In this book, the concept of a hypothesis about the values of all attributes is added to the standard decision tree model, considered, in particular, in test theory and rough set theory. This extension allows us to use the analog of equivalence queries from exact learning and explore decision trees that are based on various combinations of attributes, hypotheses, and proper hypotheses (analog of proper equivalence queries). The two main goals of this book are (i) to provide tools for the experimental and theoretical study of decision trees with hypotheses and (ii) to compare these decision trees with conventional decision trees that use only queries, each based on a single attribute.
Both experimental and theoretical results show that decision trees with hypotheses can have less complexity than conventional decision trees. These results open up some prospects for using decision trees with hypotheses as a means of knowledge representation and algorithms for computing Boolean functions. The obtained theoretical results and tools for studying decision trees with hypotheses are useful for researchers using decision trees and rules in data analysis. This book can also be used as the basis for graduate courses.
Inhoudsopgave
Introduction.- Main Notions.- Dynamic Programming Algorithms for Minimization of Decision Tree Complexity.- Construction of Optimal Decision Trees and Deriving Decision Rules from Them.- Greedy Algorithms for Construction of Decision Trees with Hypotheses.- Decision Trees with Hypotheses for Recognition of Monotone Boolean Functions and for Sorting.- Infinite Binary Information Systems. Decision Trees of Types 1, 2, and 3.- Infinite Binary Information Systems. Decision Trees of Types 4 and 5.- Infinite Families of Concepts.
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