Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model, where all questions are specified before the dataset is drawn. Recent work by Dwork et al. (STOC, 2015) and Hardt and Ullman (FOCS, 2014) initiated the formal study of this problem, and gave the first upper and lower bounds on the achievable generalization error for adaptive data analysis. Specifically, suppose there is an unknown distribution P and a set of n independent samples x is drawn from P. We seek an algorithm that, given x as input, accurately answers a sequence of adaptively chosen queries about the unknown distribution P. How many samples n must we draw from the distribution, as a function of the type of queries, the number of queries, and the desired level of accuracy? In this work we make two new contributions: (i) We give upper bounds on the number of samples n that are needed to answer statistical queries. The bounds improve and simplify the work of Dwork et al. (STOC, 2015), and have been applied in subsequent work by those authors (Science, 2015, NIPS, 2015). (ii) We prove the first upper bounds on the number of samples required to answer more general families of queries. These include arbitrary low-sensitivity queries and an important class of optimization queries. As in Dwork et al., our algorithms are based on a connection with algorithmic stability in the form of differential privacy. We extend their work by giving a quantitatively optimal, more general, and simpler proof of their main theorem that stability implies low generalization error. We also study weaker stability guarantees such as bounded KL divergence and total variation distance.
"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by giving an appropriate definition of "approximate concentrated differential privacy."
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information. Thus it is important to design statistical tests that guarantee the privacy of subjects in the data. In this work, we study hypothesis testing subject to differential privacy, specifically chi-squared tests for goodness of fit for multinomial data and independence between two categorical variables. We propose new tests for goodness of fit and independence testing that like the classical versions can be used to determine whether a given model should be rejected or not, and that additionally can ensure differential privacy. We give both Monte Carlo based hypothesis tests as well as hypothesis tests that more closely follow the classical chi-squared goodness of fit test and the Pearson chi-squared test for independence. Crucially, our tests account for the distribution of the noise that is injected to ensure privacy in determining significance. We show that these tests can be used to achieve desired significance levels, in sharp contrast to direct applications of classical tests to differentially private contingency tables which can result in wildly varying significance levels. Moreover, we study the statistical power of these tests. We empirically show that to achieve the same level of power as the classical non-private tests our new tests need only a relatively modest increase in sample size.
merging large-scale data sources hold tremendous potential for new scientific research into human biology, behaviors, and relationships. At the same time, big data research presents privacy and ethical challenges that the current regulatory framework is ill-suited to address. In light of the immense value of large-scale research data, the central question moving forward is not whether such data should be made available for research, but rather how the benefits can be captured in a way that respects fundamental principles of ethics and privacy.
In response, this Essay outlines elements of a new ethical framework for big data research. It argues that oversight should aim to provide universal coverage of human subjects research, regardless of funding source, across all stages of the information lifecycle. New definitions and standards should be developed based on a modern understanding of privacy science and the expectations of research subjects. In addition, researchers and review boards should be encouraged to incorporate systematic risk-benefit assessments and new procedural and technological solutions from the wide range of interventions that are available. Finally, oversight mechanisms and the safeguards implemented should be tailored to the intended uses, benefits, threats, harms, and vulnerabilities associated with a specific research activity.
Development of a new ethical framework with these elements should be the product of a dynamic multistakeholder process that is designed to capture the latest scientific understanding of privacy, analytical methods, available safeguards, community and social norms, and best practices for research ethics as they evolve over time. Such a framework would support big data utilization and help harness the value of big data in a sustainable and trust-building manner.
We present a new algorithm for locating a small cluster of points with differential privacy [Dwork, McSherry, Nissim,and Smith, 2006]. Our algorithm has implications to private data exploration, clustering, and removal of outliers. Furthermore, we use it to significantly relax the requirements of the sample and aggregate technique [Nissim, Raskhodnikova,and Smith, 2007], which allows compiling of "off the shelf" (non-private) analyses into analyses that preserve differential privacy.
An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning from efficient (ϵ,δ)-differentially private PAC learning. That is, we construct a concept class that is efficiently PAC learnable, but for which every efficient learner fails to be differentially private. This answers a question of Kasiviswanathan et al. (FOCS '08, SIAM J. Comput. '11). To prove our result, we give a generic transformation from an order-revealing encryption scheme into one with strongly correct comparison, which enables the consistent comparison of ciphertexts that are not obtained as the valid encryption of any message. We believe this construction may be of independent interest.
