# Probabilistic electric load forecasting through Bayesian Mixture Density Networks

arXiv: https://arxiv.org/abs/2012.14389 · HTML: https://mlsanity.com/paper/2012.14389/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [On-line conformalized neural networks ensembles for probabilistic forecasting of day-ahead electricity prices](https://mlsanity.com/paper/2404.02722/) (2024)
- [Any-Quantile Probabilistic Forecasting of Short-Term Electricity Demand](https://mlsanity.com/paper/2404.17451/) (2024)
- [Integrating Physics-Based and Data-Driven Approaches for Probabilistic Building Energy Modeling](https://mlsanity.com/paper/2507.17526/) (2025)
- [ScenGAN: Attention-Intensive Generative Model for Uncertainty-Aware Renewable Scenario Forecasting](https://mlsanity.com/paper/2509.17119/) (2025)
- [Learning-based Probabilistic Load Forecasting with Post-hoc and In-model Uncertainty](https://mlsanity.com/paper/2607.12730/) (2026)

## Abstract (arXiv)

Probabilistic load forecasting (PLF) is a key component in the extended tool-chain required for efficient management of smart energy grids. Neural networks are widely considered to achieve improved prediction performances, supporting highly flexible mappings of complex relationships between the target and the conditioning variables set. However, obtaining comprehensive predictive uncertainties from such black-box models is still a challenging and unsolved problem. In this work, we propose a novel PLF approach, framed on Bayesian Mixture Density Networks. Both aleatoric and epistemic uncertainty sources are encompassed within the model predictions, inferring general conditional densities, depending on the input features, within an end-to-end training framework. To achieve reliable and computationally scalable estimators of the posterior distributions, both Mean Field variational inference and deep ensembles are integrated. Experiments have been performed on household short-term load forecasting tasks, showing the capability of the proposed method to achieve robust performances in different operating conditions.