# Online Distributional Regression

arXiv: https://arxiv.org/abs/2407.08750 · HTML: https://mlsanity.com/paper/2407.08750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 64 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [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)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean](https://mlsanity.com/paper/2301.11862/) (2023)
- [XGBoostLSS -- An extension of XGBoost to probabilistic forecasting](https://mlsanity.com/paper/1907.03178/) (2019)
- [M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond](https://mlsanity.com/paper/2107.06675/) (2021)
- [Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes](https://mlsanity.com/paper/1502.06557/) (2015)
- [Probabilistic Load Forecasting Based on Adaptive Online Learning](https://mlsanity.com/paper/2011.14721/) (2020)
- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)

## Built on by (most cited first, 3 of 3)

- [Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2504.02518/) (2025)
- [Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning](https://mlsanity.com/paper/2601.02856/) (2026)
- [From Distributional to Quantile Neural Basis Models: the case of Electricity Price Forecasting](https://mlsanity.com/paper/2509.14113/) (2025)

## Abstract (arXiv)

Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted toward probabilistic forecasting. This results in the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity and conditional moments. Against this backdrop, we present a methodology for online estimation of regularized, linear distributional models. The proposed algorithm combines recent developments in online estimation of LASSO models with the well-known GAMLSS framework. We provide a case study on day-ahead electricity price forecasting, in which we show the competitive performance of the incremental estimation combined with strongly reduced computational effort. Our algorithms are implemented in a computationally efficient Python package ondil.