Defense Date

3-30-2015

Graduation Date

2015

Availability

Immediate Access

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Karl Wimmer

Committee Member

Jeffrey Jackson

Keywords

Boolean function, DNF expression, graph, ID3, monotone, variable influence

Abstract

Since the Probably Approximately Correct learning model was introduced in 1984, there has been much effort in designing computationally efficient algorithms for learning Boolean functions from random examples drawn from a uniform distribution. In this paper, I take the ID3 information-gain-first classification algorithm and apply it to the task of learning monotone Boolean functions from examples that are uniformly distributed over {0,1}^n. I limited my scope to the class of monotone Boolean functions that can be represented as read-2 width-2 disjunctive normal form expressions. I modeled these functions as graphs and examined each type of connected component contained in these models, i.e. path graphs and cycle graphs. I determined the influence of the variables in the pieces of these graph models in order to understand how ID3 behaves when learning these functions. My findings show that ID3 will produce an optimal decision tree for this class of Boolean functions.

Format

PDF

Language

English

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