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Interpretable Regional Descriptors: Hyperbox-Based Local Explanations

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Machine Learning and Knowledge Discovery in Databases: Research Track (ECML PKDD 2023)


This work introduces interpretable regional descriptors, or IRDs, for local, model-agnostic interpretations. IRDs are hyperboxes that describe how an observation’s feature values can be changed without affecting its prediction. They justify a prediction by providing a set of “even if” arguments (semi-factual explanations), and they indicate which features affect a prediction and whether pointwise biases or implausibilities exist. A concrete use case shows that this is valuable for both machine learning modelers and persons subject to a decision. We formalize the search for IRDs as an optimization problem and introduce a unifying framework for computing IRDs that covers desiderata, initialization techniques, and a post-processing method. We show how existing hyperbox methods can be adapted to fit into this unified framework. A benchmark study compares the methods based on several quality measures and identifies two strategies to improve IRDs.

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  1. 1.

    In contrast, a counterfactual would be “if you had rich savings and become highly skilled, your credit would be a low risk”. Such statements are not covered by IRDs.

  2. 2.

    However, the concrete strategies can only reveal counterfactual explanations [31].

  3. 3.

    Note that if all genders are part of the box, it does not mean the model is fair.

  4. 4.

  5. 5.

  6. 6.

    For classification models, \(Y' \subset [0, 1]\) must hold.

  7. 7.

    For this, we extended the optimization task of Ribeiro et al. [25] to target IRDs by aiming for a precision of 1 and by including the locality constraint.

  8. 8.

    Double-in-size refers to the size of the training data, not of \(\bar{\underline{{\textbf {X}}}}\).

  9. 9.

    We prefer this measure over computation time because it is independent of the concrete implementation. We have made our best efforts to implement the methods efficiently, but there is usually room for improvement.

  10. 10.

    These data points can also be excluded from the data before training a model. However, our experiments showed the results for the RQs are almost the same.

  11. 11.

    The true hyperbox of the CART model might be larger than the terminal node-induced hyperbox (see Figure S. 5 in the Appendix).

  12. 12.

    The size decuples instead of doubles compared to the training data, because not all training data are \( \in \bar{\underline{B}}\) and, thus, not in \(\bar{\underline{{\textbf {X}}}}\).


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This work has been partially supported by the Federal Statistical Office of Germany.

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Correspondence to Ludwig Bothmann .

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For this work, no personal data was collected or processed. Only open source datasets were used for the illustrative example and the benchmark study. Furthermore, our work does not aim at a possible use for policing or military.

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Dandl, S., Casalicchio, G., Bischl, B., Bothmann, L. (2023). Interpretable Regional Descriptors: Hyperbox-Based Local Explanations. In: Koutra, D., Plant, C., Gomez Rodriguez, M., Baralis, E., Bonchi, F. (eds) Machine Learning and Knowledge Discovery in Databases: Research Track. ECML PKDD 2023. Lecture Notes in Computer Science(), vol 14171. Springer, Cham.

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