Document Type
Article
Publication Date
10-2024
Identifier
DOI: 10.3390/math12203190
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.
Journal Title
Mathematics
Volume
12
Issue
20
First Page
3190
Keywords
CART; decision trees; end-cut preference; greedy search; recursive partitioning; sigmoid function
Recommended Citation
Su X, Quaye GE, Wei Y, Kang J, Liu L, Yang Q, Fan J, Levine RA. Smooth Sigmoid Surrogate (SSS): An Alternative to Greedy Search in Decision Trees. Mathematics. 2024; 12(20):3190. https://doi.org/10.3390/math12203190
Comments
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Publisher's Link: https://www.mdpi.com/2227-7390/12/20/3190