  In the current artificial intelligence (AI) era, the scale and quality of the
dataset play a crucial role in training a high-quality AI model. However, good
data is not a free lunch and is always hard to access due to privacy
regulations like the General Data Protection Regulation (GDPR). A potential
solution is to release a synthetic dataset with a similar distribution to that
of the private dataset. Nevertheless, in some scenarios, it has been found that
the attributes needed to train an AI model belong to different parties, and
they cannot share the raw data for synthetic data publication due to privacy
regulations. In PETS 2023, Xue et al. proposed the first generative adversary
network-based model, VertiGAN, for vertically partitioned data publication.
However, after thoroughly investigating, we found that VertiGAN is less
effective in preserving the correlation among the attributes of different
parties. This article proposes a Vertical Federated Learning-based Generative
Adversarial Network, VFLGAN, for vertically partitioned data publication to
address the above issues. Our experimental results show that compared with
VertiGAN, VFLGAN significantly improves the quality of synthetic data. Taking
the MNIST dataset as an example, the quality of the synthetic dataset generated
by VFLGAN is 3.2 times better than that generated by VertiGAN w.r.t. the
Fr\'echet Distance. We also designed a more efficient and effective Gaussian
mechanism for the proposed VFLGAN to provide the synthetic dataset with a
differential privacy guarantee. On the other hand, differential privacy only
gives the upper bound of the worst-case privacy guarantee. This article also
proposes a practical auditing scheme that applies membership inference attacks
to estimate privacy leakage through the synthetic dataset.
