)
- [Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyond](https://mlsanity.com/paper/2111.14207/) (2021)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Probabilistic multivariate electricity price forecasting using implicit generative ensemble post-processing](https://mlsanity.com/paper/2005.13417/) (2020)
- [Online Missing Value Imputation and Change Point Detection with the Gaussian Copula](https://mlsanity.com/paper/2009.12326/) (2020)
- [Bidding and Scheduling in Energy Markets: Which Probabilistic Forecast Do We Need?](https://mlsanity.com/paper/2203.13159/) (2022)
- [Multi-Target XGBoostLSS Regression](https://mlsanity.com/paper/2210.06831/) (2022)
- [Multivariate Probabilistic CRPS Learning with an Application to Day-Ahead Electricity Prices](https://mlsanity.com/paper/2303.10019/) (2023)
- [Online Distributional Regression](https://mlsanity.com/paper/2407.08750/) (2024)
- [Variable Selection Using a Smooth Information Criterion for Distributional Regression Models](https://mlsanity.com/paper/2110.02643/) (2021)
- [Truly Multivariate Structured Additive Distributional Regression](https://mlsanity.com/paper/2306.02711/) (2023)
- [NBMLSS: probabilistic forecasting of electricity prices via Neural Basis Models for Location Scale and Shape](https://mlsanity.com/paper/2411.13921/) (2024)

## Built on by (most cited first, 2 of 2)

- [Probabilistic intraday electricity price forecasting using generative machine learning](https://mlsanity.com/paper/2506.00044/) (2025)
- [Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning](https://mlsanity.com/paper/2601.02856/) (2026)

## Abstract (arXiv)

Probabilistic electricity price forecasting (PEPF) is vital for short-term electricity markets, yet the multivariate nature of day-ahead prices - spanning 24 consecutive hours - remains underexplored. At the same time, real-time decision-making requires methods that are both accurate and fast. We introduce an online algorithm for multivariate distributional regression models, allowing efficient modeling of the conditional means, variances, and dependence structures of electricity prices. The approach combines multivariate distributional regression with online coordinate descent and LASSO-type regularization (absolute shrinkage and selection operator), enabling scalable estimation in high-dimensional covariate spaces. Additionally, we propose a regularized estimation path over increasingly complex dependence structures, allowing for early stopping and avoiding overfitting. In a case study using historical data from the German day-ahead market, the proposed method yields interpretable and well-calibrated joint prediction intervals for the 24-dimensional price distribution and provides robust performance across a range of proper scoring rules. The results underscore the importance of modeling the dependence structure of electricity prices. Furthermore, we analyze the trade-off between predictive accuracy and computational costs for batch and online estimation and provide a high-performing open-source Python implementation in the ondil package.