Optimal Transport for Fairness: Archival Data Repair using Small
  Research Data Sets
Abigail Langbridge Anthony Quinn Robert Shorten
With the advent of the AI Act and other regulations, there is now an urgent
need for algorithms that repair unfairness in training data. In this paper, we
define fairness in terms of conditional independence between protected
attributes ($S$) and features ($X$), given unprotected attributes ($U$). We
address the important setting in which torrents of archival data need to be
repaired, using only a small proportion of these data, which are $S|U$-labelled
(the research data). We use the latter to design optimal transport (OT)-based
repair plans on interpolated supports. This allows {\em off-sample}, labelled,
archival data to be repaired, subject to stationarity assumptions. It also
significantly reduces the size of the supports of the OT plans, with
correspondingly large savings in the cost of their design and of their {\em
sequential\/} application to the off-sample data. We provide detailed
experimental results with simulated and benchmark real data (the Adult data
set). Our performance figures demonstrate effective repair -- in the sense of
quenching conditional dependence -- of large quantities of off-sample, labelled
(archival) data.