# The Price of Interpretability

arXiv: https://arxiv.org/abs/1907.03419 · HTML: https://mlsanity.com/paper/1907.03419/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2019.

## Built on by (most cited first, 10 of 10)

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- [SoK: Explainable Machine Learning for Computer Security Applications](https://mlsanity.com/paper/2208.10605/) (2022)
- [Interpreting Deep Learning Models in Natural Language Processing: A Review](https://mlsanity.com/paper/2110.10470/) (2021)
- [Connecting Interpretability and Robustness in Decision Trees through Separation](https://mlsanity.com/paper/2102.07048/) (2021)
- [Towards Interpretable Hate Speech Detection using Large Language Model-extracted Rationales](https://mlsanity.com/paper/2403.12403/) (2024)
- [Algorithmic Insurance](https://mlsanity.com/paper/2106.00839/) (2021)
- [Rule Generation for Classification: Scalability, Interpretability, and Fairness](https://mlsanity.com/paper/2104.10751/) (2021)
- [Improving Stability in Decision Tree Models](https://mlsanity.com/paper/2305.17299/) (2023)
- [Neural-Symbolic Integration with Evolvable Policies](https://mlsanity.com/paper/2601.04799/) (2026)
- [Active Feature Acquisition for Cost-Efficient Temporal Prediction with Reduced Participant Burden](https://mlsanity.com/paper/2610.07452/) (2026)

## Abstract (arXiv)

When quantitative models are used to support decision-making on complex and important topics, understanding a model's ``reasoning'' can increase trust in its predictions, expose hidden biases, or reduce vulnerability to adversarial attacks. However, the concept of interpretability remains loosely defined and application-specific. In this paper, we introduce a mathematical framework in which machine learning models are constructed in a sequence of interpretable steps. We show that for a variety of models, a natural choice of interpretable steps recovers standard interpretability proxies (e.g., sparsity in linear models). We then generalize these proxies to yield a parametrized family of consistent measures of model interpretability. This formal definition allows us to quantify the ``price'' of interpretability, i.e., the tradeoff with predictive accuracy. We demonstrate practical algorithms to apply our framework on real and synthetic datasets.