# Fix Representation (Optimally) Before Fairness: Finite-Sample Shrinkage Population Correction and the True Price of Fairness Under Subpopulation Shift

arXiv: https://arxiv.org/abs/2602.05707 · HTML: https://mlsanity.com/paper/2602.05707/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Robust Fairness under Covariate Shift](https://mlsanity.com/paper/2010.05166/) (2020)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Does enforcing fairness mitigate biases caused by subpopulation shift?](https://mlsanity.com/paper/2011.03173/) (2020)
- [Robust Importance Weighting for Covariate Shift](https://mlsanity.com/paper/1910.06324/) (2019)
- [Optimizing importance weighting in the presence of sub-population shifts](https://mlsanity.com/paper/2410.14315/) (2024)

## Abstract (arXiv)

Machine learning practitioners frequently observe tension between predictive accuracy and group fairness constraints -- yet sometimes fairness interventions appear to improve accuracy. We show that both phenomena can be artifacts of training data that misrepresents subgroup proportions. Under subpopulation shift (stable within-group distributions, shifted group proportions), we establish: (i) full importance-weighted correction is asymptotically unbiased but finite-sample suboptimal; (ii) the optimal finite-sample correction is a shrinkage reweighting that interpolates between target and training mixtures; (iii) apparent "fairness helps accuracy" can arise from comparing fairness methods to an improperly-weighted baseline. We provide an actionable evaluation protocol: fix representation (optimally) before fairness -- compare fairness interventions against a shrinkage-corrected baseline to isolate the true, irreducible price of fairness. Experiments on synthetic and real-world benchmarks (Adult, COMPAS) validate our theoretical predictions and demonstrate that this protocol eliminates spurious tradeoffs, revealing the genuine fairness-utility frontier.