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Fair Multivariate Adaptive Regression Splines for Ensuring Equity and Transparency
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Proposes fairMARS, a fairness-aware multivariate adaptive regression splines model that adds a subgroup RSS-disparity penalty to knot selection and a weighted least-squares coefficient estimation, evaluated on three education/crime regression datasets.
Problem
Regression models in education and other high-stakes settings are often opaque, proprietary, and can produce unequal errors across sensitive subgroups, while fairness methods have focused mostly on classification.
Approach
Integrates a subgroup absolute error-difference (RSS disparity) penalty, weighted by lambda, into MARS knot optimization and uses weighted least squares for coefficient estimation, yielding interpretable, non-parametric fair regression.
Key results
- On the ELS dataset, fairMARS-knot achieved test MSE of 0.021 versus 0.020 for MARS, with the Black-subgroup error difference unchanged at 0.016 and other subgroup differences broadly similar (10-fold CV).
- On the Student Performance dataset, fairknot reduced test MSE from 3.666 (MARS) to 3.574 and gender error difference from 3.665 to 3.487, versus 10.62 MSE for the CART decision tree.
- Fold times were about 3, 2, and 0.5 minutes for ELS, Crime, and Student Performance datasets for fairMARS, compared with about 3, 2, and 1 hour per fold for fairDT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add fairness-aware knot selection | MARS · ELS, 10-fold cross-validation | test MSE: 0.020 -> 0.021 | Hurt |
| Add fairness-aware knot selection | MARS · Crime, 10-fold cross-validation | test MSE: 0.019 -> 0.020 | Hurt |
| Add fairness-aware knot selection | MARS · Student Performance, 10-fold cross-validation | test MSE: 3.666 -> 3.574 | Helped |
| Add fairness-aware knot selection (ablation) | MARS · ELS, single fold | test MSE: 0.151 -> 0.141 | Helped |
| Increase fairness penalty from λ=0 to λ=0.2 (ablation) | fairknot · ELS, single fold | test R²: 0.687 -> 0.691 | Helped |
| Increase fairness penalty from λ=0.2 to λ=0.7 (ablation) | fairknot · ELS, single fold | test R²: 0.691 -> 0.708 | Helped |
| Increase fairness penalty from λ=0 to λ=0.2 (ablation) | fairknot · ELS, single fold | Black subgroup absolute error difference: 0.172 -> 0.150 | Helped |
| Increase fairness penalty from λ=0.2 to λ=0.7 (ablation) | fairknot · ELS, single fold | Asian subgroup absolute error difference: 0.003 -> 0.056 | Hurt |
| Increase fairness penalty from λ=0 to λ=0.7 (ablation) | fairknot · ELS, single fold | White subgroup absolute error difference: 0.058 -> 0.031 | Helped |
| Increase fairness penalty from λ=0 to λ=0.2 (ablation) | fairknot · ELS, single fold | Hispanic subgroup absolute error difference: 0.017 -> 0.012 | Helped |
| Increase fairness penalty from λ=0 to λ=0.7 (ablation) | fairknot · ELS, single fold | Multiracial subgroup absolute error difference: 0.056 -> 0.050 | Helped |
Surprising findings
- Fairness-aware knot selection did not reduce MSE and sometimes improved it, suggesting no clear accuracy-fairness trade-off in these experiments.
- Some subgroups (e.g., Asian) saw stable or slightly worse disparity under fairknot, showing that fairness gains are not uniform across groups.
Limitations
- Fairness is defined only as absolute difference in average subgroup RSS, which may not capture other fairness notions.
- Results are reported on three small datasets (395 to 1994 instances) with limited sensitive-attribute categories.
- Accuracy-fairness trade-off depends on lambda, which must be tuned and was chosen per model to minimize discrimination.
Experimental setup
Datasets: ELS Crime Student Performance
Benchmarks: ELS Crime Student Performance
Metrics: MSE R^2 subgroup absolute error difference
Baselines: MARS MIP-DT fair regression tree (fairDT) CART decision tree (DT) fair linear regression (fairLR)
Builds on: MARS fair decision tree (MIP-DT) fair regression with bounded group loss Py-earth
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