It is crucial to be able to explain black-box prediction models to use them effectively and safely in practice. Most existing tools for model explanations are associational rather than causal, and we use two paradoxical examples to show that such explanations are generally inadequate. Motivated by the concept of genetic heritability in twin studies, we propose a new notion called counterfactual explainability for black-box prediction models. Counterfactual explainability has three key advantages: (1) it leverages counterfactual outcomes and extends methods for global sensitivity analysis (such as functional analysis of variance and Sobol's indices) to a causal setting; (2) it is defined not only for the totality of a set of input factors but also for their interactions (indeed, it is a probability measure on a whole ``explanation algebra''); (3) it also applies to dependent input factors whose causal relationship can be modeled by a directed acyclic graph, thus incorporating causal mechanisms into the explanation.
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