Deep neural networks with their large number of parameters are highly flexible learning systems. The high flexibility in such networks brings with some serious problems such as overfitting, and regularization is used to address this problem. A currently popular and effective regularization technique for controlling the overfitting is dropout. Often, large data collections required for neural networks contain sensitive information such as the medical histories of patients, and the privacy of the training data should be protected. In this paper, we modify the recently proposed variational dropout technique which provided an elegant Bayesian interpretation to dropout, and show that the intrinsic noise in the variational dropout can be exploited to obtain a degree of differential privacy. The iterative nature of training neural networks presents a challenge for privacy-preserving estimation since multiple iterations increase the amount of noise added. We overcome this by using a relaxed notion of differential privacy, called concentrated differential privacy, which provides tighter estimates on the overall privacy loss. We demonstrate the accuracy of our privacy-preserving variational dropout algorithm on benchmark datasets.
Many machine learning applications are based on data collected from people, such as their tastes and behaviour as well as biological traits and genetic data. Regardless of how important the application might be, one has to make sure individuals' identities or the privacy of the data are not compromised in the analysis. Differential privacy constitutes a powerful framework that prevents breaching of data subject privacy from the output of a computation. Differentially private versions of many important Bayesian inference methods have been proposed, but there is a lack of an efficient unified approach applicable to arbitrary models. In this contribution, we propose a differentially private variational inference method with a very wide applicability. It is built on top of doubly stochastic variational inference, a recent advance which provides a variational solution to a large class of models. We add differential privacy into doubly stochastic variational inference by clipping and perturbing the gradients. The algorithm is made more efficient through privacy amplification from subsampling. We demonstrate the method can reach an accuracy close to non-private level under reasonably strong privacy guarantees, clearly improving over previous sampling-based alternatives especially in the strong privacy regime.  We provide a general framework for privacy-preserving variational Bayes (VB) for a large class of probabilistic models, called the conjugate exponential (CE) family. Our primary observation is that when models are in the CE family, we can privatise the variational posterior distributions simply by perturbing the expected sufficient statistics of the complete-data likelihood. For widely used non-CE models with binomial likelihoods, we exploit the P 'o lya-Gamma data augmentation scheme to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) a relaxed notion of differential privacy, called concentrated differential privacy, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets. We introduce Concentrated Differential Privacy, a relaxation of Differential Privacy enjoying better accuracy than both pure differential privacy and its popular "(epsilon,delta)" relaxation without compromising on cumulative privacy loss over multiple computations.