The Price of Interpretability

Abstract

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.

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• Discussion of "Least angle regression" by Efron et al
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• Model Distillation for Revenue Optimization: Interpretable Personalized Pricing
• Interpreting Deep Learning Models in Natural Language Processing: A Review
• Deep Neural Networks for Choice Analysis: A Statistical Learning Theory Perspective
• Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items