Fair CoVariance Neural Networks

TL;DR

Fair Covariance Neural Networks (FVNNs) are introduced to improve fairness and stability in covariance-based data processing, especially in low sample regimes, by combining graph convolutions on covariance matrices with fairness regularization.

Contribution

The paper proposes FVNNs, a novel model that enhances fairness and stability in covariance-based learning through graph convolutions and end-to-end training with fairness regularizers.

Findings

FVNNs outperform PCA-based methods in low sample regimes.

FVNNs effectively mitigate bias while maintaining accuracy.

The model demonstrates robustness and fairness on synthetic and real-world data.

Abstract

Covariance-based data processing is widespread across signal processing and machine learning applications due to its ability to model data interconnectivities and dependencies. However, harmful biases in the data may become encoded in the sample covariance matrix and cause data-driven methods to treat different subpopulations unfairly. Existing works such as fair principal component analysis (PCA) mitigate these effects, but remain unstable in low sample regimes, which in turn may jeopardize the fairness goal. To address both biases and instability, we propose Fair coVariance Neural Networks (FVNNs), which perform graph convolutions on the covariance matrix for both fair and accurate predictions. Our FVNNs provide a flexible model compatible with several existing bias mitigation techniques. In particular, FVNNs allow for mitigating the bias in two ways: first, they operate on fair covariance estimates that remove biases from their principal components; second, they are trained in an end-to-end fashion via a fairness regularizer in the loss function so that the model parameters are tailored to solve the task directly in a fair manner. We prove that FVNNs are intrinsically fairer than analogous PCA approaches thanks to their stability in low sample regimes. We validate the robustness and fairness of our model on synthetic and real-world data, showcasing the flexibility of FVNNs along with the tradeoff between fair and accurate performance.