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Less is More: Fewer Interpretable Region via Submodular Subset Selection
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Reformulates image attribution as submodular subset selection over masked image sub-regions, scoring subsets by confidence, effectiveness, consistency, and collaboration terms, and greedily selecting regions to improve Deletion/Insertion faithfulness and explain misclassifications.
Problem
Existing image attribution methods produce small regions that are not dense enough and fail to explain samples the model predicts incorrectly (the attribution does not suppress the wrong-class response).
Approach
Treats attribution as maximizing a monotone submodular set function over sub-regions built from a prior saliency map, combining four scores (EDL-based confidence, feature-distance effectiveness, cosine consistency with target feature, and collaboration/leave-out effect), and selects regions greedily with a (1-1/e) guarantee.
Key results
- On CUB-200-2011, HSIC-Attribution with the method improves Deletion from 0.0647 to 0.0613 and Insertion from 0.6843 to 0.7262 for correctly predicted samples.
- For misclassified CUB samples, average highest confidence over the 0-100% range rises 81.0% over HSIC-Attribution (0.2493 to 0.4513) with Insertion up 18.4%.
- Gains persist across VGG-19, MobileNetV2, and EfficientNetV2-M backbones per the appendix.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · Celeb-A validation | Deletion AUC: 0.1151 -> 0.1054 | Helped |
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · Celeb-A validation | Insertion AUC: 0.5692 -> 0.5752 | Helped |
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · VGG-Face2 validation | Insertion AUC: 0.6694 -> 0.6705 | Helped |
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · CUB-200-2011 validation | Insertion AUC: 0.6843 -> 0.7262 | Helped |
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · CUB-200-2011 validation, misclassified samples | Average highest confidence, 0-100% search: 0.2493 -> 0.4513 | Helped |
| Apply submodular subset selection to HSIC-Attribution | HSIC-Attribution · CUB-200-2011 validation, misclassified samples | Insertion AUC: 0.1446 -> 0.1772 | Helped |
| Add confidence score (ablation) | Full submodular attribution function · CUB-200-2011 validation | Deletion AUC: 0.0811 -> 0.0613 | Helped |
| Add effectiveness score (ablation) | Full submodular attribution function · Celeb-A validation | Deletion AUC: 0.1067 -> 0.1054 | Helped |
| Add consistency score (ablation) | Full submodular attribution function · CUB-200-2011 validation | Deletion AUC: 0.0811 -> 0.0613 | Helped |
| Add collaboration score (ablation) | Full submodular attribution function · CUB-200-2011 validation | Deletion AUC: 0.0651 -> 0.0613 | Helped |
| Use HSIC-Attribution saliency map as a prior instead of plain patches (ablation) | Sub-region division · Celeb-A validation | Deletion AUC: 0.1284 -> 0.1054 | Helped |
| Increase confidence-score weight to 20 (ablation) | Full submodular attribution function · CUB-200-2011 validation | Insertion AUC: 0.7262 -> 0.5979 | Hurt |
Surprising findings
- On VGGFace2 the improvement over HSIC-Attribution is marginal (Deletion 0.1317 to 0.1304, Insertion 0.6694 to 0.6705), attributed to noisy images.
Limitations
- Gains are small on VGGFace2, possibly due to noisy images.
- Pixel-level or overly fine division performs worse, and results depend on the quality of the prior attribution map.
- Submodularity proof relies on Taylor approximations and small-region assumptions rather than a rigorous argument.
Experimental setup
Datasets: Celeb-A VGG-Face2 CUB-200-2011
Benchmarks: Celeb-A VGG-Face2 CUB-200-2011
Metrics: Deletion AUC Insertion AUC average highest confidence
Baselines: Saliency Grad-CAM Grad-CAM++ Score-CAM LIME Kernel Shap RISE HSIC-Attribution
Builds on: HSIC-Attribution RISE evidential deep learning submodular greedy maximization (Nemhauser et al.)
Closest papers by meaning
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- GEFA: A General Feature Attribution Framework Using Proxy Gradient Estimation (ICML 2025 · similarity 0.85)
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