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Delivering Inflated Explanations
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Defines inflated abductive and contrastive explanations that replace point literals x_i=v_i with maximal value sets, gives algorithms to compute them for categorical and ordinal features, and shows minimal hitting set duality extends to them.
Problem
Formal abductive explanations use narrow literals (x_i = v_i), which show only that exact feature values yield the decision and say little about whether nearby values would also do so.
Approach
Inflate each AXp feature literal into a maximal set of admissible values E_j (or interval for ordinal features) that preserves sufficiency, via linear/exponential-binary search for ordinal features and value-by-value checks for categorical ones; also generalize CXp's to sets and extend MHS duality to inflated explanations.
Key results
- Inflated AXp computation succeeds in expanding all feature sets except three exceptions across 38 datasets (per the paper's claim).
- Average runtime across datasets is 7.11 seconds (min 0.02, max 144.48), on a MacBook Pro with a dual-core i5.
- For 20 of 38 datasets the average expansion size lies between 100 and 720 values/intervals.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Inflate the feature-value literals in abductive explanations | AXp explanations for random forests · 38 UCI/PMB datasets | feature-domain expansion: 20 out of 38 datasets: 100 to 720; 13 over 38 datasets: 13 to 99 | Helped |
| Inflate the feature-value literals in abductive explanations | AXp explanations for random forests · 38 UCI/PMB datasets | runtime (seconds): 7.11 seconds (resp. 0.02 and 144.48 seconds) | Mixed |
| Use inflated literals instead of single-value literals | Abductive explanations · 38 UCI/PMB datasets | feature-domain expansion | Helped |
Limitations
- Linear search with precision delta is inefficient for small delta; binary search analysis left out of scope.
- Set-wise CXp duality requires reconstructing uninflated explanations first; the stronger CXp form needs MILP/MaxSAT hitting-set computation.
Experimental setup
Datasets: UCI Machine Learning Repository datasets (38 selected) Penn Machine Learning Benchmarks
Benchmarks: 38 UCI/PMLB tabular datasets
Metrics: average explanation length runtime average number of intervals/values in inflated sets
Baselines: AXp (standard abductive explanations)
Builds on: abductive explanations contrastive explanations minimal hitting set duality SAT-based encoding of random forests
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