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Algorithmic Fairness Generalization under Covariate and Dependence Shifts Simultaneously

Chen Zhao, Kai Jiang, Xintao Wu, Haoliang Wang, Latifur Khan, Christan Grant, Feng Chen

TL;DR

This work addresses fairness-aware domain generalization under simultaneous covariate and dependence shifts by introducing FEDORA, a transformation-based framework that disentangles semantic, sensitive, and style factors and augments data with synthetic domains. It formalizes a fairness-invariant objective through a transformation model and a constrained learning problem, and provides empirical duality guarantees and an unseen-domain fairness bound. The FEDORA algorithm co-trains a disentangled transformation T with a fairness-aware classifier, using synthetic domain augmentation and a primal–dual optimization scheme to enforce invariance across domains. The method demonstrates consistent improvements over 19 baselines across four benchmarks, with notable gains in both DP and AUC_fair, and includes thorough ablations and theoretical insights on duality gaps and target-domain fairness.

Abstract

The endeavor to preserve the generalization of a fair and invariant classifier across domains, especially in the presence of distribution shifts, becomes a significant and intricate challenge in machine learning. In response to this challenge, numerous effective algorithms have been developed with a focus on addressing the problem of fairness-aware domain generalization. These algorithms are designed to navigate various types of distribution shifts, with a particular emphasis on covariate and dependence shifts. In this context, covariate shift pertains to changes in the marginal distribution of input features, while dependence shift involves alterations in the joint distribution of the label variable and sensitive attributes. In this paper, we introduce a simple but effective approach that aims to learn a fair and invariant classifier by simultaneously addressing both covariate and dependence shifts across domains. We assert the existence of an underlying transformation model can transform data from one domain to another, while preserving the semantics related to non-sensitive attributes and classes. By augmenting various synthetic data domains through the model, we learn a fair and invariant classifier in source domains. This classifier can then be generalized to unknown target domains, maintaining both model prediction and fairness concerns. Extensive empirical studies on four benchmark datasets demonstrate that our approach surpasses state-of-the-art methods.

Algorithmic Fairness Generalization under Covariate and Dependence Shifts Simultaneously

TL;DR

This work addresses fairness-aware domain generalization under simultaneous covariate and dependence shifts by introducing FEDORA, a transformation-based framework that disentangles semantic, sensitive, and style factors and augments data with synthetic domains. It formalizes a fairness-invariant objective through a transformation model and a constrained learning problem, and provides empirical duality guarantees and an unseen-domain fairness bound. The FEDORA algorithm co-trains a disentangled transformation T with a fairness-aware classifier, using synthetic domain augmentation and a primal–dual optimization scheme to enforce invariance across domains. The method demonstrates consistent improvements over 19 baselines across four benchmarks, with notable gains in both DP and AUC_fair, and includes thorough ablations and theoretical insights on duality gaps and target-domain fairness.

Abstract

The endeavor to preserve the generalization of a fair and invariant classifier across domains, especially in the presence of distribution shifts, becomes a significant and intricate challenge in machine learning. In response to this challenge, numerous effective algorithms have been developed with a focus on addressing the problem of fairness-aware domain generalization. These algorithms are designed to navigate various types of distribution shifts, with a particular emphasis on covariate and dependence shifts. In this context, covariate shift pertains to changes in the marginal distribution of input features, while dependence shift involves alterations in the joint distribution of the label variable and sensitive attributes. In this paper, we introduce a simple but effective approach that aims to learn a fair and invariant classifier by simultaneously addressing both covariate and dependence shifts across domains. We assert the existence of an underlying transformation model can transform data from one domain to another, while preserving the semantics related to non-sensitive attributes and classes. By augmenting various synthetic data domains through the model, we learn a fair and invariant classifier in source domains. This classifier can then be generalized to unknown target domains, maintaining both model prediction and fairness concerns. Extensive empirical studies on four benchmark datasets demonstrate that our approach surpasses state-of-the-art methods.
Paper Structure (24 sections, 8 theorems, 32 equations, 8 figures, 15 tables, 5 algorithms)

This paper contains 24 sections, 8 theorems, 32 equations, 8 figures, 15 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries
  4. Methodology
  5. Learning the Transformation Model
  6. Fair Disentangled Domain Generalization
  7. The FEDORA Algorithm
  8. Analysis
  9. Experiments
  10. Settings
  11. Results
  12. Conclusion
  13. Notations
  14. Experimental Settings
  15. Evaluation Metrics.
  16. ...and 9 more sections

Key Result

Theorem 1

Given $\xi>0$, assuming $\{\hat{f}(\cdot,\boldsymbol{\theta}):\boldsymbol{\theta}\in\Theta\}\subseteq\mathcal{F}$ has finite VC-dimension, with $M$ datapoints sampled from $\mathbb{P}_{XZY}$ we have where $\boldsymbol{\gamma}=[\gamma_1,\gamma_2]^T$; $L$ is the Lipschitz constant of $P^\star(\gamma_1,\gamma_2)$; $k$ is a small universal constant defined in prop:gap2 of app:proofs; and $\boldsymbol

Figures (8)

  • Figure 1: Illustration of the problem in generalizing fair classifiers across different data domains under covariate and dependence shifts simultaneously. (Left) Images in source and target domains have different styles (Photos and Arts). Each data domain is linked to a distinct correlation between class labels (NC and C) and sensitive attributes (Male and Female). (Right) We consider $\mathbf{x}=[x_1,x_2]^T$ a simple example of a two-dimensional feature vector. A fair classifier $f$ learned using source data is applied to data sampled from various types of shifted target domains, resulting in misclassification and unfairness. $f^*$ represents the true classifier in the target domain.
  • Figure 2: (Left) A transformation model $T$ is trained using a bi-directional reconstruction loss (data reconstruction and factor reconstruction) and a sensitiveness loss. (Right) To enhance the generalization of the classifier $f$ to unseen target domains, the transformation model $T$ is used for augmentation in synthetic domains by generating data based on invariant semantic factors and randomly sampled sensitive and style factors that encode synthetic domains. We demonstrate the concept using the ccMNIST dataset, where the domains are distinguished by different digit colors and fair dependencies between class labels and sensitive attributes. Here, sensitive attributes are defined by image background colors.
  • Figure 3: Visualizations for images under reconstruction and the transformation model $T$ with random style and sensitive factors.
  • Figure 4: Example results of generating images using latent factors encoded from three images.
  • Figure 5: Ablation study on FairFace. Averaged results are plotted across all domains.
  • ...and 3 more figures

Theorems & Definitions (14)

  • Definition 1: Group Fairness Notion Wu-2019-WWWLohaus-2020-ICML
  • Definition 2: Covariate Shift robey2021model and Dependence Shiftroh2023improving
  • Definition 3: Fairness-aware $T$-Invariance
  • Theorem 1: Fairness-aware Data-dependent Duality Gap
  • Theorem 2: Fairness Upper Bound of the Unseen Target Domain
  • Proposition 1
  • Proposition 2
  • Definition 4
  • Proposition 3
  • Proposition 4: Empirical gap
  • ...and 4 more