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Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samples

Shreyas Havaldar, Jatin Chauhan, Karthikeyan Shanmugam, Jay Nandy, Aravindan Raghuveer

TL;DR

The paper tackles fairness under covariate shift in an unsupervised test-adaptation setting with a small unlabeled test set ${\mathcal D}^T$. It introduces a composite objective that couples a weighted entropy term on ${\mathcal D}^T$ with a Wasserstein-based representation-matching loss, optimized in a min-max fashion via a density-ratio network ${\mathsf F}_w$, and it formalizes a theoretical bound linking test loss to training loss through the weighted-entropy surrogate. A novel Asymmetric Covariate Shift setting is studied, and the method achieves Pareto-optimal fairness-accuracy tradeoffs on four standard benchmarks, significantly outperforming a range of baselines including density-estimation and DRO-based approaches. The approach provides practical guarantees against high-variance importance sampling and demonstrates robust performance under both symmetric and asymmetric shifts, offering a scalable path for fair ML under realistic distributional changes.

Abstract

Covariate shift in the test data is a common practical phenomena that can significantly downgrade both the accuracy and the fairness performance of the model. Ensuring fairness across different sensitive groups under covariate shift is of paramount importance due to societal implications like criminal justice. We operate in the unsupervised regime where only a small set of unlabeled test samples along with a labeled training set is available. Towards improving fairness under this highly challenging yet realistic scenario, we make three contributions. First is a novel composite weighted entropy based objective for prediction accuracy which is optimized along with a representation matching loss for fairness. We experimentally verify that optimizing with our loss formulation outperforms a number of state-of-the-art baselines in the pareto sense with respect to the fairness-accuracy tradeoff on several standard datasets. Our second contribution is a new setting we term Asymmetric Covariate Shift that, to the best of our knowledge, has not been studied before. Asymmetric covariate shift occurs when distribution of covariates of one group shifts significantly compared to the other groups and this happens when a dominant group is over-represented. While this setting is extremely challenging for current baselines, We show that our proposed method significantly outperforms them. Our third contribution is theoretical, where we show that our weighted entropy term along with prediction loss on the training set approximates test loss under covariate shift. Empirically and through formal sample complexity bounds, we show that this approximation to the unseen test loss does not depend on importance sampling variance which affects many other baselines.

Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samples

TL;DR

The paper tackles fairness under covariate shift in an unsupervised test-adaptation setting with a small unlabeled test set . It introduces a composite objective that couples a weighted entropy term on with a Wasserstein-based representation-matching loss, optimized in a min-max fashion via a density-ratio network , and it formalizes a theoretical bound linking test loss to training loss through the weighted-entropy surrogate. A novel Asymmetric Covariate Shift setting is studied, and the method achieves Pareto-optimal fairness-accuracy tradeoffs on four standard benchmarks, significantly outperforming a range of baselines including density-estimation and DRO-based approaches. The approach provides practical guarantees against high-variance importance sampling and demonstrates robust performance under both symmetric and asymmetric shifts, offering a scalable path for fair ML under realistic distributional changes.

Abstract

Covariate shift in the test data is a common practical phenomena that can significantly downgrade both the accuracy and the fairness performance of the model. Ensuring fairness across different sensitive groups under covariate shift is of paramount importance due to societal implications like criminal justice. We operate in the unsupervised regime where only a small set of unlabeled test samples along with a labeled training set is available. Towards improving fairness under this highly challenging yet realistic scenario, we make three contributions. First is a novel composite weighted entropy based objective for prediction accuracy which is optimized along with a representation matching loss for fairness. We experimentally verify that optimizing with our loss formulation outperforms a number of state-of-the-art baselines in the pareto sense with respect to the fairness-accuracy tradeoff on several standard datasets. Our second contribution is a new setting we term Asymmetric Covariate Shift that, to the best of our knowledge, has not been studied before. Asymmetric covariate shift occurs when distribution of covariates of one group shifts significantly compared to the other groups and this happens when a dominant group is over-represented. While this setting is extremely challenging for current baselines, We show that our proposed method significantly outperforms them. Our third contribution is theoretical, where we show that our weighted entropy term along with prediction loss on the training set approximates test loss under covariate shift. Empirically and through formal sample complexity bounds, we show that this approximation to the unseen test loss does not depend on importance sampling variance which affects many other baselines.
Paper Structure (33 sections, 9 theorems, 18 equations, 12 figures, 7 tables, 1 algorithm)

This paper contains 33 sections, 9 theorems, 18 equations, 12 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setup
  4. Covariate Shift Assumption
  5. Fairness Regularization with no Labels
  6. Issues with Applying Existing Techniques
  7. Method and Algorithm
  8. Theoretical Analysis
  9. Weighted Entropy Objective
  10. Experiments
  11. Shift Construction
  12. Fairness-Accuracy Tradeoff
  13. Results on Asymmetric Shift
  14. Conclusion
  15. Appendix
  16. ...and 18 more sections

Key Result

Theorem 4.1

Suppose that ${\mathbb{P}^{T}}(\cdot)$ and ${\mathbb{P}^{S}}(\cdot)$ are absolutely continuous with respect to each other over domain ${\mathcal{X}}$. Let $\epsilon \in \mathbb{R}^{+}$ be such that $\frac{{\mathbb{P}^{T}}({\textnormal{Y}}=y|{X})}{P({\textnormal{$\hat{{\textnormal{Y}}}$}}=y|{X})} \l where $\mathcal{H({\textnormal{$\hat{{\textnormal{Y}}}$}}|{X})} = \sum_{y \in \{0,1\}} -P({\textnor

Figures (12)

  • Figure 1: Asymmetric Shift Illustrated
  • Figure 2: Both Error (in % left) and Equalized Odds (right) for SOTA fairness method - Adversarial Debiasing exhibit strong degradation on increasing the magnitude of covariate shift. Three scenarios corresponding to no shift, intermediate shift and high shift are plotted (details on shift construction are explained in the experimental section).
  • Figure 3: Fairness-Error Tradeoff Curves for our method (Pareto Frontier) against the optimal performance of the baselines. Our method provides better tradeoffs in all cases. (On Drug dataset, the performance is concentrated around the optimal point). All figures best viewed in colour.
  • Figure 4: Comparison of our method against the baselines under Asymmetric Covariate Shift for group ${\textnormal{A}} = 0$.
  • Figure 5: High level architecture of our method. Colored blocks represent parameterized sub-networks.
  • ...and 7 more figures

Theorems & Definitions (16)

  • Definition 3.1: Asymmetric Covariate Shift
  • Definition 3.2
  • Theorem 4.1
  • proof
  • Theorem 4.3
  • Theorem 4.4
  • proof : Proof of Theorem \ref{['theorem:th_1']}
  • Theorem B.1: cortes2010learning
  • Theorem B.2
  • proof
  • ...and 6 more