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Fair Risk Control: A Generalized Framework for Calibrating Multi-group Fairness Risks
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Proposes (s,G,α)-GMC, a multi-dimensional generalization of multicalibration with a functional-gradient post-processing algorithm, applied to FNR control in segmentation, conditional coverage in hierarchical classification, and debiased text generation.
Problem
Post-processing machine learning predictors so that multi-dimensional outputs satisfy multi-group fairness risk constraints, which prior one-dimensional multicalibration and fair-risk methods do not cover.
Approach
Generalizes multicalibration to multi-dimensional mapping functionals s and constraint vectors g, and solves it with an iterative projected-gradient update on a potential functional that terminates after a bounded number of violation-correcting steps.
Key results
- In text generation, the gender disparity is kept below alpha=0.002 while test cross-entropy moves from 9.9291 to 9.9285.
- In hierarchical classification on Web of Science (46,985 documents, 134 categories), GMC keeps prediction-set conditional coverage within 95±2.5% for all predictions, while split conformal fails on 'CS' and 'Medical'.
- In face segmentation on FASSEG (118 images), GMC reaches accuracy 0.86 versus 0.84 and 0.92 for baselines, with FNR deviations controlled across subgroups.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Post-process BERT probabilities with GMC | BERT · Text-generation test set | cross-entropy: 9.9291 -> 9.9285 | Helped |
| Post-process BERT probabilities with GMC | BERT · Text-generation prompts with male-indicator words | gender disparity gap | Helped |
| Use GMC for prediction-set conditional coverage | HiAGM · Web of Science | prediction-set conditional coverage deviation | Helped |
| Use GMC instead of unprocessed leaf predictions or split conformal | HiAGM · Web of Science | prediction-set conditional coverage deviation | Mixed |
| Calibrate FNR across gender and racial subgroups with GMC | U-net · FASSEG | FNR deviation from target | Helped |
| Use GMC rather than the unprocessed U-net or split conformal baseline | U-net · FASSEG | FNR deviation from target | Helped |
| Calibrate FNR across subgroups with GMC | U-net · FASSEG | accuracy: 0.84 -> 0.86; 0.92 -> 0.86 | Mixed |
Surprising findings
- Equalizing FNR trivially via a large threshold would destroy accuracy, so the authors stress accuracy checks; the paper's GMC accuracy (0.86) is between the two baselines (0.84 and 0.92).
Limitations
- Theoretical guarantees rely on assumptions (smoothness, bounded potential, density bounds) that may be strong for some applications.
- Finite-sample results use a dimension-of-class argument that gives sample complexity scaling with the number of constraints, and the paper's experiments are small-scale.
- Fairness-accuracy tradeoff only empirically checked on a few datasets.
Experimental setup
Datasets: Web of Science FASSEG corpus of biased sentences for gender bias in text generation synthetic templates for gender bias
Benchmarks: Web of Science FASSEG
Metrics: gender disparity gap cross-entropy prediction-set conditional coverage deviation false negative rate deviation accuracy
Baselines: U-net unprocessed split conformal unprocessed HiAGM leaf prediction
Builds on: multicalibration outcome indistinguishability conformal prediction
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