We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Modern mobile devices have access to a wealth of data suitable for learning models, which in turn can greatly improve the user experience on the device. For example, language models can improve speech recognition and text entry, and image models can automatically select good photos. However, this rich data is often privacy sensitive, large in quantity, or both, which may preclude logging to the data center and training there using conventional approaches. We advocate an alternative that leaves the training data distributed on the mobile devices, and learns a shared model by aggregating locally-computed updates. We term this decentralized approach Federated Learning. 
We present a practical method for the federated learning of deep networks based on iterative model averaging, and conduct an extensive empirical evaluation, considering five different model architectures and four datasets. These experiments demonstrate the approach is robust to the unbalanced and non-IID data distributions that are a defining characteristic of this setting. Communication costs are the principal constraint, and we show a reduction in required communication rounds by 10-100x as compared to synchronized stochastic gradient descent.

Communication-Efficient Learning of Deep Networks from Decentralized Data

The problem of privacy-preserving data analysis has a long history spanning multiple disciplines. As electronic data about individuals becomes increasingly detailed, and as technology enables ever more powerful collection and curation of these data, the need increases for a robust, meaningful, and mathematically rigorous definition of privacy, together with a computationally rich class of algorithms that satisfy this definition. Differential Privacy is such a definition.After motivating and discussing the meaning of differential privacy, the preponderance of this monograph is devoted to fundamental techniques for achieving differential privacy, and application of these techniques in creative combinations, using the query-release problem as an ongoing example. A key point is that, by rethinking the computational goal, one can often obtain far better results than would be achieved by methodically replacing each step of a non-private computation with a differentially private implementation. Despite some astonishingly powerful computational results, there are still fundamental limitations — not just on what can be achieved with differential privacy but on what can be achieved with any method that protects against a complete breakdown in privacy. Virtually all the algorithms discussed herein maintain differential privacy against adversaries of arbitrary computational power. Certain algorithms are computationally intensive, others are efficient. Computational complexity for the adversary and the algorithm are both discussed.We then turn from fundamentals to applications other than queryrelease, discussing differentially private methods for mechanism design and machine learning. The vast majority of the literature on differentially private algorithms considers a single, static, database that is subject to many analyses. Differential privacy in other models, including distributed databases and computations on data streams is discussed.Finally, we note that this work is meant as a thorough introduction to the problems and techniques of differential privacy, but is not intended to be an exhaustive survey — there is by now a vast amount of work in differential privacy, and we can cover only a small portion of it.

/pdf/the-algorithmic-foundations-of-differential-privacy-1n8bb9a7eo.pdf

The Algorithmic Foundations of Differential Privacy

We continue a line of research initiated in [10, 11] on privacy-preserving statistical databases. Consider a trusted server that holds a database of sensitive information. Given a query function f mapping databases to reals, the so-called true answer is the result of applying f to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user. Previous work focused on the case of noisy sums, in which f = Σ i g(x i ), where x i denotes the ith row of the database and g maps database rows to [0,1]. We extend the study to general functions f, proving that privacy can be preserved by calibrating the standard deviation of the noise according to the sensitivity of the function f. Roughly speaking, this is the amount that any single argument to f can change its output. The new analysis shows that for several particular applications substantially less noise is needed than was previously understood to be the case. The first step is a very clean characterization of privacy in terms of indistinguishability of transcripts. Additionally, we obtain separation results showing the increased value of interactive sanitization mechanisms over non-interactive.

Calibrating noise to sensitivity in private data analysis

Over the past five years a new approach to privacy-preserving data analysis has born fruit [13, 18, 7, 19, 5, 37, 35, 8, 32]. This approach differs from much (but not all!) of the related literature in the statistics, databases, theory, and cryptography communities, in that a formal and ad omnia privacy guarantee is defined, and the data analysis techniques presented are rigorously proved to satisfy the guarantee. The key privacy guarantee that has emerged is differential privacy. Roughly speaking, this ensures that (almost, and quantifiably) no risk is incurred by joining a statistical database.

In this survey, we recall the definition of differential privacy and two basic techniques for achieving it. We then show some interesting applications of these techniques, presenting algorithms for three specific tasks and three general results on differentially private learning.

/pdf/differential-privacy-a-survey-of-results-36msco9vw4.pdf

Differential privacy: a survey of results

Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask, What concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in contexts where aggregate information is released about a database containing sensitive information about individuals. Our goal is a broad understanding of the resources required for private learning in terms of samples, computation time, and interaction. We demonstrate that, ignoring computational constraints, it is possible to privately agnostically learn any concept class using a sample size approximately logarithmic in the cardinality of the concept class. Therefore, almost anything learnable is learnable privately: specifically, if a concept class is learnable by a (nonprivate) algorithm with polynomial sample complexity and output size, then it can be learned privately using a polynomial number of samples. We also present a computationally efficient private probabilistically approximately correct learner for the class of parity functions. This result dispels the similarity between learning with noise and private learning (both must be robust to small changes in inputs), since parity is thought to be very hard to learn given random classification noise. Local (or randomized response) algorithms are a practical class of private algorithms that have received extensive investigation. We provide a precise characterization of local private learning algorithms. We show that a concept class is learnable by a local algorithm if and only if it is learnable in the statistical query (SQ) model. Therefore, for local private learning algorithms, the similarity to learning with noise is stronger: local learning is equivalent to SQ learning, and SQ algorithms include most known noise-tolerant learning algorithms. Finally, we present a separation between the power of interactive and noninteractive local learning algorithms. Because of the equivalence to SQ learning, this result also separates adaptive and nonadaptive SQ learning.

