  Multiple synthetic data generation models have emerged, among which deep
learning models have become the vanguard due to their ability to capture the
underlying characteristics of the original data. However, the resemblance of
the synthetic to the original data raises important questions on the protection
of individuals' privacy. As synthetic data is perceived as a means to fully
protect personal information, most current related work disregards the impact
of re-identification risk. In particular, limited attention has been given to
exploring outliers, despite their privacy relevance. In this work, we analyze
the privacy of synthetic data w.r.t the outliers. Our main findings suggest
that outliers re-identification via linkage attack is feasible and easily
achieved. Furthermore, additional safeguards such as differential privacy can
prevent re-identification, albeit at the expense of the data utility.
