[Paper Review] Rényi Fair Inference

Sina Baharlouei, Maher Nouiehed+2 more|arXiv (Cornell University)|Jun 28, 2019

Ethics and Social Impacts of AI59 references14 citations

TL;DR

This paper proposes Rényi Fair Inference, a novel in-processing framework that enforces fairness in machine learning by minimizing Rényi correlation between sensitive attributes and model outputs. Using a min-max optimization formulation with convergence guarantees for discrete attributes, it achieves superior fairness-accuracy trade-offs compared to Pearson correlation and HSIC-based methods, especially in capturing nonlinear dependencies.

ABSTRACT

Machine learning algorithms have been increasingly deployed in critical automated decision-making systems that directly affect human lives. When these algorithms are only trained to minimize the training/test error, they could suffer from systematic discrimination against individuals based on their sensitive attributes such as gender or race. Recently, there has been a surge in machine learning society to develop algorithms for fair machine learning. In particular, many adversarial learning procedures have been proposed to impose fairness. Unfortunately, these algorithms either can only impose fairness up to first-order dependence between the variables, or they lack computational convergence guarantees. In this paper, we use Rényi correlation as a measure of fairness of machine learning models and develop a general training framework to impose fairness. In particular, we propose a min-max formulation which balances the accuracy and fairness when solved to optimality. For the case of discrete sensitive attributes, we suggest an iterative algorithm with theoretical convergence guarantee for solving the proposed min-max problem. Our algorithm and analysis are then specialized to fair classification and the fair clustering problem under disparate impact doctrine. Finally, the performance of the proposed Rényi fair inference framework is evaluated on Adult and Bank datasets.

Motivation & Objective

• To address the limitations of existing fairness methods that rely on linear dependence measures or lack convergence guarantees.
• To develop a general in-processing framework that promotes statistical independence between sensitive attributes and model outputs.
• To ensure computational convergence for discrete sensitive attributes while maintaining strong fairness-accuracy trade-offs.
• To evaluate the method on fair classification and fair clustering tasks using benchmark datasets.

Proposed method

• Formulates fairness as minimizing Rényi correlation (maximal correlation) between sensitive attributes and model predictions.
• Proposes a min-max optimization problem to balance accuracy and fairness, with theoretical convergence guarantees for discrete sensitive attributes.
• Uses an iterative algorithm based on alternating optimization to solve the min-max problem, ensuring first-order optimality.
• Specializes the framework to fair classification and fair clustering, using fairness metrics like equalized opportunity and cluster balance.
• Employs Rényi correlation as a nonparametric surrogate for statistical independence, capable of capturing nonlinear dependencies.
• Introduces a regularization hyperparameter λ to control the trade-off between model accuracy and fairness.

Experimental results

Research questions

• RQ1 Can Rényi correlation serve as an effective and computationally tractable surrogate for statistical independence in fairness constraints?
• RQ2 Does the proposed min-max formulation with iterative optimization yield convergence guarantees for discrete sensitive attributes?
• RQ3 How does Rényi Fair Inference compare to Pearson correlation and HSIC-based methods in capturing nonlinear dependencies in fairness constraints?
• RQ4 To what extent does increasing the regularization parameter λ improve fairness without significantly degrading model accuracy?
• RQ5 Can the framework be effectively extended to fair clustering, as measured by balance in cluster composition across protected groups?

Key findings

• The Rényi fair inference framework achieves lower equalized opportunity (EO) violation than state-of-the-art methods at comparable accuracy levels, especially on the Adult dataset.
• For logistic regression, Rényi regularization results in a smaller drop in accuracy compared to HSIC and Pearson correlation regularization across German Credit, Adult, and Bank datasets.
• Unlike Pearson and HSIC, Rényi correlation can effectively reduce fairness violations beyond a threshold, even when multiple or non-binary sensitive attributes are present.
• In fair k-means clustering, increasing λ reduces the standard deviation of the proportion vector w (representing privileged group share per cluster), achieving near-uniform cluster composition at λ ≥ 1.
• The method shows a rapid decrease in fairness deviation (standard deviation of w) with increasing λ, while the increase in clustering loss remains small for λ ≤ 0.005.
• Theoretical convergence is guaranteed for the iterative algorithm when the sensitive attribute is discrete, and optimal convergence is proven for binary sensitive attributes.