Explainability in machine learning is crucial for iterative model development, compliance with regulation, and providing operational nuance to model predictions. Shapley values provide a general framework for explainability by attributing a model's output prediction to its input features in a mathematically principled and model-agnostic way. However, practical implementations of the Shapley framework make an untenable assumption: that the model's input features are uncorrelated. In this work, we articulate the dangers of this assumption and introduce two solutions for computing Shapley explanations that respect the data manifold. One solution, based on generative modelling, provides flexible access to on-manifold data imputations, while the other directly learns the Shapley value function in a supervised way, providing performance and stability at the cost of flexibility. While the commonly used "off-manifold" Shapley values can (i) break symmetries in the data, (ii) give rise to misleading wrong-sign explanations, and (iii) lead to uninterpretable explanations in high-dimensional data, our approach to on-manifold explainability demonstrably overcomes each of these problems.

As the decisions made or influenced by machine learning models increasingly impact our lives, it is crucial to detect, understand, and mitigate unfairness. But even simply determining what "unfairness" should mean in a given context is non-trivial: there are many competing definitions, and choosing between them often requires a deep understanding of the underlying task. It is thus tempting to use model explainability to gain insights into model fairness, however existing explainability tools do not reliably indicate whether a model is indeed fair. In this work we present a new approach to explaining fairness in machine learning, based on the Shapley value paradigm. Our fairness explanations attribute a model's overall unfairness to individual input features, even in cases where the model does not operate on sensitive attributes directly. Moreover, motivated by the linearity of Shapley explainability, we propose a meta algorithm for applying existing trainingtime fairness interventions, wherein one trains a perturbation to the original model, rather than a new model entirely. By explaining the original model, the perturbation, and the fair-corrected model, we gain insight into the accuracy-fairness trade-off that is being made by the intervention. We further show that this meta algorithm enjoys both flexibility and stability benefits with no loss in performance.

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