Decomposing Direct and Indirect Biases in Linear Models under Demographic Parity Constraint

TL;DR

This paper introduces a post-processing method to decompose and interpret direct and indirect biases in linear models under demographic parity constraints, enhancing fairness transparency without retraining.

Contribution

It extends existing fairness analysis by providing a framework that explicitly decomposes bias into direct and indirect components at the feature level for any linear model.

Findings

Effectively decomposes bias into direct and indirect components.

Reveals how demographic parity reshapes model coefficients.

Captures fairness dynamics missed by prior methods.

Abstract

Linear models are widely used in high-stakes decision-making due to their simplicity and interpretability. Yet when fairness constraints such as demographic parity are introduced, their effects on model coefficients, and thus on how predictive bias is distributed across features, remain opaque. Existing approaches on linear models often rely on strong and unrealistic assumptions, or overlook the explicit role of the sensitive attribute, limiting their practical utility for fairness assessment. We extend the work of (Chzhen and Schreuder, 2022) and (Fukuchi and Sakuma, 2023) by proposing a post-processing framework that can be applied on top of any linear model to decompose the resulting bias into direct (sensitive-attribute) and indirect (correlated-features) components. Our method analytically characterizes how demographic parity reshapes each model coefficient, including those of both sensitive and non-sensitive features. This enables a transparent, feature-level interpretation of fairness interventions and reveals how bias may persist or shift through correlated variables. Our framework requires no retraining and provides actionable insights for model auditing and mitigation. Experiments on both synthetic and real-world datasets demonstrate that our method captures fairness dynamics missed by prior work, offering a practical and interpretable tool for responsible deployment of linear models.