We propose Bayesian differential privacy, a relaxation of differential privacy for similarly distributed data, that provides sharper privacy guarantees in difficult scenarios, such as deep learning. We also derive a general privacy accounting method for iterative learning algorithms under Bayesian differential privacy and show that it is a generalisation of the well-known moments accountant. Our experiments demonstrate significant advantage over the state-of-the-art differential privacy bounds for deep learning models on classic supervised learning tasks, bringing the privacy budget from 8 down to 0.5 in some cases. Lower amounts of injected noise also benefit the model accuracy and the speed of learning. Additionally, we demonstrate applicability of Bayesian differential privacy to variational inference and achieve the state-of-the-art privacy-accuracy trade-off.
We examine the information-theoretic foundations of the increasingly popular notion of differential privacy. We establish a connection between differential private mechanisms and the rate-distortion framework. Additionally, we also show how differentially private distributions arise out of the application of the Maximum Entropy Principle. This helps us locate differential privacy within the wider framework of information-theory and helps formalize some intuitive aspects of our understanding of differential privacy.