Abstract
Explanations of Machine Learning (ML) models often address a
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
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
and
explanations. Concretely, the paper proves that, for any given instance,
explanations are minimal hitting sets of
explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.
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Notes
- 1.
There is also a recent XAI service offered by Google: https://cloud.google.com/explainable-ai/, inspired on similar ideas [28].
- 2.
In contrast with recent work [39], which studies the relationship between global model-based (abductive) explanations and adversarial examples.
- 3.
A local abductive (resp. contrastive) explanation is a minimal hitting set of the set of all local contrastive (resp. abductive) explanations.
- 4.
- 5.
- 6.
- 7.
The definitions in this section are often presented for the propositional case, but the extension to the first-order case is straightforward.
- 8.
The choice of a decision tree aims only at keeping the example(s) presented in the paper as simple as possible. The ideas proposed in the paper apply to any ML model that can be represented with FOL. This encompasses any existing ML model, with minor adaptations in case the ML model keeps state.
- 9.
The abbreviations used relate with the names in the decision tree, and serve for saving space.
- 10.
- 11.
Which in this case are used as propositional variables.
- 12.
- 13.
The prototype and the experimental setup are available at https://github.com/alexeyignatiev/xdual.
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Acknowledgments
This work is supported by the AI Interdisciplinary Institute ANITI (Artificial and Natural Intelligence Toulouse Institute), funded by the French program “Investing for the Future – PIA3” under Grant agreement no ANR-19-PI3A-0004.
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Ignatiev, A., Narodytska, N., Asher, N., Marques-Silva, J. (2021). From Contrastive to Abductive Explanations and Back Again. In: Baldoni, M., Bandini, S. (eds) AIxIA 2020 – Advances in Artificial Intelligence. AIxIA 2020. Lecture Notes in Computer Science(), vol 12414. Springer, Cham. https://doi.org/10.1007/978-3-030-77091-4_21
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