References:
Tolomei et al. (2017), Wachter et al. (2017), Karlsson et al. (2018), Zhang et al. (2018c), Guidotti et al. (2019), Albini et al. (2020), Artelt and Hammer (2020), Dandl et al. (2020), Kanamori et al. (2020), Karimi et al. (2020), Le et al. (2020), Mothilal et al. (2020), Pawelczyk et al. (2020), Ramon et al. (2020), Sharma et al. (2020), Abrate and Bonchi (2021), Hvilshøj et al. (2021), Pawelczyk et al. (2021), Rasouli and Yu (2021), Looveren and Klaise (2021), Albini et al. (2022), Chou et al. (2022), Bayrak and Bach (2023b), Huang et al. (2023b), Verma et al. (2024)
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To ensure that counterfactuals are understandable and believable, the induced changes should be minimal. This can be assessed by evaluating both the proximity of the counterfactual to the original instance and the sparsity of the changes.
Proximity is commonly measured as the distance between the counterfactual and the original instance . A variety of distance measures are used, with the choice significantly impacting the results [Wachter et al. (2017), Artelt and Hammer (2020), Bayrak and Bach (2023b), Verma et al. (2024)]. Common options include (feature-wise weighted) distances (especially ) [Wachter et al. (2017), Artelt and Hammer (2020), Le et al. (2020), Mothilal et al. (2020), Sharma et al. (2020), Rasouli and Yu (2021), Chou et al. (2022), Verma et al. (2024)], as well as Jaccard or cosine distance [Tolomei et al. (2017)], or combinations thereof [Karimi et al. (2020), Hvilshøj et al. (2021)]. Other notable choices are Mahalanobis distance [Artelt and Hammer (2020), Kanamori et al. (2020), Verma et al. (2024)], Gower distance [Dandl et al. (2020), Karimi et al. (2020)], or feature-wise cumulative density-based distances [Pawelczyk et al. (2020)]. Dataset-specific alternatives include computing the quantile-shift per feature [Albini et al. (2022)]. Different data types require suitable distance measures, e.g.: for graphs, the symmetric difference of adjacency matrices or cosine similarity between node features [Abrate and Bonchi (2021)]; for images, the inverse SSIM score [Sharma et al. (2020)]; and for time series, distances measured per time step [Karlsson et al. (2018)].
Sparsity, in contrast, concerns the number of features changed rather than the extent of change. It is often quantified via the norm, that is, the number (or fraction) of altered features [Albini et al. (2020), Dandl et al. (2020), Le et al. (2020), Mothilal et al. (2020), Ramon et al. (2020), Pawelczyk et al. (2021), Bayrak and Bach (2023b), Verma et al. (2024)].
Bridging sparsity and proximity, measures like [Wachter et al. (2017)] or elastic-net regularization [Looveren and Klaise (2021)] are sometimes used. Depending on the representation, alternative definitions may apply, for example, counting the number of changed rules in rule-based counterfactuals [Guidotti et al. (2019)].
Proximity is commonly measured as the distance between the counterfactual and the original instance . A variety of distance measures are used, with the choice significantly impacting the results [Wachter et al. (2017), Artelt and Hammer (2020), Bayrak and Bach (2023b), Verma et al. (2024)]. Common options include (feature-wise weighted) distances (especially ) [Wachter et al. (2017), Artelt and Hammer (2020), Le et al. (2020), Mothilal et al. (2020), Sharma et al. (2020), Rasouli and Yu (2021), Chou et al. (2022), Verma et al. (2024)], as well as Jaccard or cosine distance [Tolomei et al. (2017)], or combinations thereof [Karimi et al. (2020), Hvilshøj et al. (2021)]. Other notable choices are Mahalanobis distance [Artelt and Hammer (2020), Kanamori et al. (2020), Verma et al. (2024)], Gower distance [Dandl et al. (2020), Karimi et al. (2020)], or feature-wise cumulative density-based distances [Pawelczyk et al. (2020)]. Dataset-specific alternatives include computing the quantile-shift per feature [Albini et al. (2022)]. Different data types require suitable distance measures, e.g.: for graphs, the symmetric difference of adjacency matrices or cosine similarity between node features [Abrate and Bonchi (2021)]; for images, the inverse SSIM score [Sharma et al. (2020)]; and for time series, distances measured per time step [Karlsson et al. (2018)].
Sparsity, in contrast, concerns the number of features changed rather than the extent of change. It is often quantified via the norm, that is, the number (or fraction) of altered features [Albini et al. (2020), Dandl et al. (2020), Le et al. (2020), Mothilal et al. (2020), Ramon et al. (2020), Pawelczyk et al. (2021), Bayrak and Bach (2023b), Verma et al. (2024)].
Bridging sparsity and proximity, measures like [Wachter et al. (2017)] or elastic-net regularization [Looveren and Klaise (2021)] are sometimes used. Depending on the representation, alternative definitions may apply, for example, counting the number of changed rules in rule-based counterfactuals [Guidotti et al. (2019)].