Explaining the decisions of black-box models has been a central theme in the study of trustworthy ML. Numerous measures have been proposed in the literature; however, none of them have been able to adopt a provably causal take on explainability. Building upon Halpern and Pearls formal definition of a causal explanation, we derive an analogous set of axioms for the classification setting, and use them to derive three explanation measures. Our first measure is a natural adaptation of Chockler and Halperns notion of causal responsibility, whereas the other two correspond to existing game-theoretic influence measures. We present an axiomatic treatment for our proposed indices, showing that they can be uniquely characterized by a set of desirable properties. We compliment this with computational analysis, providing probabilistic approximation schemes for all of our proposed measures. Thus, our work is the first to formally bridge the gap between model explanations, game-theoretic influence, and causal analysis.
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