[Paper Review] Towards Threshold Invariant Fair Classification

Mingliang Chen, Min Wu|arXiv (Cornell University)|Jun 18, 2020

Ethics and Social Impacts of AI19 references4 citations

TL;DR

This paper proposes threshold-invariant fairness in machine learning by equalizing risk score distributions across sensitive groups, using histogram approximation and Gaussian assumption to make fairness robust to decision threshold changes. The method achieves significantly reduced variance in fairness metrics (e.g., DP and EO) across thresholds, outperforming baseline constrained models in consistency and stability.

ABSTRACT

Effective machine learning models can automatically learn useful information from a large quantity of data and provide decisions in a high accuracy. These models may, however, lead to unfair predictions in certain sense among the population groups of interest, where the grouping is based on such sensitive attributes as race and gender. Various fairness definitions, such as demographic parity and equalized odds, were proposed in prior art to ensure that decisions guided by the machine learning models are equitable. Unfortunately, the "fair" model trained with these fairness definitions is threshold sensitive, i.e., the condition of fairness may no longer hold true when tuning the decision threshold. This paper introduces the notion of threshold invariant fairness, which enforces equitable performances across different groups independent of the decision threshold. To achieve this goal, this paper proposes to equalize the risk distributions among the groups via two approximation methods. Experimental results demonstrate that the proposed methodology is effective to alleviate the threshold sensitivity in machine learning models designed to achieve fairness.

Motivation & Objective

• Address the limitation of existing fairness definitions (e.g., demographic parity, equalized odds) that are sensitive to decision threshold tuning.
• Develop a fairness notion that ensures equitable classifier performance across groups regardless of threshold adjustments.
• Propose two differentiable methods—histogram approximation and Gaussian assumption—to equalize risk score distributions across protected groups.
• Ensure compatibility with various differentiable classifiers like logistic regression and SVM, enabling integration into standard training pipelines.
• Demonstrate that fairness stability improves without sacrificing model accuracy, especially under dynamic threshold settings.

Proposed method

• Introduce threshold-invariant fairness as a stronger fairness condition than classification parity, requiring consistent fairness across all decision thresholds.
• Use histogram approximation (HA) to model risk score distributions via N-bin histograms with differentiable Gaussian kernel approximation for gradient-based optimization.
• Apply Gaussian assumption (GA) to represent risk distributions using only first and second moments (mean and variance), reducing computational complexity to O(M).
• Incorporate both methods as differentiable constraints into the training objective of classifiers like logistic regression and SVM.
• Optimize the risk distribution equalization using stochastic gradient descent, enabling batch-based training compatible with deep learning frameworks.
• Ensure the fairness constraint is enforced during training by minimizing distribution divergence between groups while preserving model accuracy.

Experimental results

Research questions

• RQ1 Can fairness in machine learning be made robust to changes in decision thresholds, beyond existing classification parity definitions?
• RQ2 How can risk score distributions be equalized across sensitive groups to achieve threshold-invariant fairness?
• RQ3 What are the trade-offs between computational efficiency and approximation accuracy in modeling risk distribution equality?
• RQ4 To what extent can the proposed methods improve fairness consistency across varying decision thresholds compared to existing fairness-aware training methods?
• RQ5 Can the proposed methods be generalized across different types of differentiable classifiers, including neural networks?

Key findings

• The proposed methods significantly reduce the variance and range of fairness metric fluctuations (ΔDP and ΔEO) across decision thresholds compared to baseline fairness-constrained models.
• The Gaussian assumption (GA) method achieves comparable fairness performance to histogram approximation (HA) with lower computational complexity (O(M) vs. O(MN)).
• Classifiers trained with the proposed methods show minor fluctuations in fairness curves, indicating strong robustness to threshold changes.
• The proposed approach maintains high accuracy while improving fairness stability, outperforming Zafar-DP and Zafar-EO in threshold-invariant fairness metrics.
• The methods are compatible with batch-based training and extendable to multi-attribute fairness and neural network classifiers.
• Experimental results confirm that risk distribution equalization leads to more consistent fairness outcomes, especially under dynamic threshold settings.