Regression Trees With Fused Leaves

Statistics in Medicine, vol. 43, pp. 5872–5884

Abstract

We propose a novel regression tree method named "TreeFuL," an abbreviation for 'Tree with Fused Leaves.' TreeFuL innovatively combines recursive partitioning with fused regularization, offering a distinct approach to the conventional pruning method. One of TreeFuL's noteworthy advantages is its capacity for cross-validated amalgamation of non-neighboring terminal nodes. This is facilitated by a leaf coloring scheme that supports tree shearing and node amalgamation. As a result, TreeFuL facilitates the development of more parsimonious tree models without compromising predictive accuracy. The refined model offers enhanced interpretability, making it particularly well-suited for biomedical applications of decision trees, such as disease diagnosis and prognosis. We demonstrate the practical advantages of our proposed method through simulation studies and an analysis of data collected in an obesity study.

Authors 7

1. Xiaogang Su

   The University of Texas at El Paso

   Affiliation as printed

   Department of Mathematical Sciences The University of Texas El Paso Texas USA

   Department of Mathematical Sciences, The University of Texas, El Paso, Texas, USA

2. Lei Liu corresponding

   Washington University in St. Louis

   Affiliation as printed

   Division of Biostatistics Washington University in St. Louis St. Louis Missouri USA

   Division of Biostatistics, Washington University in St. Louis, St. Louis, Missouri, USA

3. Lili Liu

   Washington University in St. Louis

   Affiliation as printed

   Division of Biostatistics Washington University in St. Louis St. Louis Missouri USA

   Division of Biostatistics, Washington University in St. Louis, St. Louis, Missouri, USA

4. Ruiwen Zhou Aachen Institute of Psychology, Leiden University

   Leiden University · Washington University in St. Louis

   Affiliation as printed

   Division of Biostatistics Washington University in St. Louis St. Louis Missouri USA

   Institute of Psychology, Leiden University, EZ Leiden, The Netherlands

5. Guoqiao Wang

   Washington University in St. Louis · California State University, Long Beach

   Affiliation as printed

   Department of Neurology Washington University in St. Louis St. Louis Missouri USA

   Division of Biostatistics Washington University in St. Louis St. Louis Missouri USA

   Department of Mathematics and Statistics, California State University, Long Beach, California, USA

6. Elise Dusseldorp Aachen Institute of Psychology Leiden University EZ Leiden The Netherlands

   Leiden University

   Affiliation as printed

   Institute of Psychology Leiden University EZ Leiden The Netherlands

7. Tianni Zhou

   California State University, Long Beach

   Affiliation as printed

   Department of Mathematics and Statistics California State University Long Beach California USA