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Computing Inflated Explanations for Boosted Trees: A Compilation-Based Approach

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Abstract

Explaining a classification made by tree-ensembles is an inherently hard problem that is traditionally solved approximately, without guaranteeing sufficiency or necessity. Abductive explanations were the first attempt to provide concise sufficient information: Given a sample, they consist of the minimal set of features that are relevant for the outcome. Inflated explanations are a refinement that additionally specify how much at least one feature must be altered in order to allow a change of the prediction. In this paper, we present the first algorithm for generating inflated explanations for gradient boosted trees, today’s de facto standard for tree-based classifiers. Key to our algorithm is a compilation approach based on algebraic decision diagrams. The impact of our approach is illustrated along a number of popular data sets.

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Notes

  1. 1.

    Neither abductive nor inflated explanations are unique in general (cf. [3]).

  2. 2.

    All of our techniques in this paper can also be applied to decision trees learned on categorical features.

  3. 3.

    These are also known as PI explanations [29] and sufficient reasons [8].

  4. 4.

    This is an extension of classic ADDs which are defined over a domain \(\{0,1\}^n\). By allowing predicates over \(\mathbb F\) we extend the expressiveness of ADDs at the cost of semantic dependencies along paths [13].

  5. 5.

    Based on the class characterization the value 0 represents any class different from \(c_i\).

  6. 6.

    While there are also other approaches to generating abductive explanations such as [1] that is able to achieve slight performance improvement over [17], our approach remains significantly faster by several orders of magnitude compared to [17]. Moreover, our primary contribution lies in the generation of inflated explanations, that neither [17] nor [1] can handle.

  7. 7.

    Note that (1) the learning process can terminate early which results in less than 50 trees and (2) for 2 classes it is sufficient to learn 50 trees in total.

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Murtovi, A., Schlüter, M., Steffen, B. (2025). Computing Inflated Explanations for Boosted Trees: A Compilation-Based Approach. In: Hinchey, M., Steffen, B. (eds) The Combined Power of Research, Education, and Dissemination. Lecture Notes in Computer Science, vol 15240. Springer, Cham. https://doi.org/10.1007/978-3-031-73887-6_14

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