Interpretable Two-level Boolean Rule Learning for Classification
It addresses the need for human-interpretable classification models in domains requiring transparency, though it is incremental by extending existing one-level rule methods to two-level rules.
This paper tackles the problem of learning interpretable two-level Boolean rules for classification by proposing algorithms that balance accuracy and simplicity, showing that two-level rules outperform one-level rules with noticeable performance improvements and superior results compared to other methods.
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.