Research map / Adversarial robustness and security / Certified and empirical robustness
Promoting Counterfactual Robustness through Diversity
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Proposes theory of robust counterfactual explanations via sets of approximate counterfactuals, and a diversity-based approximation algorithm that is more robust than DiCE on tabular classifiers.
Problem
Counterfactual explainers can be non-robust: small input changes near the midpoint between decision boundaries cause large changes in the returned counterfactual explanation.
Approach
Shows theoretically that reporting all epsilon-approximate counterfactuals gives weak robustness guarantees, then approximates this exhaustive explainer by selecting a small, diverse, distance-filtered set of dataset counterfactual candidates refined by binary search toward the input.
Key results
- On diabetes, the proposed angle-based method reaches set-distance max 0.59 (L1) vs DiCE 0.66, and runtime 0.02 s vs about 70 s for DiCE.
- On the news dataset the proposed method's L2 set-distance max is 0.52 vs DiCE's 0.94, with runtime 0.30 s vs about 340 s.
- The method achieved 100% validity on three datasets, with DiCE also at 100%; DiCE was more diverse on credit and spambase.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use diversity-based counterfactual generation instead of DiCE | Counterfactual generation · diabetes, no2, credit, spambase, news | set distance (Σ and max; L1): diabetes: 0.33 ±0.1 -> 0.21 ± 0.20; no2: 0.87 ± 0.16 -> 0.16 ± 0.12; credit: 0.72 ± 0.21 -> 0.35 ± 0.18; spambase: 4.20 | Helped |
| Use diversity-based counterfactual generation instead of DiCE | Counterfactual generation · diabetes, no2, credit, spambase, news | set distance max (L1): diabetes: 0.66 ± 0.25 -> 0.51 ± 0.44; no2: 0.47 ± 0.24 -> 0.33 ± 0.24; credit: 1.24 ± 0.31 -> 0.76 ± 0.32; spambase: 7.3 | Helped |
| Use diversity-based counterfactual generation instead of DiCE | Counterfactual generation · diabetes, no2, credit, spambase, news | k-diversity (L1): diabetes: 1.39 ± 0.46 vs 1.32 ± 0.19; no2: 0.78 ± 0.28 vs 0.87 ± 0.16; credit: 1.02 ± 0.37 vs 1.98 ± 0.31; spambase: 0.6 | Mixed |
| Remove binary-search minimisation (ablation) | Diversity method (angle-based) · diabetes, no2, credit, spambase, news | k-distance (L1): diabetes: 1.13 ± 0.43 -> 1.38 ± 0.29; no2: 0.62 ±0.23 -> 0.87 ± 0.20; credit: 0.85 ± 0.33 -> 0.88 ± 0.33; spambase: 1.12 | Hurt |
| Remove binary-search minimisation (ablation) | Diversity method (angle-based) · diabetes, no2, credit, spambase, news | k-diversity (L1): diabetes: 1.39 ± 0.46 -> 1.71 ± 0.3; no2: 0.78 ± 0.28 -> 1.11 ± 0.24; credit: 1.02 ± 0.37 -> 1.06 ± 0.36; spambase: 0.61 | Helped |
| Remove binary-search minimisation (ablation) | Diversity method (angle-based) · diabetes, no2, credit, spambase, news | set distance max (L1): diabetes: 0.51 ± 0.44 -> 0.63 ± 0.56; no2: 0.33 ± 0.24 -> 0.39 ± 0.35; credit: 0.76 ± 0.32 -> 0.78 ± 0.33; spambase: 0.7 | Hurt |
| Remove binary-search minimisation (ablation) | Diversity method (angle-based) · diabetes, no2, credit, spambase, news | set distance Σ (L1): diabetes: 0.21 ± 0.20 -> 0.22 ± 0.24; no2: 0.16 ± 0.12 -> 0.15 ± 0.16; credit: 0.35 ± 0.18 -> 0.35 ± 0.18; spambase: 0.5 | Mixed |
Surprising findings
- Removing the distance minimisation step increased k-diversity and also slightly increased the robustness metrics, suggesting a connection between diversity and robustness.
- DiCE achieved higher k-diversity on credit and spambase, so the proposed method does not dominate on all diversity metrics.
Limitations
- Theoretical exhaustive explainer yields possibly infinite or exponentially large sets, so the approximation loses the formal guarantees.
- Experiments use only 20 or 50 instances per dataset and small neural networks on five tabular datasets.
- Robustness guarantees do not hold for boundary counterfactuals with zero safety margin.
Experimental setup
Datasets: diabetes no2 credit spambase online news popularity
Benchmarks: diabetes no2 credit spambase online news popularity
Metrics: validity k-distance k-diversity set distance (sum) set distance (max) runtime
Baselines: DiCE
Builds on: DiCE Wachter et al. counterfactual explanations
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