  Synthetic data generation (SDG) has become increasingly popular as a
privacy-enhancing technology. It aims to maintain important statistical
properties of its underlying training data, while excluding any personally
identifiable information. There have been a whole host of SDG algorithms
developed in recent years to improve and balance both of these aims. Many of
these algorithms provide robust differential privacy guarantees.
  However, we show here that if the differential privacy parameter
$\varepsilon$ is set too high, then unambiguous privacy leakage can result. We
show this by conducting a novel membership inference attack (MIA) on two
state-of-the-art differentially private SDG algorithms: MST and PrivBayes. Our
work suggests that there are vulnerabilities in these generators not previously
seen, and that future work to strengthen their privacy is advisable.
  We present the heuristic for our MIA here. It assumes knowledge of auxiliary
"population" data, and also assumes knowledge of which SDG algorithm was used.
We use this information to adapt the recent DOMIAS MIA uniquely to MST and
PrivBayes. Our approach went on to win the SNAKE challenge in November 2023.
