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arXiv 1907.03419cs.LGstat.ML

The Price of Interpretability

Sloan School of Management(斯隆管理学院);Massachusetts Institute of Technology(麻省理工学院);Operations Research Center(运筹学研究中心);Dep. of Electrical Engineering and Computer Science(电气工程与计算机科学系)

Dimitris Bertsimas, Arthur Delarue, Patrick Jaillet, Sebastien Martin

英文摘要:

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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