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Measurable Counterfactual Local Explanations for Any Classifier
Adam White, Artur d'Avila Garcez
TL;DR
Local explanations are needed when complex classifier boundaries resist global accounts, yet counterfactuals and local regressions each leave gaps. CLEAR combines counterfactual cases with regression and fidelity evaluation; its regressions outperform LIME in fidelity across the reported case studies.
Problem
Local explanations should convey both why a prediction occurred and how it would change under different conditions, while LIME does not measure fidelity or generate counterfactuals.
Source: §1 · p. 1, §2.2 · p. 2Method
Results
Across five case studies, CLEAR improves on LIME’s fidelity by an average of over 40%.
Source: §1 · p. 2Takeaways & Limitations
CLEAR’s regression captures counterfactual dependencies in a neighborhood containing the observation and its b-counterfactuals, and reports its own fidelity.
Source: §5 · p. 6High fidelity may require many regression terms, which may make CLEAR’s equations difficult for lay people to interpret.
Source: §3 · p. 5
Abstract
from arXiv · showhide
We propose a novel method for explaining the predictions of any classifier. In our approach, local explanations are expected to explain both the outcome of a prediction and how that prediction would change if 'things had been different'. Furthermore, we argue that satisfactory explanations cannot be dissociated from a notion and measure of fidelity, as advocated in the early days of neural networks' knowledge extraction. We introduce a definition of fidelity to the underlying classifier for local explanation models which is based on distances to a target decision boundary. A system called CLEAR: Counterfactual Local Explanations via Regression, is introduced and evaluated. CLEAR generates w-counterfactual explanations that state minimum changes necessary to flip a prediction's classification. CLEAR then builds local regression models, using the w-counterfactuals to measure and improve the fidelity of its regressions. By contrast, the popular LIME method, which also uses regression to generate local explanations, neither measures its own fidelity nor generates counterfactuals. CLEAR's regressions are found to have significantly higher fidelity than LIME's, averaging over 45% higher in this paper's four case studies.
1 Introduction
Local explanations address decisions from classifiers whose complex boundaries resist global explanation. CLEAR combines counterfactual cases with local regression and fidelity evaluation, addressing limitations of counterfactual-only and LIME-style explanations.
1 Introduction
- Local explanations are needed when a classifier’s decision boundary is too complex for a global explanation.Source: §1 · p. 1
- Counterfactual cases show how a prediction would change under different input conditions, while regression captures local input-output behavior.Source: §1 · p. 1
- Boundary counterfactuals alone lack generalizations, while LIME neither measures regression fidelity nor produces counterfactual explanations.Source: §1 · pp. 1–2
- CLEAR’s three contributions are counterfactuals explained through regression coefficients, fidelity evaluation, and using b-counterfactual values to improve regression fidelity.Source: §1 · p. 2
- Across five case studies, CLEAR improves on LIME’s fidelity by an average of over 40%.The paper evaluates local regression explanations against the underlying learning system.Source: §1 · p. 2
2 Background
The background contrasts counterfactual explanations, which identify changes that flip a prediction, with local regression explanations, which model behavior near an observation. It motivates combining them because each alone leaves explanatory gaps.
2.1 b-Counterfactual Explanations
- A b-counterfactual identifies the minimum change needed to move an observation across the classifier’s decision boundary; satisfactory explanations also need a generalization relating inputs to predictions.The paper illustrates that a fuller account can include feature contributions and interactions, such as employment years mattering only below a salary threshold.Source: §2.1 · p. 2
2.2 Local Interpretable Model-Agnostic Explanations
- LIME fits a locally weighted regression to classifier-labeled synthetic observations, but does not measure regression fidelity or provide counterfactuals.In the toy figure, LIME uses all 15,000 synthetic observations, while CLEAR selects a balanced subset of approximately 200 and shows corresponding b-perturbations.Source: §2.2 · p. 2, Figure 1 · p. 3
- LIME’s regression scores can diverge from classifier probabilities, and its sampling and weighting may fail to represent the decision-boundary neighborhood needed for counterfactuals.The paper reports score differences above 0.4 in approximately 20% of explanations in its Iris tutorial analysis; adjusted R-squared can also mislead when evaluating counterfactual fidelity.Source: §2.2 · pp. 2–3
2.3 Other Related Work
- SHAP’s values apply to binarized features rather than numeric feature changes, while Anchors and LIME variants do not supply the b-counterfactual basis sought here.The paper says SHAP and Anchors therefore cannot be directly compared with CLEAR, and notes that LIME-SUP, K-LIME, and SLIME do not address its identified LIME problems.Source: §2.3 · p. 3
3 The CLEAR Method
CLEAR explains a prediction through feature changes that would cross a decision boundary, then uses local regression to estimate those changes and measure fidelity. Its workflow balances a neighborhood around the prediction and lets users trade regression complexity against fidelity.
