Probabilistic electric load forecasting through Bayesian Mixture Density Networks

This work presents a novel approach to address a challenging and still unsolved problem of neural network based load forecasting systems, that despite the significant results reached in terms of prediction error reduction, still lack suitable indications regarding sample-wise trustworthiness of their predictions. The present approach is framed on Bayesian Mixture Density Networks, enhancing the mapping capabilities of neural networks by integrated predictive distributions, and encompassing both aleatoric and epistemic uncertainty sources. An end-to-end training method is developed, aimed to discover the latent functional relation to conditioning variables, characterize the inherent load stochasticity, and convey parameters uncertainty in a unique framework. To achieve reliable and computationally scalable estimators, both Mean Field variational inference and deep ensembles are integrated. Experiments have been performed on short-term load forecasting tasks at both regional and fine-grained household scale, to investigate heterogeneous operating conditions. Different architectural configurations are compared, showing by Continuous Ranked Probability Score based tests that significant performance improvements are achieved by integrating flexible aleatoric uncertainty patterns and multi-modalities in the parameters posterior space.