Partially Interpretable Models with Guarantees on Coverage and Accuracy

Simple, sufficient explanations furnished by short decision lists can be useful for guiding stakeholder actions. Unfortunately, this transparency can come at the expense of the higher accuracy enjoyed by black box methods, like deep nets. To date, practitioners typically either (i) insist on the simpler model, forsaking accuracy; or (ii) insist on maximizing accuracy, settling for post-hoc explanations of dubious faithfulness. In this paper, we propose a hybrid \emph{partially interpretable model} that represents a compromise between the two extremes. In our setup, each input is first processed by a decision list that can either execute a decision or abstain, handing off authority to the opaque model. The key to optimizing the decision list is to optimally trade off the accuracy of the composite system against coverage (the fraction of the population that receives explanations). We contribute a new principled algorithm for constructing partially interpretable decision lists, providing theoretical guarantees addressing both interpretability and accuracy. As an instance of our result, we prove that when the optimal decision list has length $k$, coverage $c$, and $b$ mistakes, our algorithm will generate a decision list that has length no greater than $4k$, coverage at least $c/2$, and makes at most $4b$ mistakes. Finally, we empirically validate the effectiveness of the new model.