Statistical Models and Artificial Neural Networks: Supervised Classification and Prediction Via Soft Trees

摘要

It is well known that any statistical model for supervised or unsu-pervised classification can be realized as a neural network. This discussion is devoted to supervised classification and therefore the essential framework is the family of feedforward nets. Ciampi and Lechevallier have studied two- and three-hidden-layer feedforward neural nets that are equivalent to trees, characterized by neurons with "hard" thresholds. Softening the thresholds has led to more general models. Also, neural nets that realize additive models have been studied, as well as networks of networks that represent a "mixed" classifier (predictor) consisting of a tree component and an additive component. Various "dependent" variables have been studied, including the case of censored survival times. A new development has recently been proposed: the soft tree. A soft tree can be represented as a particular type of hierarchy of experts. This representation can be shown to be equivalent to that of Ciampi and Lechevallier. However, it leads to an appealing interpretation, to other possible generalizations and to a new approach to training. Soft trees for classification and prediction of a continuous variable will be presented. Comparisons between conventional trees (trees with hard thresholds) and soft trees will be discussed and it will be shown that the soft trees achieve better predictions than the hard tree.