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Learning Fair Invariant Representations under Covariate and Correlation Shifts Simultaneously

Dong Li, Chen Zhao, Minglai Shao, Wenjun Wang

TL;DR

This work tackles fairness-aware domain generalization under simultaneous covariate and correlation shifts, enabling robust generalization to unseen test domains. It introduces FLAIR, a framework that disentangles content and style via latent spaces and learns fair content representations using a Gaussian-mixture of prototypes across sensitive subgroups, guided by a transformation model $T$ to enforce invariance. The predictor $f=h_c\circ g\circ \omega$ is trained with a composite loss $R_{total}=R_{cls}+\lambda_1 R_{inv}+\lambda_2 R_{fair}$, leveraging EM for fairness responsibilities and primal-dual optimization to balance invariance and fairness; it demonstrates superior accuracy and both group and individual fairness on RC MNIST, NYPD, and FairFace. Overall, FLAIR offers a practical algorithmic path for reliable, fair generalization across diverse domains under covariate and correlation shifts.

Abstract

Achieving the generalization of an invariant classifier from training domains to shifted test domains while simultaneously considering model fairness is a substantial and complex challenge in machine learning. Existing methods address the problem of fairness-aware domain generalization, focusing on either covariate shift or correlation shift, but rarely consider both at the same time. In this paper, we introduce a novel approach that focuses on learning a fairness-aware domain-invariant predictor within a framework addressing both covariate and correlation shifts simultaneously, ensuring its generalization to unknown test domains inaccessible during training. In our approach, data are first disentangled into content and style factors in latent spaces. Furthermore, fairness-aware domain-invariant content representations can be learned by mitigating sensitive information and retaining as much other information as possible. Extensive empirical studies on benchmark datasets demonstrate that our approach surpasses state-of-the-art methods with respect to model accuracy as well as both group and individual fairness.

Learning Fair Invariant Representations under Covariate and Correlation Shifts Simultaneously

TL;DR

This work tackles fairness-aware domain generalization under simultaneous covariate and correlation shifts, enabling robust generalization to unseen test domains. It introduces FLAIR, a framework that disentangles content and style via latent spaces and learns fair content representations using a Gaussian-mixture of prototypes across sensitive subgroups, guided by a transformation model to enforce invariance. The predictor is trained with a composite loss , leveraging EM for fairness responsibilities and primal-dual optimization to balance invariance and fairness; it demonstrates superior accuracy and both group and individual fairness on RC MNIST, NYPD, and FairFace. Overall, FLAIR offers a practical algorithmic path for reliable, fair generalization across diverse domains under covariate and correlation shifts.

Abstract

Achieving the generalization of an invariant classifier from training domains to shifted test domains while simultaneously considering model fairness is a substantial and complex challenge in machine learning. Existing methods address the problem of fairness-aware domain generalization, focusing on either covariate shift or correlation shift, but rarely consider both at the same time. In this paper, we introduce a novel approach that focuses on learning a fairness-aware domain-invariant predictor within a framework addressing both covariate and correlation shifts simultaneously, ensuring its generalization to unknown test domains inaccessible during training. In our approach, data are first disentangled into content and style factors in latent spaces. Furthermore, fairness-aware domain-invariant content representations can be learned by mitigating sensitive information and retaining as much other information as possible. Extensive empirical studies on benchmark datasets demonstrate that our approach surpasses state-of-the-art methods with respect to model accuracy as well as both group and individual fairness.
Paper Structure (17 sections, 18 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 18 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Fairness-aware Learning Invariant Representations (FLAIR)
  5. Disentanglement of Domain Variation
  6. Learning Fair Content Representations
  7. Learning the Predictor $\boldsymbol{f}$
  8. An Effective Algorithm
  9. Experimental Settings
  10. Datasets
  11. Evaluation Metrics
  12. Compared Methods
  13. Results
  14. Overall Performance
  15. Ablation Study
  16. ...and 2 more sections

Figures (7)

  • Figure 1: Taking a digit dataset (e.g.RCMNIST) as an example to illustrate covariate shift and correlation shift across domains. Here, domain is uniquely determined by the rotation angle and $Corr(digit,color)$, the color serves as the sensitive attribute. $Corr(digit,color)$ represents the correlation between the digit (3 and 6) and color (red and green).
  • Figure 2: Illustrating the pipeline of FLAIR using RCMNIST dataset as an example. The content encoder $h_c$ first maps instances to the latent content space to obtain latent content factors. Subsequently, these content factors are grouped based on the sensitive attributes (color) into $\textbf{c}_i^1$ and $\textbf{c}_i^{-1}$. Consequently, the fair content representations $\tilde{\textbf{c}}_i^1$ and $\tilde{\textbf{c}}_i^{-1}$ are reconstructed using weighted prototypes. Each prototype represents a statistical mean estimated from its corresponding cluster, which is fitted by the content factors of the respective subgroups, while ensuring fairness through Eq.(\ref{['eq:fair_constraint']}). Further, instances are transformed into different domains using the style factor $\textbf{s}$ extracted by the style encoder $h_s$.
  • Figure 3: Ablation study over four metrics for FLAIR and its two variants on (a) RCMNIST, (b) NYPD and (c) FairFace datasets. Results are averaged across all domains.
  • Figure 4: t-SNE visualization of the representations learned by (c) FLAIR and its variants (a) FLAIR w/o $R_{fair}$ and (b) FLAIR w/o primal-dual on RCMNIST dataset. The main parts of (a)-(c) simultaneously visualize representations of two sensitive subgroups in the same latent space $\mathcal{C}$, while the bottom-left ($a=-1$) and bottom-right ($a=1$) visualize each group separately.
  • Figure 5: The convergence curves of $R_{fair}$ and $\hat{R}_{fair}$ during training. Both of them converge after 30 iterations.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Definition 1: Covariate shift and correlation shift
  • Definition 2: $T$-invariance