Research map / Learning theory and algorithms / Prediction and decision losses
Counterfactual Metarules for Local and Global Recourse
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Introduces T-CREx, a model-agnostic method that uses tree-based surrogates to learn hyperrectangular counterfactual rules and metarules (regions where each rule is optimal), enabling both local and global recourse explanations.
Problem
Counterfactual explanations are usually given per instance or as single group-level points, which are hard to summarise and provide poor global insight; existing rule-based CE methods are slow, binary-only, or use arbitrary binning.
Approach
Grow tree-based surrogate(s) on model outputs, extract hyperrectangular candidate rules, keep maximal-valid rules under accuracy and feasibility thresholds, partition the input space into grid cells whose optimal rule is found via a sparsity-plus-feasibility cost, and merge cells into metarules with a second constrained tree so each leaf gives a rule and its region of optimality.
Key results
- T-CREx-hi (tau=0.99) returns the most accurate rules on eight of nine binary datasets, while T-CREx-lo (tau=0.9) returns the most feasible rules on every dataset.
- T-CREx variants are 3-4 orders of magnitude faster than the slowest baseline; total runtime for all test inputs across all folds and datasets is 4.16s (lo) and 4.52s (hi), 13x less than mean per-input ARES runtime on HELOC.
- Consistency: T-CREx outperforms all baselines on eight of nine datasets, and it generates regression CEs in about 0.1 ms per instance on Wine Quality.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use T-CREx with τ=0.99 instead of τ=0.9 (ablation) | T-CREx on nine binary classification datasets · Nine binary classification datasets | accuracy | Helped |
| Use T-CREx with τ=0.99 instead of τ=0.9 (ablation) | T-CREx on nine binary classification datasets · Nine binary classification datasets | feasibility | Hurt |
| Use T-CREx with τ=0.99 instead of τ=0.9 (ablation) | T-CREx on nine binary classification datasets · Nine binary classification datasets | complexity | Hurt |
| Use T-CREx with τ=0.99 instead of τ=0.9 (ablation) | T-CREx on nine binary classification datasets · Nine binary classification datasets | counterfactual distance (total percentile shift) | Hurt |
| Increase the surrogate tree count from one tree to multiple trees (ablation) | T-CREx · Binary classification datasets | consistency | Hurt |
| Increase the surrogate tree count from one tree to multiple trees (ablation) | T-CREx · Binary classification datasets | runtime | Hurt |
| Increase the surrogate tree count from one tree to multiple trees (ablation) | T-CREx · Binary classification datasets | feasibility | Mixed |
| Increase the surrogate tree count from one tree to multiple trees (ablation) | T-CREx · Binary classification datasets | accuracy | No clear effect |
| Increase the accuracy threshold τ (ablation) | T-CREx · Binary classification datasets | accuracy | Helped |
| Increase the accuracy threshold τ (ablation) | T-CREx · Binary classification datasets | feasibility | Hurt |
| Use T-CREx instead of ARES | Counterfactual rule generation · Nine binary classification datasets | runtime: 4.16s and 4.52s; 13× less than the mean runtime per input of ARES on HELOC | Helped |
| Use T-CREx instead of RFocse | Counterfactual rule generation · Every binary classification dataset | runtime: at least an order of magnitude | Helped |
Surprising findings
- Using a single surrogate tree outperforms two trees on feasibility, sparsity and complexity in many cases, attributed to using the full dataset rather than bootstrap samples.
- RFOCSE returns rules so specific that they often contain zero test instances, giving poor feasibility.
Limitations
- Tied to a specific sparsity-plus-feasibility cost function and lacks actionability constraints, so it can return non-actionable counterfactuals (e.g., lowering age).
- Does not optimise for distance-based counterfactual magnitude; its distance performance is only comparable to baselines.
- Runtime of the rule/metarule construction grows exponentially with input dimensionality D and the number of trees; a cell limit is needed.
Experimental setup
Datasets: Abalone Adult Banknote COMPAS Credit HELOC Mammographic Mass Occupancy Pima Indians Diabetes Wine Quality
Benchmarks: Abalone Adult Banknote COMPAS Credit HELOC Mammographic Mass Occupancy Pima Indians Diabetes Wine Quality
Metrics: feasibility accuracy sparsity complexity consistency runtime total percentile shift distance
Baselines: ARES LORE RFOCSE
Builds on: LORE RFOCSE ARES CART XGBoost
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