  Fairness in machine learning has received considerable attention. However,
most studies on fair learning focus on either supervised learning or
unsupervised learning. Very few consider semi-supervised settings. Yet, in
reality, most machine learning tasks rely on large datasets that contain both
labeled and unlabeled data. One of key issues with fair learning is the balance
between fairness and accuracy. Previous studies arguing that increasing the
size of the training set can have a better trade-off. We believe that
increasing the training set with unlabeled data may achieve the similar result.
Hence, we develop a framework for fair semi-supervised learning, which is
formulated as an optimization problem. This includes classifier loss to
optimize accuracy, label propagation loss to optimize unlabled data prediction,
and fairness constraints over labeled and unlabeled data to optimize the
fairness level. The framework is conducted in logistic regression and support
vector machines under the fairness metrics of disparate impact and disparate
mistreatment. We theoretically analyze the source of discrimination in
semi-supervised learning via bias, variance and noise decomposition. Extensive
experiments show that our method is able to achieve fair semi-supervised
learning, and reach a better trade-off between accuracy and fairness than fair
supervised learning.
