Counterfactual Models for Fair and Adequate Explanations

Recent efforts have uncovered various methods for providing explanations that can help interpret the behavior of machine learning programs. Exact explanations with a rigorous logical foundation provide valid and complete explanations, but they have an epistemological problem: they are often too complex for humans to understand and too expensive to compute even with automated reasoning methods. Interpretability requires good explanations that humans can grasp and can compute. We take an important step toward specifying what good explanations are by analyzing the epistemically accessible and pragmatic aspects of explanations. We characterize sufficiently good, or fair and adequate, explanations in terms of counterfactuals and what we call the conundra of the explainee, the agent that requested the explanation. We provide a correspondence between logical and mathematical formulations for counterfactuals to examine the partiality of counterfactual explanations that can hide biases; we define fair and adequate explanations in such a setting. We provide formal results about the algorithmic complexity of fair and adequate explanations. We then detail two sophisticated counterfactual models, one based on causal graphs, and one based on transport theories. We show transport based models have several theoretical advantages over the competition as explanation frameworks for machine learning algorithms.