Abstract
Surrogate models play a crucial role in retrospectively interpreting complex and powerful black box machine learning models via model distillation. This paper focuses on using model-based trees as surrogate models which partition the feature space into interpretable regions via decision rules. Within each region, interpretable models based on additive main effects are used to approximate the behavior of the black box model, striking for an optimal balance between interpretability and performance. Four model-based tree algorithms, namely SLIM, GUIDE, MOB, and CTree, are compared regarding their ability to generate such surrogate models. We investigate fidelity, interpretability, stability, and the algorithms’ capability to capture interaction effects through appropriate splits. Based on our comprehensive analyses, we finally provide an overview of user-specific recommendations.
J. Herbinger and S. Dandl—Contributed equally to this work.
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Notes
- 1.
In regions where only a few feature interactions are present, an additive main effect model is expected to be a good approximation.
- 2.
Meaning surrogate models that partition the feature space into interpretable regions and fit an additive main effect model within each region (e.g., a linear model using only first-order feature effects).
- 3.
For example, until a certain depth of the tree, a certain improvement of the objective after splitting, or a certain significance level for the parameter instability is reached.
- 4.
According to [11] an algorithm for recursive partitioning is called unbiased when, under the conditions of the null hypothesis of independence between target y and features \({\textbf {x}}_{1}, ..., {\textbf {x}}_{p}\), the probability of selecting feature \({\textbf {x}}_{j}\) is 1/p for all \(j = 1, ..., p\) regardless of the measurement scales or the number of missing values.
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Herbinger, J., Dandl, S., Ewald, F.K., Loibl, S., Casalicchio, G. (2024). Leveraging Model-Based Trees as Interpretable Surrogate Models for Model Distillation. In: Nowaczyk, S., et al. Artificial Intelligence. ECAI 2023 International Workshops. ECAI 2023. Communications in Computer and Information Science, vol 1947. Springer, Cham. https://doi.org/10.1007/978-3-031-50396-2_13
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