Learning customized and optimized lists of rules with mathematical programming

Rudin C., Ertekin Ş.

MATHEMATICAL PROGRAMMING COMPUTATION, vol.10, pp.659-702, 2018 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10
  • Publication Date: 2018
  • Doi Number: 10.1007/s12532-018-0143-8
  • Page Numbers: pp.659-702
  • Keywords: Mixed-integer programming, Decision trees, Decision lists, Sparsity, Interpretable modeling, Associative classification 68T05-Computer Science, Artificial intelligence, Learning and adaptive systems, DECISION LISTS, BAYESIAN CART, MODELS


We introduce a mathematical programming approach to building rule lists, which are a type of interpretable, nonlinear, and logical machine learning classifier involving IF-THEN rules. Unlike traditional decision tree algorithms like CART and C5.0, this method does not use greedy splitting and pruning. Instead, it aims to fully optimize a combination of accuracy and sparsity, obeying user-defined constraints. This method is useful for producing non-black-box predictive models, and has the benefit of a clear user-defined tradeoff between training accuracy and sparsity. The flexible framework of mathematical programming allows users to create customized models with a provable guarantee of optimality. The software reviewed as part of this submission was given the DOI (Digital Object Identifier) https://doi.org/10.5281/zenodo.1344142.