Urysohn Forest for Aleatoric Uncertainty Quantification

The terms tree and forest are normally associated with an ensemble of classifiers. In this article Urysohn tree is a regression model representing multiple discrete Urysohn operators connected as a tree, where the inputs of one operator are outputs of the others. This structure, referred as Urysohn tree, is not completely new. One example of such tree is known for more than half a century. It is Kolmogorov-Arnold representation. The authors of this paper in their recently published research offered the new computational technique for constructing of Kolmogorov-Arnold representation as a deep machine learning process. This article is two steps further into this research. It has two parts. First is a lightweight binary Urysohn tree which is adequate replacement of Kolmogorov-Arnold model and second is a boosting algorithm for building of the forest of these trees for variance reduction and modeling of aleatoric uncertainty of the data.