# An Interpretable Probabilistic Model for Short-Term Solar Power Forecasting Using Natural Gradient Boosting

arXiv: https://arxiv.org/abs/2108.04058 · HTML: https://mlsanity.com/paper/2108.04058/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 80 references that are in the map.
- First posted on arXiv 5 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Neural network interpretability for forecasting of aggregated renewable generation](https://mlsanity.com/paper/2106.10476/) (2021)
- [Bayesian rules and stochastic models for high accuracy prediction of solar radiation](https://mlsanity.com/paper/1309.4999/) (2013)

## Built on by (most cited first, 6 of 6)

- [Quantifying and Explaining Machine Learning Uncertainty in Predictive Process Monitoring: An Operations Research Perspective](https://mlsanity.com/paper/2304.06412/) (2023)
- [Understanding electricity prices beyond the merit order principle using explainable AI](https://mlsanity.com/paper/2212.04805/) (2022)
- [Boosted Ensemble Learning based on Randomized NNs for Time Series Forecasting](https://mlsanity.com/paper/2203.00980/) (2022)
- [Why Reinforcement Learning in Energy Systems Needs Explanations](https://mlsanity.com/paper/2405.18823/) (2024)
- [An Explainable Framework for Machine learning-Based Reactive Power Optimization of Distribution Network](https://mlsanity.com/paper/2311.03863/) (2023)
- [Improving the Accuracy and Interpretability of Neural Networks for Wind Power Forecasting](https://mlsanity.com/paper/2312.15741/) (2023)

## Abstract (arXiv)

PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural gradient boosting (NGBoost) for yielding probabilistic forecasts, while in the second stage, we calculate the Shapley additive explanation (SHAP) values in order to fully comprehend why a prediction was made. To highlight the performance and the applicability of the proposed framework, real data from two PV parks located in Southern Germany are employed. Comparative results with two state-of-the-art algorithms, namely Gaussian process and lower upper bound estimation, manifest a significant increase in the point forecast accuracy and in the overall probabilistic performance. Most importantly, a detailed analysis of the model's complex nonlinear relationships and interaction effects between the various features is presented. This allows interpreting the model, identifying some learned physical properties, explaining individual predictions, reducing the computational requirements for the training without jeopardizing the model accuracy, detecting possible bugs, and gaining trust in the model. Finally, we conclude that the model was able to develop complex nonlinear relationships which follow known physical properties as well as human logic and intuition.