  Machine learning models, especially deep neural networks have been shown to
be susceptible to privacy attacks such as membership inference where an
adversary can detect whether a data point was used for training a black-box
model. Such privacy risks are exacerbated when a model's predictions are used
on an unseen data distribution. To alleviate privacy attacks, we demonstrate
the benefit of predictive models that are based on the causal relationships
between input features and the outcome. We first show that models learnt using
causal structure generalize better to unseen data, especially on data from
different distributions than the train distribution. Based on this
generalization property, we establish a theoretical link between causality and
privacy: compared to associational models, causal models provide stronger
differential privacy guarantees and are more robust to membership inference
attacks. Experiments on simulated Bayesian networks and the colored-MNIST
dataset show that associational models exhibit upto 80% attack accuracy under
different test distributions and sample sizes whereas causal models exhibit
attack accuracy close to a random guess.
