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A comparison of instance-level counterfactual explanation algorithms for behavioral and textual data: SEDC, LIME-C and SHAP-C


Predictive systems based on high-dimensional behavioral and textual data have serious comprehensibility and transparency issues: linear models require investigating thousands of coefficients, while the opaqueness of nonlinear models makes things worse. Counterfactual explanations are becoming increasingly popular for generating insight into model predictions. This study aligns the recently proposed linear interpretable model-agnostic explainer and Shapley additive explanations with the notion of counterfactual explanations, and empirically compares the effectiveness and efficiency of these novel algorithms against a model-agnostic heuristic search algorithm for finding evidence counterfactuals using 13 behavioral and textual data sets. We show that different search methods have different strengths, and importantly, that there is much room for future research.

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Fig. 1


  1. The original paper presented the framework for counterfactual explanations, subsequently referred to as Evidence Counterfactuals (Provost 2014; Moeyersoms et al. 2016; Chen et al. 2017). The paper discussed several methods for finding such explanations. We evaluate the heuristic best-first search SEDC algorithm here.

  2.  Fernandez et al. (2019) show that having a high importance weight (from SHAP) is neither necessary nor sufficient for a feature to be part of a counterfactual explanation. Therefore, we should be clear that this is an alternative heuristic approach.

  3. Such explanations have been called Evidence Counterfactuals, referring to the feature evidence that leads the classifier to make its classification (Provost 2014; Chen et al. 2017); we will adopt this terminology to differentiate such explanations from the additive feature attribution explanations described next.

  4. The cosine distance is defined as \(cosine(\mathbf {x}',\mathbf {z}') = \frac{\mathbf {x}' \cdot \mathbf {z}'}{||\mathbf {x}'|| \cdot ||\mathbf {z}'||}\) and measures how similar two data instances are irrespective of their size i.e., the number of active features. This seems a suitable choice for behavioral and textual data instances, which can vary a lot in size (e.g., documents with varying lengths, users with different number of movies watched or Facebook pages “Liked”, etc.).

  5. The distance function of SHAP is defined as \(\pi _{\mathbf {x}'}(\mathbf {z}') = \frac{(m'-1)}{(m' \, choose \, s)s(m'-s)}\) where \((m' \, choose \, s) = \frac{m'!}{s!(m'-s)!}\). The number of active features of \(\mathbf {x}'\) is represented by \(m'\) and the subset size s refers to the number of non-zero elements in perturbed instance \(\mathbf {z}'\).

  6. See for open-source code (see Martens and Provost (2014) for more details on the algorithm).

  7. TF-IDF is short for term frequency and inverse document frequency.

  8. See for open-source code.

  9. See for open-source code.

  10. See Currently, no implementation exists for behavioral data, where a single reference value of zero is used. For this reason, we artificially generated text data from the behavioral features and use the CountVectorizer.

  11. See for open-source code.

  12. See We used version 0.29.3 for the experiments.

  13. Median and interquantile range reported rather than the mean and standard deviation because the switching point only takes positive values and is right-skewed.

  14. These instances are “harder” to explain by counterfactuals as they, for example, have many active features that contribute to the model prediction (positive evidence).


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Funding was provided by Research Foundation – Flanders (Grant No. 11G4319N).

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Correspondence to Yanou Ramon.

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Ramon, Y., Martens, D., Provost, F. et al. A comparison of instance-level counterfactual explanation algorithms for behavioral and textual data: SEDC, LIME-C and SHAP-C. Adv Data Anal Classif 14, 801–819 (2020).

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  • Comparative study
  • Counterfactual explanations
  • Instance-level explanations
  • Explainable artificial intelligence
  • Explanation algorithms
  • Binary classification
  • Behavioral data
  • Textual data

Mathematics Subject Classification

  • 90C27 (Combinatorial optimization)
  • 90C59 (Approximation methods and heuristics in MP)
  • 68T01 (General topics in AI)