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Evaluate with the Inverse: Efficient Approximation of Latent Explanation Quality Distribution
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Proposes the Quality Gap Estimate (QGE), which scores an attribution explanation by subtracting the quality of its order-reversed "inverse" explanation, giving a cheap relative-standing measure that works with any quality metric.
Problem
Explanation quality metrics (faithfulness, localization, robustness) report absolute numbers that do not tell practitioners how an explanation compares to the full space of alternative explanations; existing relative comparisons use random explanations, which are noisy and need many samples.
Approach
Use the inverse explanation (feature ranking reversed, with attribution values permuted accordingly) as a reference point instead of a random explanation; QGE = q(e) - q(e_inv) needs only two metric evaluations and centres near zero for average-quality explanations.
Key results
- On Avila, QGE attains Kendall tau of about 0.7 (85% pair order preserved), comparable to QRAND_K with k above 6 random samples.
- On ImageNet with superpixel explanations, QGE improves Kendall tau over QRAND_1 by 0.108 to 0.150 across five architectures.
- On fMNIST with LeNet, the MC score for Pixel-Flipping rises from 0.579 (QRAND_1) to 0.801 (QGE).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use inverse-ranked explanations in QGE rather than comparing with one random explanation | Pixel-Flipping quality ranking · 20newsgroups, MNIST, CIFAR, and ImageNet | Kendall correlation increase over QRAND1: 0.090±0.05; 0.214±0.04; 0.054±0.04; 0.110±0.02; 0.150±0.03; 0.108±0.08; 0.139±0.03; 0.132±0.08 | Helped |
| Compare against multiple random explanations rather than one random explanation | QGE versus QRANDK · Avila and Glass | Kendall rank correlation | Helped |
| Use QGE with Pixel-Flipping | ImageNet explanation quality ranking · ImageNet | Δτ: 0.142±0.07 | Helped |
| Use QGE with Faithfulness Correlation | Faithfulness Correlation · ImageNet | ΔPA: 0.007±0.01; 0.009±0.01 | No clear effect |
| Use QGE with Faithfulness Estimate | Faithfulness Estimate · ImageNet | ΔPA: 0.368±0.02; 0.397±0.02 | Helped |
| Use QGE with Monotonicity Correlation | Monotonicity Correlation · ImageNet | ΔPA: 0.353±0.05; 0.374±0.03 | Helped |
| Use QGE with localization metrics | Attribution Localisation, TopKIntersection, Relevance Rank Accuracy, Relevance Mass Accuracy, and AUC · CMNIST | Kendall and Spearman correlation increase over QRAND1: 0.500±0.00; 0.015±0.01; 0.089±0.02; 0.501±0.01; 0.496±0.00 | Helped |
| Use QGE rather than QRAND1 for Pixel-Flipping | Faithfulness metric reliability · fMNIST and ImageNet | MC score: 0.579 -> 0.801; 0.634 -> 0.849 | Helped |
| Use QGE rather than QRAND1 for localization reliability | Relevance Rank Accuracy and Relevance Mass Accuracy · fMNIST and ImageNet | MC score: 0.599 -> 0.598; 0.594 -> 0.568; 0.585 -> 0.587; 0.596 -> 0.619 | Mixed |
| Use QGE over QRAND1 with Pixel-Flipping across trained, masked-input, undertrained, and untrained models | Explanation quality ranking · Avila and Glass | Δτ: 0.198±0.12; 0.288±0.05; 0.247±0.09; 0.315±0.06; 0.434±0.01; 0.241±0.11; 0.314±0.01; 0.267±0.06; 0.191±0.02; 0.173±0.10 | Helped |
Surprising findings
- QGE gives little or no advantage over QRAND_1 for Faithfulness Correlation, which is unstable across runs.
- The advantage of QGE grows with model accuracy and explanation quality, and shrinks for untrained models with concentrated quality distributions.
Limitations
- Gains are small or absent for unstable metrics such as Faithfulness Correlation.
- Experiments on exhaustive explanation spaces are limited to small tabular datasets; larger settings use sampled random explanations.
- Pixel-Flipping perturbations with zero masking push inputs out of distribution, which affects the measured advantage.
Experimental setup
Datasets: Avila Glass Identification 20newsgroups MNIST CIFAR ImageNet CMNIST fMNIST
Benchmarks: Avila Glass Identification 20newsgroups MNIST CIFAR ImageNet CMNIST fMNIST
Metrics: Kendall tau Spearman rho MC score (MetaQuantus meta-consistency)
Baselines: QRAND_1 QRAND_K Pixel-Flipping random-baseline comparison
Builds on: Pixel-Flipping Quantus MetaQuantus
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