  In this paper, we deal with bias mitigation techniques that remove specific
data points from the training set to aim for a fair representation of the
population in that set. Machine learning models are trained on these
pre-processed datasets, and their predictions are expected to be fair. However,
such approaches may exclude relevant data, making the attained subsets less
trustworthy for further usage. To enhance the trustworthiness of prior methods,
we propose additional requirements and objectives that the subsets must fulfill
in addition to fairness: (1) group coverage, and (2) minimal data loss. While
removing entire groups may improve the measured fairness, this practice is very
problematic as failing to represent every group cannot be considered fair. In
our second concern, we advocate for the retention of data while minimizing
discrimination. By introducing a multi-objective optimization problem that
considers fairness and data loss, we propose a methodology to find
Pareto-optimal solutions that balance these objectives. By identifying such
solutions, users can make informed decisions about the trade-off between
fairness and data quality and select the most suitable subset for their
application.
