Abstract
Conventional decision trees use queries each of which is based on one attribute. In this study, we also examine decision trees that handle additional queries based on hypotheses. This kind of query is similar to the equivalence queries considered in exact learning. Earlier, we designed dynamic programming algorithms for the computation of the minimum depth and the minimum number of internal nodes in decision trees that have hypotheses. Modification of these algorithms considered in the present paper permits us to build decision trees with hypotheses that are optimal relative to the depth or relative to the number of the internal nodes. We compare the length and coverage of decision rules extracted from optimal decision trees with hypotheses and decision rules extracted from optimal conventional decision trees to choose the ones that are preferable as a tool for the representation of information. To this end, we conduct computer experiments on various decision tables from the UCI Machine Learning Repository. In addition, we also consider decision tables for randomly generated Boolean functions. The collected results show that the decision rules derived from decision trees with hypotheses in many cases are better than the rules extracted from conventional decision trees.
Highlights
Decision trees are commonly used as classifiers, as an algorithmic tool for solving various problems, and a means of representing information [1,2,3]
The novelty of the paper is directly related to its two main contributions: (i) the modification of dynamic programming algorithms described in [12] such that the modified algorithms can construct optimal decision trees of five types relative to two cost functions and (ii) the experimental confirmation that the decision rules derived from the decision trees with hypotheses can be more suitable for the representation of information than the decision rules derived from conventional decision trees
The experimental results show that the decision rules derived from decision trees with hypotheses in many cases are better than the ones derived from conventional decision trees
Summary
Decision trees are commonly used as classifiers, as an algorithmic tool for solving various problems, and a means of representing information [1,2,3]. The novelty of the paper is directly related to its two main contributions: (i) the modification of dynamic programming algorithms described in [12] such that the modified algorithms can construct optimal decision trees of five types relative to two cost functions and (ii) the experimental confirmation that the decision rules derived from the decision trees with hypotheses can be more suitable for the representation of information than the decision rules derived from conventional decision trees.
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