  Generative Adversarial Networks (GANs) have been widely used for generating
synthetic data for cases where there is a limited size real-world dataset or
when data holders are unwilling to share their data samples. Recent works
showed that GANs, due to overfitting and memorization, might leak information
regarding their training data samples. This makes GANs vulnerable to Membership
Inference Attacks (MIAs). Several defense strategies have been proposed in the
literature to mitigate this privacy issue. Unfortunately, defense strategies
based on differential privacy are proven to reduce extensively the quality of
the synthetic data points. On the other hand, more recent frameworks such as
PrivGAN and PAR-GAN are not suitable for small-size training datasets. In the
present work, the overfitting in GANs is studied in terms of the discriminator,
and a more general measure of overfitting based on the Bhattacharyya
coefficient is defined. Then, inspired by Fano's inequality, our first defense
mechanism against MIAs is proposed. This framework, which requires only a
simple modification in the loss function of GANs, is referred to as the maximum
entropy GAN or MEGAN and significantly improves the robustness of GANs to MIAs.
As a second defense strategy, a more heuristic model based on minimizing the
information leaked from generated samples about the training data points is
presented. This approach is referred to as mutual information minimization GAN
(MIMGAN) and uses a variational representation of the mutual information to
minimize the information that a synthetic sample might leak about the whole
training data set. Applying the proposed frameworks to some commonly used data
sets against state-of-the-art MIAs reveals that the proposed methods can reduce
the accuracy of the adversaries to the level of random guessing accuracy with a
small reduction in the quality of the synthetic data samples.
