Generative models are used in a wide range of applications building on large amounts of contextually rich information. Due to possible privacy violations of the individuals whose data is used to train these models, however, publishing or sharing generative models is not always viable. In this paper, we present a novel technique for privately releasing generative models and entire high-dimensional datasets produced by these models. We model the generator distribution of the training data with a mixture of @math generative neural networks. These are trained together and collectively learn the generator distribution of a dataset. Data is divided into @math clusters, using a novel differentially private kernel @math -means, then each cluster is given to separate generative neural networks, such as Restricted Boltzmann Machines or Variational Autoencoders, which are trained only on their own cluster using differentially private gradient descent. We evaluate our approach using the MNIST dataset, as well as call detail records and transit datasets, showing that it produces realistic synthetic samples, which can also be used to accurately compute arbitrary number of counting queries.
Privacy in Deep Learning. Our work builds on the Differential Privacy (DP) framework, specifically, using the Gaussian mechanism @cite_53 . Due to its generality, DP has served as a building block in several recent efforts at the intersection of privacy and machine learning @cite_45 @cite_9 . In general, the majority of privacy-preserving learning schemes focus on convex optimization problems @cite_37 @cite_7 @cite_3 . Also, training neural networks typically requires to optimize non-convex objective functions -- as with Restricted Boltzmann Machine (RBM) @cite_57 and Variational Autoencoder (VAE) @cite_39 -- which is usually done through the application of Stochastic Gradient Descent (SGD) with poor theoretical guarantees. @cite_3 introduce a privacy-preserving technique which runs SGD for convex cases for a constant number of iterations and only adds noise to the final output. By contrast, we introduce a novel differentially private SGD algorithm for optimizing general non-convex loss functions.
@cite_37 @cite_7 @cite_9 @cite_53 @cite_3 @cite_39 @cite_57 @cite_45
1985511977 2964237819 2964064173 2949611647
Differential privacy is a recent framework for computation on sensitive data, which has shown considerable promise in the regime of large datasets. Stochastic gradient methods are a popular approach for learning in the data-rich regime because they are computationally tractable and scalable. In this paper, we derive differentially private versions of stochastic gradient descent, and test them empirically. Our results show that standard SGD experiences high variability due to differential privacy, but a moderate increase in the batch size can improve performance significantly. While machine learning has proven to be a powerful data-driven solution to many real-life problems, its use in sensitive domains has been limited due to privacy concerns. A popular approach known as differential privacy offers provable privacy guarantees, but it is often observed in practice that it could substantially hamper learning accuracy. In this paper we study the learnability (whether a problem can be learned by any algorithm) under Vapnik's general learning setting with differential privacy constraint, and reveal some intricate relationships between privacy, stability and learnability. In particular, we show that a problem is privately learnable if an only if there is a private algorithm that asymptotically minimizes the empirical risk (AERM). In contrast, for non-private learning AERM alone is not sufficient for learnability. This result suggests that when searching for private learning algorithms, we can restrict the search to algorithms that are AERM. In light of this, we propose a conceptual procedure that always finds a universally consistent algorithm whenever the problem is learnable under privacy constraint. We also propose a generic and practical algorithm and show that under very general conditions it privately learns a wide class of learning problems. Lastly, we extend some of the results to the more practical (e, δ)-differential privacy and establish the existence of a phase-transition on the class of problems that are approximately privately learnable with respect to how small δ needs to be. In this paper, we consider the problem of preserving privacy in the context of online learning. Online learning involves learning from data in real-time, due to which the learned model as well as its predictions are continuously changing. This makes preserving privacy of each data point significantly more challenging as its effect on the learned model can be easily tracked by observing changes in the subsequent predictions. Furthermore, with more and more online systems (e.g. search engines like Bing, Google etc.) trying to learn their customers’ behavior by leveraging their access to sensitive customer data (through cookies etc.), the problem of privacy preserving online learning has become critical. We study the problem in the framework of online convex programming (OCP)—a popular online learning setting with several theoretical and practical implications—while using differential privacy as the formal measure of privacy. For this problem, we provide a generic framework that can be used to convert any given OCP algorithm into a private OCP algorithm with provable privacy as well as regret guarantees (utility), provided that the given OCP algorithm satisfies the following two criteria: 1) linearly decreasing sensitivity, i.e., the effect of the new data points on the learned model decreases linearly, 2) sub-linear regret. We then illustrate our approach by converting two popular OCP algorithms into corresponding differentially private algorithms while guaranteeing O( p T ) regret for strongly convex functions. Next, we consider the practically important class of online linear regression problems, for which we generalize the approach by (2010a) to provide a differentially private algorithm with just poly-log regret. Finally, we show that our online learning framework can be used to provide differentially private algorithms for the offline learning problem as well. For the offline learning problem, our approach guarantees better error bounds and is more practical than the existing state-of-the-art methods (, 2011; , 2009). We compare the sample complexity of private learning [ 2008] and sanitization [ 2008] under pure @math -differential privacy [ TCC 2006] and approximate @math -differential privacy [ Eurocrypt 2006]. We show that the sample complexity of these tasks under approximate differential privacy can be significantly lower than that under pure differential privacy. We define a family of optimization problems, which we call Quasi-Concave Promise Problems, that generalizes some of our considered tasks. We observe that a quasi-concave promise problem can be privately approximated using a solution to a smaller instance of a quasi-concave promise problem. This allows us to construct an efficient recursive algorithm solving such problems privately. Specifically, we construct private learners for point functions, threshold functions, and axis-aligned rectangles in high dimension. Similarly, we construct sanitizers for point functions and threshold functions. We also examine the sample complexity of label-private learners, a relaxation of private learning where the learner is required to only protect the privacy of the labels in the sample. We show that the VC dimension completely characterizes the sample complexity of such learners, that is, the sample complexity of learning with label privacy is equal (up to constants) to learning without privacy.