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Causal Fair Metric: Bridging Causality, Individual Fairness, and Adversarial Robustness

Ahmad-Reza Ehyaei, Golnoosh Farnadi, Samira Samadi

TL;DR

This work tackles the challenge of integrating causality, individual fairness, and adversarial robustness by introducing a causal fair metric defined on structural causal models. It develops a semi-latent space embedding to separate sensitive from non-sensitive factors, enabling a push-forward distance that remains zero for counterfactual twins and continuous with respect to non-sensitive perturbations. Since SCMs are often unknown, the paper proposes data-driven metric learning methods and introduces ECAPIFY for causality-aware fair adversarial learning that does not require full SCM knowledge, achieving competitive or superior results to oracle-based approaches. The findings advance counterfactual fairness while enhancing robustness, with practical implications for deploying fair, robust AI systems in real-world, causally structured data settings; the authors also outline avenues for future theoretical guarantees and broader causal ML applications.

Abstract

Despite the essential need for comprehensive considerations in responsible AI, factors like robustness, fairness, and causality are often studied in isolation. Adversarial perturbation, used to identify vulnerabilities in models, and individual fairness, aiming for equitable treatment of similar individuals, despite initial differences, both depend on metrics to generate comparable input data instances. Previous attempts to define such joint metrics often lack general assumptions about data or structural causal models and were unable to reflect counterfactual proximity. To address this, our paper introduces a causal fair metric formulated based on causal structures encompassing sensitive attributes and protected causal perturbation. To enhance the practicality of our metric, we propose metric learning as a method for metric estimation and deployment in real-world problems in the absence of structural causal models. We also demonstrate the application of our novel metric in classifiers. Empirical evaluation of real-world and synthetic datasets illustrates the effectiveness of our proposed metric in achieving an accurate classifier with fairness, resilience to adversarial perturbations, and a nuanced understanding of causal relationships.

Causal Fair Metric: Bridging Causality, Individual Fairness, and Adversarial Robustness

TL;DR

This work tackles the challenge of integrating causality, individual fairness, and adversarial robustness by introducing a causal fair metric defined on structural causal models. It develops a semi-latent space embedding to separate sensitive from non-sensitive factors, enabling a push-forward distance that remains zero for counterfactual twins and continuous with respect to non-sensitive perturbations. Since SCMs are often unknown, the paper proposes data-driven metric learning methods and introduces ECAPIFY for causality-aware fair adversarial learning that does not require full SCM knowledge, achieving competitive or superior results to oracle-based approaches. The findings advance counterfactual fairness while enhancing robustness, with practical implications for deploying fair, robust AI systems in real-world, causally structured data settings; the authors also outline avenues for future theoretical guarantees and broader causal ML applications.

Abstract

Despite the essential need for comprehensive considerations in responsible AI, factors like robustness, fairness, and causality are often studied in isolation. Adversarial perturbation, used to identify vulnerabilities in models, and individual fairness, aiming for equitable treatment of similar individuals, despite initial differences, both depend on metrics to generate comparable input data instances. Previous attempts to define such joint metrics often lack general assumptions about data or structural causal models and were unable to reflect counterfactual proximity. To address this, our paper introduces a causal fair metric formulated based on causal structures encompassing sensitive attributes and protected causal perturbation. To enhance the practicality of our metric, we propose metric learning as a method for metric estimation and deployment in real-world problems in the absence of structural causal models. We also demonstrate the application of our novel metric in classifiers. Empirical evaluation of real-world and synthetic datasets illustrates the effectiveness of our proposed metric in achieving an accurate classifier with fairness, resilience to adversarial perturbations, and a nuanced understanding of causal relationships.
Paper Structure (25 sections, 6 theorems, 35 equations, 4 figures, 4 tables)

This paper contains 25 sections, 6 theorems, 35 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background
  4. Structural Causal Model.
  5. Causal Identifiability.
  6. Interventions.
  7. Counterfactuals.
  8. Sensitive Attribute.
  9. Individual Fairness.
  10. Fair Metric
  11. Protected Causal Perturbation
  12. Fair Metric Learning
  13. Causality-aware Fair Adversarial Learning
  14. Numerical Experiments
  15. Results of Metric Learning
  16. ...and 10 more sections

Key Result

Proposition 1

Let $d: \mathcal{V} \times \mathcal{V} \rightarrow \mathbb{R}$ be a causal fair metric, then $d$ can be written as a form: where $\varphi_{\mathcal{X}}(v) = P_{\mathcal{X}}(\varphi(v))$, $\varphi$ is the mapping from feature space to semi-latent space, $P_{\mathcal{X}}$ is a projection on the non-sensitive subspace of exogenous space, and $d_{\mathcal{X}}$ represents the metric defined on the non

Figures (4)

  • Figure 1: illustrates the progression from a basic perturbation to a protected causal perturbation ball. Consider a simple linear SCM with Euclidean norm in both exogenous and endogenous spaces. (a) a perturbation ball that does not account for causality or the protection of sensitive features, (b) a perturbation ball that includes causality but assumes the absence of sensitive features, and (c) The counterfactual perturbation space, created using a counterfactual space based on a sensitive attribute, can be visualized as the axis $L$ of a cylinder. Surrounding ellipses represent a causal perturbation ball $B^{\textbf{\tiny CP}}_{\Delta}$, encompassing perturbations of non-sensitive variables with radii $\Delta$.
  • Figure 2: This figure demonstrates the effect of causal metric assumptions on the accuracy of deep metric models: (up) Accuracy performance comparison based on embedding layer sizes and embedding space metric knowledge shows improved prediction accuracy. (down) In simpler models, the network efficiently learns embedding space properties. However, with less precise metric data, as in Triplet-based scenarios, adding decorrelation methods boosts accuracy.
  • Figure 3: Presents the results of our numerical experiment, evaluating ECAPIFY's performance across various models and datasets. (Top left) Bar plot comparing models using unfair area percentage (lower is better) at $\Delta = .01$. (Top right) Counterfactual unfair area percentage (lower is better). (Bottom left) Matthews correlation coefficient illustrating classifier performance (higher is better). (Bottom right) Bar plot contrasting methods by prediction performance (higher is better).
  • Figure 4: The performance metric of the learning scenario with varying knowledge regarding the embedding layer size.

Theorems & Definitions (16)

  • Definition 1: Additive Noise Intervention
  • Definition 2: Causal Fair Metric
  • Example 1
  • Definition 3: Semi-latent Space ehyaei2023causal
  • Proposition 1
  • Definition 4: Protected Causal Perturbation
  • Proposition 2
  • Proposition 3
  • Example 2
  • Proposition 4: Metric Estimation Not Guaranteed
  • ...and 6 more