# Learning customized and optimized lists of rules with mathematical programming

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## Abstract

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.

## Keywords

Mixed-integer programming Decision trees Decision lists Sparsity Interpretable modeling Associative classification 68T05—Computer Science Artificial intelligence Learning and adaptive systems## Mathematics Subject Classification

68T05 Learning and adaptive systems 90C11 Mixed integer programming 62-04 Explicit machine computation and programs (not the theory of computation or programming)## Notes

### Acknowledgements

We gratefully acknowledge funding from the MIT Big Data Initiative, and the National Science Foundation under grant IIS-1053407. Thanks to Daniel Bienstock and anonymous reviewers for encouragement and for helping us to improve the readability of the manuscript.

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