FBP: A Frontier-Based Tree-Pruning Algorithm

Authors:
Xiaoming Huo;Seoung Bum Kim;Kwok-Leung Tsui;Shuchun Wang
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA
Venue:
INFORMS Journal on Computing
Year:
2006

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Abstract

A frontier-based tree-pruning algorithm (FBP) is proposed. The new method has an order of computational complexity comparable to cost-complexity pruning (CCP). Regarding tree pruning, it provides a full spectrum of information: namely, (1) given the value of the penalization parameter λ, it gives the decision tree specified by the complexity-penalization approach; (2) given the size of a decision tree, it provides the range of the penalization parameter λ, within which the complexity-penalization approach renders this tree size; (3) it finds the tree sizes that are inadmissible---no matter what the value of the penalty parameter is, the resulting tree based on a complexity-penalization framework will never have these sizes. Simulations on real data sets reveal a “surprise:” in the complexity-penalization approach, most of the tree sizes are inadmissible. FBP facilitates a more faithful implementation of cross validation (CV), which is favored by simulations. Using FBP, a stability analysis of CV is proposed.