Chapter 2 Interpretability
There is no mathematical definition of interpretability. A (non-mathematical) definition I like by Miller (2017)3 is: Interpretability is the degree to which a human can understand the cause of a decision. Another one is: Interpretability is the degree to which a human can consistently predict the model's result 4. The higher the interpretability of a machine learning model, the easier it is for someone to comprehend why certain decisions or predictions have been made. A model is better interpretable than another model if its decisions are easier for a human to comprehend than decisions from the other model. I will use both the terms interpretable and explainable interchangeably. Like Miller (2017), I think it makes sense to distinguish between the terms interpretability/explainability and explanation. I will use "explanation" for explanations of individual predictions. See the section about explanations to learn what we humans see as a good explanation.
Miller, Tim. "Explanation in artificial intelligence: Insights from the social sciences." arXiv Preprint arXiv:1706.07269. (2017).↩
Kim, Been, Rajiv Khanna, and Oluwasanmi O. Koyejo. "Examples are not enough, learn to criticize! Criticism for interpretability." Advances in Neural Information Processing Systems (2016).↩