3 The CLEAR Method
- A b-perturbation is the minimum change to one feature that makes the classifier assign the observation to a different target class.CLEAR represents an explanation as actual and estimated b-perturbations, a regression equation, and fidelity errors.Source: §3 · pp. 3–4
- CLEAR generates labeled synthetic data, selects a balanced neighborhood near the observation and across decision-boundary regions, then fits a regression constrained to pass through the observation.The defaults are 50,000 synthetic observations and a 200-observation neighborhood; the paper reports that an imbalanced neighborhood reduced fidelity.Source: §3 · p. 4
- CLEAR estimates each b-perturbation from the regression, compares it with the actual change, and uses the resulting fidelity errors to guide model adjustments.Users can vary features and quadratic or interaction terms; actual b-counterfactuals can optionally be added as weighted soft constraints.Source: §3 · p. 4
- Table 1 reports that CLEAR generally achieves considerably higher % fidelity than LIME, even without b-counterfactual training, and optional training increases fidelity further.The table caption identifies balanced neighborhoods, centering, and quadratic terms as helpful configuration choices.Source: Table 1 · p. 5
- Percentage fidelity is the share of feasible b-perturbations whose fidelity error is below the chosen threshold.Interactive reports can simplify equations, while showing the resulting fidelity reduction so users can manage the interpretability–fidelity trade-off.Source: §3 · p. 5
4 Experimental Results
Across five UCI datasets, CLEAR’s regressions are reported as significantly more faithful than LIME’s. Experiments examine the effects of neighborhood construction, regression complexity, and adding boundary counterfactuals.
4 Experimental Results
- The comparison uses five UCI datasets and evaluates fidelity on 100 selected test observations per dataset.Iris uses an RBF-kernel SVM; the other datasets use MLPs.Source: §4 · p. 5
- CLEAR’s regressions are significantly better than LIME’s, and adding boundary counterfactuals to neighborhood datasets yields the best results.The best configuration also uses balanced neighborhood data, centers the regression at x, includes quadratic and interaction terms, and selects regression type by dataset.Source: §4 · p. 5
- Figure 3 reports lower fidelity when configurations depart from the best setup; balanced neighborhoods help, and CLEAR without quadratic and interaction terms remains more faithful than LIME.The experiments include CLEAR configuration variants and LIME algorithms.Source: Figure 3 · p. 6, §4 · p. 6
- On the Credit dataset, LIME’s fidelity was only 12%, despite over 94% test-set classification accuracy.The authors report that LIME’s kernel partly failed to isolate the neighborhood needed to calculate boundary counterfactuals accurately.Source: §4 · p. 6
- Without boundary counterfactuals, fidelity initially improves as the maximum number of regression variables increases, then plateaus.Table 2 reports variation in fidelity by the choice of number of variables.Source: §4 · p. 6, Table 2 · p. 6
- Adding each identified boundary counterfactual with weight 10 sharply improved CLEAR’s fidelity.For Pima, an average of approximately three boundary counterfactuals was added per neighborhood dataset.Source: §4 · p. 6
5 Conclusion and Future Work
CLEAR explains predictions with boundary counterfactuals and a regression equation, and reports its fidelity. The authors identify further development and practical comprehensibility evaluation as future work.
5 Conclusion and Future Work
- CLEAR combines boundary counterfactuals with a regression equation that represents counterfactual dependencies in a neighborhood containing the observation and counterfactual points.The paper says adding boundary counterfactuals to the neighborhood sharply improves fidelity and that CLEAR reports its own fidelity.Source: §5 · p. 6
- Future work includes improving neighborhood selection and perturbation search, exploring more complex learning algorithms, and evaluating CLEAR in comprehensibility studies.The authors also suggest adding multi-feature boundary counterfactuals or user-selected perturbations.Source: §5 · p. 6