Urysohn Forest for Aleatoric Uncertainty Quantification

This paper focuses on building models of stochastic systems with aleatoric uncertainty. The main novelty is an algorithm of boosted ensemble training of multiple models for obtaining a probability distribution of an individual output as a function of the system input. The second novel contribution is a new regression model to be used in the ensemble. The model is a multi-layered tree of hierarchically-connected discrete Urysohn operators (or generalised additive models, which are mathematically equivalent to the discrete Urysohn operators in this case). Since multiple models (trees) are trained in the ensemble, the authors refer them as an Urysohn forest. The source code is freely available online.