On Relating "Why?" and "Why Not?" Explanations

Alexey Ignatiev, Nina Narodytska, Nicholas Asher, Joao Marques-Silva

Keywords: Explanability, contrastive explanations, duality

Abstract:

Explanations of Machine Learning (ML) models often address a ‘Why?’ question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address
a ‘Why Not?’ question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between ‘Why?’ and ‘Why Not?’ explanations. Concretely, the paper proves that, for any given instance, ‘Why?’ explanations are minimal hitting sets of ‘Why Not?’ explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.

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Reviewed Version (pdf): https://openreview.net/references/pdf?id=GYkzgOKfnG