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 evaluate our method on two popular classes of learning algorithms: deep neural networks and variational inference (VI). Privacy-preserving deep learning is now extensively studied, and is frequently used in combination with moments accountant @cite_27 @cite_25 @cite_28 , which makes it a perfect setting for comparison. Bayesian inference methods, on the other hand, receive less attention from the private learning community. There are, nonetheless, very interesting results suggesting one could obtain DP guarantees "for free" (without adding noise) in some methods like posterior sampling @cite_8 @cite_2 and stochastic gradient Monte Carlo @cite_7 . A differentially private version of variational inference, obtained by applying noise to the gradients and using moments accountant, has also been proposed @cite_3 . We show that with our accountant it is possible to build VI that is both highly accurate and differentially private by sampling from variational distribution.
@cite_7 @cite_8 @cite_28 @cite_3 @cite_27 @cite_2 @cite_25
1886087434 1553111043 2785361959 2539938672 2473418344 2608609295 2950602864
We consider the problem of Bayesian learning on sensitive datasets and present two simple but somewhat surprising results that connect Bayesian learning to "differential privacy", a cryptographic approach to protect individual-level privacy while permitting database-level utility. Specifically, we show that under standard assumptions, getting one sample from a posterior distribution is differentially private "for free"; and this sample as a statistical estimator is often consistent, near optimal, and computationally tractable. Similarly but separately, we show that a recent line of work that use stochastic gradient for Hybrid Monte Carlo (HMC) sampling also preserve differentially privacy with minor or no modifications of the algorithmic procedure at all, these observations lead to an "anytime" algorithm for Bayesian learning under privacy constraint. We demonstrate that it performs much better than the state-of-the-art differential private methods on synthetic and real datasets. We examine the robustness and privacy of Bayesian inference, under assumptions on the prior, and with no modifications to the Bayesian framework. First, we generalise the concept of differential privacy to arbitrary dataset distances, outcome spaces and distribution families. We then prove bounds on the robustness of the posterior, introduce a posterior sampling mechanism, show that it is differentially private and provide finite sample bounds for distinguishability-based privacy under a strong adversarial model. Finally, we give examples satisfying our assumptions. The rapid adoption of machine learning has increased concerns about the privacy implications of machine learning models trained on sensitive data, such as medical records or other personal information. To address those concerns, one promising approach is Private Aggregation of Teacher Ensembles, or PATE, which transfers to a "student" model the knowledge of an ensemble of "teacher" models, with intuitive privacy provided by training teachers on disjoint data and strong privacy guaranteed by noisy aggregation of teachers' answers. However, PATE has so far been evaluated only on simple classification tasks like MNIST, leaving unclear its utility when applied to larger-scale learning tasks and real-world datasets. In this work, we show how PATE can scale to learning tasks with large numbers of output classes and uncurated, imbalanced training data with errors. For this, we introduce new noisy aggregation mechanisms for teacher ensembles that are more selective and add less noise, and prove their tighter differential-privacy guarantees. Our new mechanisms build on two insights: the chance of teacher consensus is increased by using more concentrated noise and, lacking consensus, no answer need be given to a student. The consensus answers used are more likely to be correct, offer better intuitive privacy, and incur lower-differential privacy cost. Our evaluation shows our mechanisms improve on the original PATE on all measures, and scale to larger tasks with both high utility and very strong privacy ( @math < 1.0). 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. Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addressing this goal, we develop new algorithmic techniques for learning and a refined analysis of privacy costs within the framework of differential privacy. Our implementation and experiments demonstrate that we can train deep neural networks with non-convex objectives, under a modest privacy budget, and at a manageable cost in software complexity, training efficiency, and model quality. Differential privacy formalises privacy-preserving mechanisms that provide access to a database. Can Bayesian inference be used directly to provide private access to data? The answer is yes: under certain conditions on the prior, sampling from the posterior distribution can lead to a desired level of privacy and utility. For a uniform treatment, we define differential privacy over arbitrary data set metrics, outcome spaces and distribution families. This allows us to also deal with non-i.i.d or non-tabular data sets. We then prove bounds on the sensitivity of the posterior to the data, which delivers a measure of robustness. We also show how to use posterior sampling to provide differentially private responses to queries, within a decision-theoretic framework. Finally, we provide bounds on the utility of answers to queries and on the ability of an adversary to distinguish between data sets. The latter are complemented by a novel use of Le Cam's method to obtain lower bounds on distinguishability. Our results hold for arbitrary metrics, including those for the common definition of differential privacy. For specific choices of the metric, we give a number of examples satisfying our assumptions. Some machine learning applications involve training data that is sensitive, such as the medical histories of patients in a clinical trial. A model may inadvertently and implicitly store some of its training data; careful analysis of the model may therefore reveal sensitive information. To address this problem, we demonstrate a generally applicable approach to providing strong privacy guarantees for training data: Private Aggregation of Teacher Ensembles (PATE). The approach combines, in a black-box fashion, multiple models trained with disjoint datasets, such as records from different subsets of users. Because they rely directly on sensitive data, these models are not published, but instead used as "teachers" for a "student" model. The student learns to predict an output chosen by noisy voting among all of the teachers, and cannot directly access an individual teacher or the underlying data or parameters. The student's privacy properties can be understood both intuitively (since no single teacher and thus no single dataset dictates the student's training) and formally, in terms of differential privacy. These properties hold even if an adversary can not only query the student but also inspect its internal workings. Compared with previous work, the approach imposes only weak assumptions on how teachers are trained: it applies to any model, including non-convex models like DNNs. We achieve state-of-the-art privacy utility trade-offs on MNIST and SVHN thanks to an improved privacy analysis and semi-supervised learning.