Building decision trees with constraints

Classification is an important problem in data mining. Given a database of records, each with a class label, a classifier generates a concise and meaningful description for each class that can be used to classify subsequent records. A number of popular classifiers construct decision trees to generate class models. Frequently, however, the constructed trees are complex with hundreds of nodes and thus difficult to comprehend, a fact that calls into question an often-cited benefit that decision trees are easy to interpret. In this paper, we address the problem of constructing ``simple{''} decision trees with few nodes that are easy for humans to interpret. By permitting users to specify constraints on tree size or accuracy, and then building the ``best{''} tree that satisfies the constraints, we ensure that the final tree is both easy to understand and has good accuracy. We develop novel branch-and-bound algorithms for pushing the constraints into the building phase of classifiers, and pruning early tree nodes that cannot possibly satisfy the constraints. Our experimental results with real-life and synthetic data sets demonstrate that significant performance speedups and reductions in the number of nodes expanded can be achieved as a result of incorporating knowledge of the constraints into the building step as opposed to applying the constraints after the entire tree is built.