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Title: Trees garrote for regression analysis Authors:  Masatoshi Nakamura - Oita university (United States) [presenting]
Abstract: In regression analysis, stochastic models are often constructed to model relationships between outcomes and explanatory variables, and we derive statistical interpretations for data based on these models. However, if we use only linear regression models, constructing a true model reflecting actual characteristics can be difficult. A tree-structured approach is recommended, such as classification and regression trees (CART), which develops a tree and provides an interpretation of the data based on the fundamental model derived from the tree. Random Forest (RF) involves an ensemble learning method based on the trees and can predict outcomes more precisely. However, RF cannot provide a tree-structured model for interpreting the data. A nonnegative garrote (NNG), a shrinkage estimator, is examined, and trees garrote (TG) is proposed as an adjustment of RF based on NNG. Some shrinkage estimators for ensemble learning are reported to yield better predictive performance. In addition, TG can lead to tree-structured models that are useful for interpretation of data. Simulation studies show that the proposed method is highly accurate predictively. Finally, two case studies of diabetes and prostate cancer data illustrate descriptive features of tree-structured models based on TG.