Jointly Robust Fairness: Overcoming Simultaneous Label and Attribute Noise

Fairness in machine learning typically relies on the assumption of clean training data. However, in high-stakes applications like healthcare and criminal justice, privacy mechanisms and proxy variables frequently introduce simultaneous noise into both sensitive attributes and target labels. While existing methods address label or attribute noise in isolation, they fail under this "double noise" regime, often inadvertently amplifying bias. In this paper, we propose $\textbf{Jointly Robust Fairness (JRF)}$, a unified framework that guarantees fairness under simultaneous data corruption. JRF integrates a Forward Loss correction to handle label noise with a novel Matrix-Inverse Robust Loss (MIRL) that algebraically recovers the true demographic parity gap from noisy attribute observations. We provide rigorous theoretical guarantees for our estimator, including a finite-sample concentration bound demonstrating that the sample complexity scales quadratically with the inverse of the noise transition determinant. Furthermore, our framework naturally generalizes to both symmetric and highly asymmetric noise distributions. Extensive experiments on the Adult, Bank, and COMPAS datasets demonstrate that JRF reduces fairness violations by over 91\% in high-noise regimes ($\rho \ge 0.3$) compared to standard robust baselines, maintaining strict fairness without significant degradation in predictive utility.