  Synthetic data is seen as the most promising solution to share
individual-level data while preserving privacy. Shadow modeling-based
Membership Inference Attacks (MIAs) have become the standard approach to
evaluate the privacy risk of synthetic data. While very effective, they require
a large number of datasets to be created and models trained to evaluate the
risk posed by a single record. The privacy risk of a dataset is thus currently
evaluated by running MIAs on a handful of records selected using ad-hoc
methods. We here propose what is, to the best of our knowledge, the first
principled vulnerable record identification technique for synthetic data
publishing, leveraging the distance to a record's closest neighbors. We show
our method to strongly outperform previous ad-hoc methods across datasets and
generators. We also show evidence of our method to be robust to the choice of
MIA and to specific choice of parameters. Finally, we show it to accurately
identify vulnerable records when synthetic data generators are made
differentially private. The choice of vulnerable records is as important as
more accurate MIAs when evaluating the privacy of synthetic data releases,
including from a legal perspective. We here propose a simple yet highly
effective method to do so. We hope our method will enable practitioners to
better estimate the risk posed by synthetic data publishing and researchers to
fairly compare ever improving MIAs on synthetic data.
