  Explaining AI systems is fundamental both to the development of high
performing models and to the trust placed in them by their users. The Shapley
framework for explainability has strength in its general applicability combined
with its precise, rigorous foundation: it provides a common, model-agnostic
language for AI explainability and uniquely satisfies a set of intuitive
mathematical axioms. However, Shapley values are too restrictive in one
significant regard: they ignore all causal structure in the data. We introduce
a less restrictive framework, Asymmetric Shapley values (ASVs), which are
rigorously founded on a set of axioms, applicable to any AI system, and
flexible enough to incorporate any causal structure known to be respected by
the data. We demonstrate that ASVs can (i) improve model explanations by
incorporating causal information, (ii) provide an unambiguous test for unfair
discrimination in model predictions, (iii) enable sequentially incremental
explanations in time-series models, and (iv) support feature-selection studies
without the need for model retraining.
