[Paper Review] Fair Regression: Quantitative Definitions and Reduction-based Algorithms

Alekh Agarwal, Miroslav Dudı́k+1 more|arXiv (Cornell University)|May 30, 2019

Ethics and Social Impacts of AI31 references63 citations

TL;DR

The paper defines fair regression under statistical parity and bounded group loss, and offers reduction-based algorithms that convert fair regression into standard learning problems with theoretical guarantees.

ABSTRACT

In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems \emph{fair regression}. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitz-continuous losses, and so they encompass least-squares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness--accuracy frontiers on several standard datasets.

Motivation & Objective

• Motivate predicting real-valued targets with a quantitative notion of fairness in regression settings.
• Define two fairness notions—statistical parity and bounded group loss—for regression tasks.
• Develop reduction-based algorithms that leverage standard risk minimization, classification, or regression oracles.
• Provide theoretical guarantees on optimality, fairness, and generalization for Lipschitz losses and bounded model classes.
• Empirically demonstrate fairness–accuracy tradeoffs on standard datasets across regression tasks.

Proposed method

• General framework for fair regression with Lipschitz losses and protected attributes.
• Two algorithmic reductions: (i) to cost-sensitive classification for SP; (ii) to weighted loss minimization with per-group constraints for BGL.
• Discretization of the prediction space to create finite constraint sets while preserving accuracy guarantees.
• Use of randomized predictors to improve fairness-accuracy tradeoffs.
• Reduction to standard learning oracles: risk minimization under weighted loss, weighted least-squares, or cost-sensitive classification.
• Theoretical results bounding computational efficiency, generalization error, and fairness violation.

Experimental results

Research questions

• RQ1 Can statistical parity be enforced in regression while maintaining close predictive accuracy using standard learning pipelines?
• RQ2 How can bounded group loss be achieved in regression through reductions to weighted or constrained learning problems?
• RQ3 What are the theoretical guarantees (cost, generalization, fairness violation) when solving fair regression via these reductions?
• RQ4 Do discretization and randomized predictors enable tractable fair regression across arbitrary Lipschitz losses and model classes?
• RQ5 How do these fair regression methods perform on standard datasets comparing fairness-accuracy frontiers?

Key findings

• Fair regression can be formulated with SP or BGL constraints while using standard risk minimization oracles.
• SP is handled by discretizing the prediction space and reducing to cost-sensitive classification with finite constraints.
• BGL is addressed by reducing to a weighted loss minimization problem with per-group loss bounds.
• The approach provides theoretical guarantees on loss, fairness violations, and generalization for Lipschitz losses and bounded complexity classes.
• Empirical results reveal fairness–accuracy frontiers across least-squares and logistic regression with linear and tree-ensemble learners.
• The framework supports randomized predictors to improve tradeoffs without sacrificing guarantees.