Abstract
Recent efforts have uncovered various methods for providing explanations that can help interpret the behavior of machine learning programs. Exact explanations with a rigorous logical foundation provide valid and complete explanations, but they have an epistemological problem: they may be too complex for humans to understand and too expensive to compute even with automated reasoning methods. Interpretability requires good explanations that humans can grasp and can compute.
We take an important step toward specifying what good explanations are by analyzing the epistemically accessible and pragmatic aspects of explanations. We characterize sufficiently good, or fair and adequate, explanations in terms of counterfactuals and what we call the conundra of the explainee, the agent that requested the explanation. We provide a correspondence between logical and mathematical formulations for counterfactuals to examine the partiality of counterfactual explanations that can hide biases; we define fair and adequate explanations in such a setting. We then provide formal results about the algorithmic complexity of fair and adequate explanations.
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Notes
- 1.
[10] provide a superficially similar picture to the pragmatic one we present, but their aim is rather different, to provide a semantics for argumentation frameworks. For us the pragmatic aspect of explanations is better explained via a game theoretic framework; see below.
- 2.
We are implicitly assuming that \(\hat{f}\) is too complex or opaque for its behaviour to be analyzed statically.
- 3.
By increasing the number of literals we can simulate non binary values, so this is not really a limitation as long as the features are finite.
- 4.
See [18] for some experimental evidence of this.
- 5.
In fact, we only assume a finite set of finitely valued features, since an n-valued feature is definable with n Boolean valued features. By complicating the language and logic [7], we can have probability estimates on literals and so encode continuous feature spaces.
- 6.
- 7.
- 8.
Of course \(\mathcal{E}\) might want to know whether her beliefs matched the bank’s reasons for denying her a loan, but that’s a different question—and in particular it’s not a why question.
- 9.
Perhaps \(\mathcal{E}\) is also mistaken about or has an incomplete grasph of f or if not, she is mistaken about how \(\hat{f}\) differs from f). But we will not pursue this here.
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Acknowledgement
We thank the ANR PRCI grant SLANT, the ICT 38 EU grant COALA and the 3IA Institute ANITI funded by the ANR-19-PI3A-0004 grant for research support. We alo thank the reviewers for their insightful comments.
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Asher, N., Paul, S., Russell, C. (2021). Fair and Adequate Explanations. In: Holzinger, A., Kieseberg, P., Tjoa, A.M., Weippl, E. (eds) Machine Learning and Knowledge Extraction. CD-MAKE 2021. Lecture Notes in Computer Science(), vol 12844. Springer, Cham. https://doi.org/10.1007/978-3-030-84060-0_6
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