Bounds on Depth of Decision Trees Derived from Decision Rule Systems

TL;DR

This paper investigates the theoretical limits on the minimum depth of decision trees that can be derived from decision rule systems, based on various system parameters, to understand their relationship and optimize their design.

Contribution

It establishes unimprovable upper and lower bounds on decision tree depth derived from decision rule systems, advancing the theoretical understanding of their relationship.

Findings

Derived bounds depend on system parameters

Bounds are proven to be unimprovable

Provides insights for optimizing decision tree construction

Abstract

Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of relationships between these two models is an important task of computer science. It is easy to transform a decision tree into a decision rule system. The inverse transformation is a more difficult task. In this paper, we study unimprovable upper and lower bounds on the minimum depth of decision trees derived from decision rule systems depending on the various parameters of these systems.