  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.
