their general applicability and considerable empirical evidence with regards to their performance on diverse tasks. Both theoretical aspects and practical applications of such algorithms are active fields of study.

At the same time in recent years another family of predictors, namely those falling under the umbrella of “deep-learning”, have met with success. Despite recent efforts to attain a better understanding of the properties of this model class, there remains much which is not well understood (from a theoretical perspective). Nonetheless, it is clear that the increase in performance of such algorithms is due, at least in part, to their ability to leverage cutting edge GPU technology to efficiently build complex models using huge datasets.

Consequently, an important and largely open question is whether other families of predictors can exploit this technology to increase their performance. In the case of decision trees, recent work [@Kont15] has in fact shown that decision trees and deep learning are not mutually exclusive and can be combined to create powerful predictors. Here, however, we are interested in investigating enhancements of the decision trees algorithms, and in particular regression trees without resorting to building hybrid deep systems.

In particular, we note that an integral component of 