[Paper Review] Learning fair representation with a parametric integral probability metric

Dong Ha Kim, Kunwoong Kim+3 more|arXiv (Cornell University)|Feb 7, 2022

Ethics and Social Impacts of AI4 citations

TL;DR

This paper proposes sIPM-LFR, a novel adversarial training method for learning fair representations using a parametric integral probability metric (IPM) with a sigmoid-based discriminator family. It provides theoretical guarantees linking representation fairness to final prediction model fairness, achieves superior computational efficiency and stability, and outperforms existing LFR methods in fairness-accuracy trade-offs across multiple datasets and models.

ABSTRACT

As they have a vital effect on social decision-making, AI algorithms should be not only accurate but also fair. Among various algorithms for fairness AI, learning fair representation (LFR), whose goal is to find a fair representation with respect to sensitive variables such as gender and race, has received much attention. For LFR, the adversarial training scheme is popularly employed as is done in the generative adversarial network type algorithms. The choice of a discriminator, however, is done heuristically without justification. In this paper, we propose a new adversarial training scheme for LFR, where the integral probability metric (IPM) with a specific parametric family of discriminators is used. The most notable result of the proposed LFR algorithm is its theoretical guarantee about the fairness of the final prediction model, which has not been considered yet. That is, we derive theoretical relations between the fairness of representation and the fairness of the prediction model built on the top of the representation (i.e., using the representation as the input). Moreover, by numerical experiments, we show that our proposed LFR algorithm is computationally lighter and more stable, and the final prediction model is competitive or superior to other LFR algorithms using more complex discriminators.

Motivation & Objective

• To address the lack of theoretical connection between representation fairness and final prediction model fairness in existing learning fair representation (LFR) methods.
• To develop a principled, computationally efficient discriminator architecture for adversarial training in LFR, moving beyond heuristic deep neural network choices.
• To ensure that fairness in the learned representation translates to fairness in downstream prediction models.
• To improve training stability and reduce computational cost compared to existing LFR algorithms using complex discriminators.
• To empirically validate that the proposed method achieves competitive or better fairness-accuracy trade-offs across diverse datasets and prediction models.

Proposed method

• Proposes a parametric family of discriminators based on sigmoid functions to define a specific integral probability metric (IPM), replacing generic deep neural networks in adversarial training.
• Uses the IPM as a fairness regularizer in the autoencoder-based LFR framework, where the encoder learns a representation that minimizes the IPM between sensitive group distributions.
• Introduces a differentiable, closed-form approximation of the IPM via the sigmoid-based discriminator, enabling stable and efficient optimization.
• Employs a two-stage training process: first pre-train the autoencoder with reconstruction loss, then jointly optimize the representation and discriminator using the parametric IPM.
• Applies the method to multiple datasets (Adult, COMPAS, Health) and prediction models (linear, SVM, neural networks) to evaluate fairness and accuracy.
• Uses the IPM to control fairness levels, enabling systematic trade-offs between fairness and accuracy through a hyperparameter λ.

Experimental results

Research questions

• RQ1 How does the fairness of the learned representation relate to the fairness of the final prediction model built on top of it?
• RQ2 Can a parametric, simple discriminator family (e.g., sigmoid-based) provide stronger theoretical fairness guarantees than complex deep neural networks in LFR?
• RQ3 Does using a parametric IPM lead to more stable and computationally efficient training compared to existing LFR methods?
• RQ4 Can the proposed method achieve better fairness-accuracy trade-offs than state-of-the-art LFR algorithms like LAFTR and FVAE?
• RQ5 How sensitive is the performance of the proposed method to the choice of representation dimension m?

Key findings

• The proposed sIPM-LFR method achieves a theoretical guarantee that the fairness of the final prediction model is bounded by the fairness of the representation, establishing a direct link between representation and model fairness.
• sIPM-LFR reduces computation time by approximately 20% compared to LAFTR, demonstrating superior computational efficiency.
• The method shows greater insensitivity to the choice of representation dimension m, as evidenced by more stable Pareto-front performance across different m values.
• In fairness-accuracy trade-off comparisons, sIPM-LFR consistently outperforms or matches LAFTR and FVAE, with lower standard errors and better median performance on DP, MDP, and SDP fairness metrics.
• The sIPM-LFR achieves lower values of ΔDP, ΔMDP, and ΔSDP across all datasets and models, indicating stronger fairness, while maintaining or improving prediction accuracy.
• Theoretical analysis shows that the MMD used in FVAE is upper bounded by the proposed sIPM, suggesting that controlling sIPM ensures MMD reduction, validating the method’s fairness robustness.