Normalise for Fairness: A Simple Normalisation Technique for Fairness in Regression Machine Learning Problems

TL;DR

The paper addresses fairness in regression, focusing on bias in ground-truth labels (labelling bias) and proposes a simple normalisation-based approach (FaiReg) and a hybrid variant (FaiRegH) that also incorporates data balancing. It develops a theoretical framework linking the training objective to a fairness–performance trade-off via the loss $\mathcal{L}$ and covariance terms, and analyzes conditions for Statistical Parity and Equal Accuracy. The methods are validated on the First Impressions multimodal dataset with Big-Five and interview-invitation labels, showing that FaiReg and FaiRegH reduce Statistical Parity violations (as measured by PCC and SPM) with minimal degradation to the original task performance, outperforming data balancing and adversarial baselines. The work highlights practical impact for regression tasks in sensitive domains, while acknowledging distributional assumptions and potential misuse that necessitate fairness monitoring.

Abstract

Algorithms and Machine Learning (ML) are increasingly affecting everyday life and several decision-making processes, where ML has an advantage due to scalability or superior performance. Fairness in such applications is crucial, where models should not discriminate their results based on race, gender, or other protected groups. This is especially crucial for models affecting very sensitive topics, like interview invitation or recidivism prediction. Fairness is not commonly studied for regression problems compared to binary classification problems; hence, we present a simple, yet effective method based on normalisation (FaiReg), which minimises the impact of unfairness in regression problems, especially due to labelling bias. We present a theoretical analysis of the method, in addition to an empirical comparison against two standard methods for fairness, namely data balancing and adversarial training. We also include a hybrid formulation (FaiRegH), merging the presented method with data balancing, in an attempt to face labelling and sampling biases simultaneously. The experiments are conducted on the multimodal dataset First Impressions (FI) with various labels, namely Big-Five personality prediction and interview screening score. The results show the superior performance of diminishing the effects of unfairness better than data balancing, also without deteriorating the performance of the original problem as much as adversarial training. Fairness is evaluated based on the Equal Accuracy (EA) and Statistical Parity (SP) constraints. The experiments present a setup that enhances the fairness for several protected variables simultaneously.

Figures (3)

• Figure 1: Plotting the relation of MAA and PCC for both gender and race, when the models are trained with gender, race, or both as a protected variable. Each point shows the Test-set performance for a hyperparameters configuration sampled by BO during hyperparameters tuning. This visualises how difference instances of one method attempts to balance the performance-fairness trade-off. The coloured region is where a model has low PCC, with $p$-value not $<10^{-3}$, while maintaining a performance above the constant baseline performance.
• Figure 2: The distributions of the Test-set ground truth labels for the six labels, and each protected variable.
• Figure 3: Demonstration of how the constant optimal point $p^*$ (yielding optimal Equal Accuracy) changes based on the variances of the distributions of the protected groups. $p^*$ is demonstrated by the vertical line.

Theorems & Definitions (16)

• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4
• Definition 3.5
• Definition 3.6
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Theorem 4.4