# MINTY: Rule-based Models that Minimize the Need for Imputing Features with Missing Values

arXiv: https://arxiv.org/abs/2311.14108 · HTML: https://mlsanity.com/paper/2311.14108/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Learning Optimized Risk Scores](https://mlsanity.com/paper/1610.00168/) (2016)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [Linear predictor on linearly-generated data with missing values: non consistency and solutions](https://mlsanity.com/paper/2002.00658/) (2020)
- [Characterization of Overlap in Observational Studies](https://mlsanity.com/paper/1907.04138/) (2019)
- [R-miss-tastic: a unified platform for missing values methods and workflows](https://mlsanity.com/paper/1908.04822/) (2019)
- [Sharing pattern submodels for prediction with missing values](https://mlsanity.com/paper/2206.11161/) (2022)
- [A New Method to Compare the Interpretability of Rule-based Algorithms](https://mlsanity.com/paper/2004.01570/) (2020)

## Built on by (most cited first, 3 of 3)

- [Interpretable Generalized Additive Models for Datasets with Missing Values](https://mlsanity.com/paper/2412.02646/) (2024)
- [Leveraging Predictive Equivalence in Decision Trees](https://mlsanity.com/paper/2506.14143/) (2025)
- [Prediction Models That Learn to Avoid Missing Values](https://mlsanity.com/paper/2505.03393/) (2025)

## Abstract (arXiv)

Rule models are often preferred in prediction tasks with tabular inputs as they can be easily interpreted using natural language and provide predictive performance on par with more complex models. However, most rule models' predictions are undefined or ambiguous when some inputs are missing, forcing users to rely on statistical imputation models or heuristics like zero imputation, undermining the interpretability of the models. In this work, we propose fitting concise yet precise rule models that learn to avoid relying on features with missing values and, therefore, limit their reliance on imputation at test time. We develop MINTY, a method that learns rules in the form of disjunctions between variables that act as replacements for each other when one or more is missing. This results in a sparse linear rule model, regularized to have small dependence on features with missing values, that allows a trade-off between goodness of fit, interpretability, and robustness to missing values at test time. We demonstrate the value of MINTY in experiments using synthetic and real-world data sets and find its predictive performance comparable or favorable to baselines, with smaller reliance on features with missing values.