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Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation
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Proposes FANS, a feature attribution method that scores feature subsets by a probability of necessity and sufficiency (PNS) computed via a dual-stage (factual and interventional) perturbation test with SIR-based resampling, outperforming 18 baselines on three image and three graph datasets.
Problem
Existing feature attribution methods based on perturbation tests cannot distinguish feature contributions when prediction changes after perturbation are similar.
Approach
Score each feature subset by the maximum probability of necessity and sufficiency (PNS) of perturbing it within a heuristically chosen neighborhood, estimating PN and PS with a counterfactual Abduction-Action-Prediction dual-stage test using sampling-importance-resampling on observed data, and optimize the subset by gradient descent.
Key results
- On image datasets FANS reduces Infidelity to 9.0e2 on MNIST versus 1.7e3 for the next best method, a 47.06% improvement on MNIST.
- On graph datasets FANS achieves FID- of 0 on all three datasets and the best FID+ (0.7000 on BACommunity, 0.7600 on Citeseer, 0.4251 on Pubmed).
- FANS yields the best robustness (lowest Max-Sensitivity) on MNIST and CIFAR10 among compared methods, improving on the second best by 13.94% and 6.02%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FANS instead of the strongest baseline | feature attribution on image datasets · MNIST | INF: 47.06% | Helped |
| use FANS instead of the strongest baseline | feature attribution on image datasets · Fashion-MNIST | INF: 29.41% | Helped |
| use FANS instead of the strongest baseline | feature attribution on image datasets · CIFAR10 | INF: 26.09% | Helped |
| remove the sufficiency module (ablation) | FANS · Citeseer and Pubmed | FID+ | Hurt |
| remove the sufficiency module (ablation) | FANS · Citeseer and Pubmed | FID- | Hurt |
| remove the necessity module (ablation) | FANS · Citeseer and Pubmed | FID+ | Hurt |
| remove the necessity module (ablation) | FANS · Citeseer and Pubmed | SPA | Hurt |
| remove SIR-based sampling (ablation) | FANS · Citeseer and Pubmed | FID+ | Hurt |
| remove SIR-based sampling (ablation) | FANS · Citeseer and Pubmed | FID- | Hurt |
| remove SIR-based sampling (ablation) | FANS · Citeseer and Pubmed | SPA | No clear effect |
Surprising findings
- Gradient-based methods show notably higher Max-Sensitivity than FANS, which the authors attribute to gradient sensitivity to noise.
Limitations
- The heuristic estimation of the neighborhood boundary b and threshold c lacks a theoretical identifiability framework.
- Performance is sensitive to the choice of resampling sample set and perturbation settings; graph experiments rely on synthetic graph augmentation because each graph contains a single instance.
Experimental setup
Datasets: MNIST Fashion-MNIST CIFAR10 BACommunity Citeseer Pubmed
Benchmarks: MNIST Fashion-MNIST CIFAR10 BACommunity Citeseer Pubmed
Metrics: Infidelity IROF Sparseness Max-Sensitivity Fidelity+ Fidelity- Recall@12
Baselines: Saliency IG DeepLift IDGI GradShap LIME Occlusion MeaningfulPerturb CIMI NSEG
Builds on: Shapley values Abduction-Action-Prediction NSEG GNNExplainer Integrated Gradients
Closest papers by meaning
- Provably Better Explanations with Optimized Aggregation of Feature Attributions (ICML 2024 · similarity 0.87)
- Data-faithful Feature Attribution: Mitigating Unobservable Confounders via Instrumental Variables (NeurIPS 2024 · similarity 0.86)
- Regional Explanations: Bridging Local and Global Variable Importance (NeurIPS 2025 · similarity 0.86)
- GEFA: A General Feature Attribution Framework Using Proxy Gradient Estimation (ICML 2025 · similarity 0.85)
- Selective Explanations (NeurIPS 2024 · similarity 0.85)
- Rethinking Robustness of Model Attributions (AAAI 2024 · similarity 0.84)
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