What Can We Learn Privately

Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask: what concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in contexts where aggregate information is released about a database containing sensitive information about individuals. We demonstrate that, ignoring computational constraints, it is possible to privately agnostically learn any concept class using a sample size approximately logarithmic in the cardinality of the concept class. Therefore, almost anything learnable is learnable privately: specifically, if a concept class is learnable by a (non-private) algorithm with polynomial sample complexity and output size, then it can be learned privately using a polynomial number of samples. We also present a computationally efficient private PAC learner for the class of parity functions. Local (or randomized response) algorithms are a practical class of private algorithms that have received extensive investigation. We provide a precise characterization of local private learning algorithms. We show that a concept class is learnable by a local algorithm if and only if it is learnable in the statistical query (SQ) model. Finally, we present a separation between the power of interactive and noninteractive local learning algorithms.

Privacy is an increasingly important aspect of data publishing. Reasoning about privacy, however, is fraught with pitfalls. One of the most significant is the auxiliary information (also called external knowledge, background knowledge, or side information) that an adversary gleans from other channels such as the web, public records, or domain knowledge. This paper explores how one can reason about privacy in the face of rich, realistic sources of auxiliary information. Specifically, we investigate the effectiveness of current anonymization schemes in preserving privacy when multiple organizations independently release anonymized data about overlapping populations.1. We investigate composition attacks, in which an adversary uses independent anonymized releases to breach privacy. We explain why recently proposed models of limited auxiliary information fail to capture composition attacks. Our experiments demonstrate that even a simple instance of a composition attack can breach privacy in practice, for a large class of currently proposed techniques. The class includes k-anonymity and several recent variants.2. On a more positive note, certain randomization-based notions of privacy (such as differential privacy) provably resist composition attacks and, in fact, the use of arbitrary side information.This resistance enables "stand-alone" design of anonymization schemes, without the need for explicitly keeping track of other releases.We provide a precise formulation of this property, and prove that an important class of relaxations of differential privacy also satisfy the property. This significantly enlarges the class of protocols known to enable modular design.

/pdf/composition-attacks-and-auxiliary-information-in-data-4hv317umbc.pdf

Composition attacks and auxiliary information in data privacy

We develop algorithms for the private analysis of network data that provide accurate analysis of realistic networks while satisfying stronger privacy guarantees than those of previous work. We present several techniques for designing node differentially private algorithms, that is, algorithms whose output distribution does not change significantly when a node and all its adjacent edges are added to a graph. We also develop methodology for analyzing the accuracy of such algorithms on realistic networks.

The main idea behind our techniques is to 'project' (in one of several senses) the input graph onto the set of graphs with maximum degree below a certain threshold. We design projection operators, tailored to specific statistics that have low sensitivity and preserve information about the original statistic. These operators can be viewed as giving a fractional (low-degree) graph that is a solution to an optimization problem described as a maximum flow instance, linear program, or convex program. In addition, we derive a generic, efficient reduction that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph. This reduction is based on analyzing the smooth sensitivity of the 'naive' truncation that simply discards nodes of high degree.

/pdf/analyzing-graphs-with-node-differential-privacy-2u2dfpdfei.pdf

Analyzing graphs with node differential privacy

Privacy is an increasingly important aspect of data publishing. Reasoning about privacy, however, is fraught with pitfalls. One of the most significant is the auxiliary information (also called external knowledge, background knowledge, or side information) that an adversary gleans from other channels such as the web, public records, or domain knowledge. This paper explores how one can reason about privacy in the face of rich, realistic sources of auxiliary information. Specifically, we investigate the effectiveness of current anonymization schemes in preserving privacy when multiple organizations independently release anonymized data about overlapping populations. 1. We investigate composition attacks, in which an adversary uses independent anonymized releases to breach privacy. We explain why recently proposed models of limited auxiliary information fail to capture composition attacks. Our experiments demonstrate that even a simple instance of a composition attack can breach privacy in practice, for a large class of currently proposed techniques. The class includes k-anonymity and several recent variants. 2. On a more positive note, certain randomization-based notions of privacy (such as differential privacy) provably resist composition attacks and, in fact, the use of arbitrary side information. This resistance enables stand-alone design of anonymization schemes, without the need for explicitly keeping track of other releases. We provide a precise formulation of this property, and prove that an important class of relaxations of differential privacy also satisfy the property. This significantly enlarges the class of protocols known to enable modular design.

Shiva Prasad Kasiviswanathan

Papers

What Can We Learn Privately

What Can We Learn Privately

Composition attacks and auxiliary information in data privacy

Analyzing graphs with node differential privacy

Composition Attacks and Auxiliary Information in Data Privacy