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.
@article{arxiv.2012.11067,
title = {On Relating 'Why?' and 'Why Not?' Explanations},
author = {Alexey Ignatiev and Nina Narodytska and Nicholas Asher and Joao Marques-Silva},
journal= {arXiv preprint arXiv:2012.11067},
year = {2020}
}