Regularizing Soft Decision Trees

Abstract

Recently, we have proposed a new decision tree family called soft decision trees where a node chooses both its left and right children with different probabilities as given by a gating function, different from a hard decision node which chooses one of the two. In this paper, we extend the original algorithm by introducing local dimension reduction via $L_1$ and $L_2$ regularization for feature selection and smoother fitting. We compare our novel approach with the standard decision tree algorithms over 27 classification data sets. We see that both regularized versions have similar generalization ability with less complexity in terms of number of nodes, where $L_2$ seems to work slightly better than $L_1$.