Smooth Sigmoid Surrogate (SSS): An Alternative to Greedy Search in Decision Trees

Xiaogang Su, George Ekow Quaye (), Yishu Wei, Joseph Kang, Lei Liu, Qiong Yang, Juanjuan Fan and Richard A. Levine
Additional contact information
Xiaogang Su: Department of Mathematical Science, University of Texas at El Paso, El Paso, TX 79968, USA
George Ekow Quaye: Division of Health Services and Outcomes Research, Children’s Mercy Kansas City, Kansas City, MO 64108, USA
Yishu Wei: Reddit Inc., San Francisco, CA 94102, USA
Joseph Kang: US Census Bureau, Washington, DC 20233, USA
Lei Liu: Division of Biostatistics, Washington University in St. Louis, St. Louis, MO 63110, USA
Qiong Yang: Department of Biostatistics, School of Public Health, Boston University, Boston, MA 02118, USA
Juanjuan Fan: Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA
Richard A. Levine: Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA

Mathematics, 2024, vol. 12, issue 20, 1-28

Abstract: Greedy search (GS) or exhaustive search plays a crucial role in decision trees and their various extensions. We introduce an alternative splitting method called smooth sigmoid surrogate (SSS) in which the indicator threshold function used in GS is approximated by a smooth sigmoid function. This approach allows for parametric smoothing or regularization of the erratic and discrete GS process, making it more effective in identifying the true cutoff point, particularly in the presence of weak signals, as well as less prone to the inherent end-cut preference problem. Additionally, SSS provides a convenient means of evaluating the best split by referencing a parametric nonlinear model. Moreover, in many variants of recursive partitioning, SSS can be reformulated as a one-dimensional smooth optimization problem, rendering it computationally more efficient than GS. Extensive simulation studies and real data examples are provided to evaluate and demonstrate its effectiveness.

Keywords: CART; decision trees; end-cut preference; greedy search; recursive partitioning; sigmoid function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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