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Axiomatic Aggregations of Abductive Explanations
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Aggregates the set of abductive explanations of a classifier's prediction into per-feature importance scores via three axiomatically characterized indices (Responsibility, Holler-Packel, Deegan-Packel) and shows them robust to LIME/SHAP adversarial attacks on COMPAS and German Credit.
Problem
Single abductive explanations are incomplete when a data point has several valid minimal sufficient feature subsets, while listing all of them is hard to interpret; LIME and SHAP are also vulnerable to manipulation.
Approach
Map the set of minimal abductive explanations to feature importance scores using three aggregators (Holler-Packel count, Deegan-Packel size-weighted count from cooperative game theory, and the degree of responsibility from causality), each characterized by axioms (monotonicity relative to a ranking function, symmetry, null feature, and efficiency variants).
Key results
- On COMPAS under the LIME attack, Race is ranked first in over 84% of test instances by the Responsibility, Holler-Packel and Deegan-Packel indices, while LIME fails to surface it.
- Under the SHAP attack on COMPAS, abductive aggregators rank Race as most important in at least 86% of test data versus 41.6% for SHAP.
- On German Credit, Gender is ranked top in over 87% of instances by the three indices in both LIME and SHAP attacks, while neither method places it first in any instance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use abductive-explanation aggregation with the Responsibility Index instead of LIME | Compas adversarial classifier · Compas, LIME attack | Race top-1 frequency: 0.0 -> 0.921 | Helped |
| Use abductive-explanation aggregation with the Responsibility Index instead of SHAP | Compas adversarial classifier · Compas, SHAP attack | Race top-1 frequency: 0.416 -> 0.946 | Helped |
| Use abductive-explanation aggregation with the Responsibility Index instead of LIME | German Credit adversarial classifier · German Credit, LIME attack | Gender top-1 frequency: 0.0 -> 1.0 | Helped |
| Use abductive-explanation aggregation with the Responsibility Index instead of SHAP | German Credit adversarial classifier · German Credit, SHAP attack | Gender top-1 frequency: 0.0 -> 0.93 | Helped |
Surprising findings
- SHAP violates the Null Feature property, while the proposed measures satisfy it.
Limitations
- Empirical comparison is limited to adversarial attack setups on two tabular datasets and the three indices are not compared against each other empirically.
- Shapley value is shown not to fit the abductive framework without relaxing the definition of abductive explanations.
Experimental setup
Datasets: COMPAS German Credit
Benchmarks: COMPAS attack experiments (LIME and SHAP) German Credit attack experiments (LIME and SHAP)
Metrics: frequency of sensitive or uncorrelated feature in top-3 rank
Baselines: LIME SHAP
Builds on: abductive explanations MARCO SHAP LIME degree of responsibility
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