A Reductions Approach to Fair Classification (1803.02453v3)

Abstract: We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special cases. The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. We introduce two reductions that work for any representation of the cost-sensitive classifier and compare favorably to prior baselines on a variety of data sets, while overcoming several of their disadvantages.

• The paper proposes a reductions framework that transforms fair binary classification into a sequence of cost-sensitive problems using an exponentiated gradient algorithm.
• It offers finite-sample guarantees and tight error bounds, ensuring a balance between accuracy and fairness measures like demographic parity and equalized odds.
• Experimental evaluations on multiple datasets demonstrate the method's efficiency, scalability, and competitive performance against standard fairness-aware techniques.

A Reductions Approach to Fair Classification

The paper, "A Reductions Approach to Fair Classification," presents a methodologically robust framework for ensuring fairness in binary classification settings. This approach is particularly valuable as it accommodates a variety of fairness definitions, operationalizes these definitions without requiring a change to the underlying classification approach, and provides practical as well as theoretical guarantees.

Introduction

Fairness in machine learning has garnered increased attention, particularly in high-stakes applications such as loan approval and employment. The paper addresses fairness in a binary classification context where fairness constraints are associated with a specified protected attribute, such as race or gender. The contributions are categorized as follows:

1. Problem Formulation: The paper formalizes fairness in terms of conditional moments, which encompass many previously studied definitions.
2. Reductions Approach: It demonstrates how the fair classification problem can be broken down into a series of cost-sensitive classification problems.
3. Algorithmic Solution: The authors propose two specific reductions that promise efficiency and flexibility in enforcing fairness constraints.
4. Experimental Validation: An empirical evaluation shows that the approach compares favorably to existing methods.

Fairness Definitions

The paper focuses on two well-regarded fairness metrics:

• Demographic Parity (DP): Ensures that the classifier's prediction is statistically independent of the protected attribute.
• Equalized Odds (EO): Ensures that the classifier’s predictions are conditionally independent of the protected attribute given the actual outcome.

Using these definitions, the paper generalizes fairness constraints as linear inequalities on conditional moments.

Reductions Approach

The core of the paper is its innovative reductions approach, which translates fair classification into a sequence of cost-sensitive classification problems:

1. Setup: The problem is reformulated into minimizing empirical error subject to fairness constraints.
2. Algorithm: An exponentiated gradient (EG) algorithm is utilized, which iteratively optimizes a Lagrangian formulation to find the classifier that minimizes error while satisfying fairness constraints.
3. Details: The paper outlines how the best response function and the cost-sensitive classification problem can be integrated, ensuring the approach's generality and applicability across different classifier types.

Theoretical Analysis

The approach is rigorously analyzed to provide finite-sample guarantees:

• Error Bound: The paper derives a statistical bound on the classification error, showing that the approach converges to an optimal fair classifier.
• Complexity Analysis: Theoretical insights into the algorithm's convergence rate demonstrate that the required number of iterations grows slowly with the number of constraints, making the algorithm scalable and efficient.

Empirical Evaluation

The experimental section validates the reductions approach using multiple datasets, comparing the results against existing fairness-aware algorithms:

• Datasets: The research tests on datasets like the Adult Income dataset, COMPAS recidivism dataset, and others.
• Baselines: Methods like reweighting, relabeling, and post-processing are used as baselines.
• Results: The proposed reductions approach not only matches but often exceeds the performance of baseline methods in achieving the desired trade-off between accuracy and fairness.

Implications and Future Work

This reductions approach carries significant theoretical and practical implications:

1. Theoretical Contribution: It provides a unifying framework that handles various definitions of fairness, backed by strong theoretical guarantees.
2. Practical Utility: The method is versatile and can be easily integrated into existing machine learning workflows without necessitating changes to the underlying classifiers.
3. Efficiency: The demonstrated computational efficiency ensures that the approach is feasible even for large-scale applications.

The paper also highlights several directions for future research, including:

• Fairness without Training-time Access: Extending the approach to scenarios where protected attributes are unavailable during training.
• Trade-offs among Multiple Fairness Definitions: Balancing different and potentially conflicting fairness constraints remains an open challenge.

Conclusion

The paper "A Reductions Approach to Fair Classification" marks a substantial advancement in the domain of fairness-aware machine learning. The systematic reductions framework, coupled with robust empirical validation and theoretically grounded guarantees, positions this approach as a critical tool for developing fair classifiers in diverse applied contexts. As fairness continues to be a critical concern in machine learning, the techniques presented in this paper pave the way for more equitable and transparent algorithmic decision-making systems.