  We propose a tree regularization framework, which enables many tree models to
perform feature selection efficiently. The key idea of the regularization
framework is to penalize selecting a new feature for splitting when its gain
(e.g. information gain) is similar to the features used in previous splits. The
regularization framework is applied on random forest and boosted trees here,
and can be easily applied to other tree models. Experimental studies show that
the regularized trees can select high-quality feature subsets with regard to
both strong and weak classifiers. Because tree models can naturally deal with
categorical and numerical variables, missing values, different scales between
variables, interactions and nonlinearities etc., the tree regularization
framework provides an effective and efficient feature selection solution for
many practical problems.
