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arXiv · 1511.07361

Interpretable Two-level Boolean Rule Learning for Classification

Guolong Su·Dennis Wei·Kush R. Varshney·Dmitry M. Malioutov
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Abstract

This paper proposes algorithms for learning two-level Boolean rules in Conjunctive Normal Form (CNF, i.e. AND-of-ORs) or Disjunctive Normal Form (DNF, i.e. OR-of-ANDs) as a type of human-interpretable classification model, aiming for a favorable trade-off between the classification accuracy and the simplicity of the rule. Two formulations are proposed. The first is an integer program whose objective function is a combination of the total number of errors and the total number of features used in the rule. We generalize a previously proposed linear programming (LP) relaxation from one-level to two-level rules. The second formulation replaces the 0-1 classification error with the Hamming distance from the current two-level rule to the closest rule that correctly classifies a sample. Based on this second formulation, block coordinate descent and alternating minimization algorithms are developed. Experiments show that the two-level rules can yield noticeably better performance than one-level rules due to their dramatically larger modeling capacity, and the two algorithms based on the Hamming distance formulation are generally superior to the other two-level rule learning methods in our comparison. A proposed approach to binarize any fractional values in the optimal solutions of LP relaxations is also shown to be effective.

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BibTeXRIS

Guolong Su, Dennis Wei, Kush R. Varshney, Dmitry M. Malioutov. 2015-11-23. Interpretable Two-level Boolean Rule Learning for Classification. https://arxiv.org/abs/1511.07361

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