Trees with leaves and without leaves

Tree is a connected and oriented graph to describe a hierarchical data structure with a set of linked nodes and the end-nodes called ”leaves”. Tree data structures are considered for supervised classification as well as for nonparametric regression in many fields of applications. Trees with leaves are exploratory trees to learn about the dependence relationship between the target variable and the set of predictors. Ensemble methods and random forest combine more tree structures to define an accurate decision rule for that there is no one tree structure and prediction is made by trees without the possibility to interpret their leaves. This approach can be fruitfully considered for incremental missing data imputation. This paper provides some methodological proposals to improve stability in tree growing and to reduce the computational cost while assuring accuracy in decision rule production.