# Distributionally Robust Regularization of Sparse Integer Programming Trained Learning Models

arXiv: https://arxiv.org/abs/2311.01994 · HTML: https://mlsanity.com/paper/2311.01994/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 7 of 7)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [The Empirical Likelihood Approach to Quantifying Uncertainty in Sample Average Approximation](https://mlsanity.com/paper/1604.02573/) (2016)
- [A Distributionally Robust Boosting Algorithm](https://mlsanity.com/paper/1905.07845/) (2019)

## Abstract (arXiv)

Building explainable machine learning models is crucial for human users to be able to interpret the proposed statistical relationship obtained from the training data. Mixed-integer optimization formulations are often used to train such models with explicit sparsity constraints, aiming to strike the right trade-off between sparsity and prediction accuracy. Existing methods to find the right choice of sparsity -- e.g., via cross-validation -- are computationally expensive. For convex model training formulations, recent advances in distributionally robust optimization (DRO) provide strong generalization while sidestepping this computational burden. We describe an extension of such regularization via DRO to mixed-integer sparse programs, providing statistical guarantees as a function of an associated sparsity parameter of the formulation. We illustrate the use of this approach in the case of building explainable binary classification models using sets of feature value rules.