Increasingly, governments and businesses are collecting, analyzing, and sharing detailed information about individuals over long periods of time. Vast quantities of data from new sources and novel methods for large-scale data analysis promise to yield deeper understanding of human characteristics, behavior, and relationships and advance the state of science, public policy, and innovation. At the same time, the collection and use of fine-grained personal data over time is associated with significant risks to individuals, groups, and society at large. In this article, we examine a range of longterm data collections, conducted by researchers in social science, in order to identify the characteristics of these programs that drive their unique sets of risks and benefits. We also examine the practices that have been established by social scientists to protect the privacy of data subjects in light of the challenges presented in long-term studies. We argue that many uses of big data, across academic, government, and industry settings, have characteristics similar to those of traditional long-term research studies. In this article, we discuss the lessons that can be learned from longstanding data management practices in research and potentially applied in the context of newly emerging data sources and uses.
In this paper we initiate the study of adaptive composition in differential privacy when the length of the composition, and the privacy parameters themselves can be chosen adaptively, as a function of the outcome of previously run analyses. This case is much more delicate than the setting covered by existing composition theorems, in which the algorithms themselves can be chosen adaptively, but the privacy parameters must be fixed up front. Indeed, it isn't even clear how to define differential privacy in the adaptive parameter setting. We proceed by defining two objects which cover the two main use cases of composition theorems. A privacy filter is a stopping time rule that allows an analyst to halt a computation before his pre-specified privacy budget is exceeded. A privacy odometer allows the analyst to track realized privacy loss as he goes, without needing to pre-specify a privacy budget. We show that unlike the case in which privacy parameters are fixed, in the adaptive parameter setting, these two use cases are distinct. We show that there exist privacy filters with bounds comparable (up to constants) with existing privacy composition theorems. We also give a privacy odometer that nearly matches non-adaptive private composition theorems, but is sometimes worse by a small asymptotic factor. Moreover, we show that this is inherent, and that any valid privacy odometer in the adaptive parameter setting must lose this factor, which shows a formal separation between the filter and odometer use-cases.
In the context of statistical databases, the release of accurate statistical information about the collected data often puts at risk the privacy of the individual contributors. The goal of differential privacy is to maximize the utility of a query while protecting the individual records in the database. A natural way to achieve differential privacy is to add statistical noise to the result of the query. In this context, a mechanism for releasing statistical information is thus a trade-off between utility and privacy. In order to balance these two "conflicting" requirements, privacy preserving mechanisms calibrate the added noise to the so-called sensitivity of the query, and thus a precise estimate of the sensitivity of the query is necessary to determine the amplitude of the noise to be added. In this paper, we initiate a systematic study of sensitivity of counting queries over relational databases. We first observe that the sensitivity of a Relational Algebra query with counting is not computable in general, and that while the sensitivity of Conjunctive Queries with counting is computable, it becomes unbounded as soon as the query includes a join. We then consider restricted classes of databases (databases with constraints), and study the problem of computing the sensitivity of a query given such constraints. We are able to establish bounds on the sensitivity of counting conjunctive queries over constrained databases. The kind of constraints studied here are: functional dependencies and cardinality dependencies. The latter is a natural generalization of functional dependencies that allows us to provide tight bounds on the sensitivity of counting conjunctive queries.
Differential privacy is a mathematical definition of privacy for statistical data analysis. It guarantees that any (possibly adversarial) data analyst is unable to learn too much information that is specific to an individual. Mironov et al. (CRYPTO 2009) proposed several computational relaxations of differential privacy (CDP), which relax this guarantee to hold only against computationally bounded adversaries. Their work and subsequent work showed that CDP can yield substantial accuracy improvements in various multiparty privacy problems. However, these works left open whether such improvements are possible in the traditional client-server model of data analysis. In fact, Groce, Katz and Yerukhimovich (TCC 2011) showed that, in this setting, it is impossible to take advantage of CDP for many natural statistical tasks. Our main result shows that, assuming the existence of sub-exponentially secure one-way functions and 2-message witness indistinguishable proofs (zaps) for NP, that there is in fact a computational task in the client-server model that can be efficiently performed with CDP, but is infeasible to perform with information-theoretic differential privacy.
This article summarizes research exploring various models by which governments release data to the public and the interventions in place to protect the privacy of individuals in the data. Applying concepts from the recent scientific and legal literature on privacy, the authors propose a framework for a modern privacy analysis and illustrate how governments can use the framework to select appropriate privacy controls that are calibrated to the specific benefits and risks in individual data releases.
The vast majority of social science research uses small (megabyte- or gigabyte-scale) datasets. These fixed-scale datasets are commonly downloaded to the researcher’s computer where the analysis is performed. The data can be shared, archived, and cited with well-established technologies, such as the Dataverse Project, to support the published results. The trend toward big data—including large-scale streaming data—is starting to transform research and has the potential to impact policymaking as well as our understanding of the social, economic, and political problems that affect human societies. However, big data research poses new challenges to the execution of the analysis, archiving and reuse of the data, and reproduction of the results. Downloading these datasets to a researcher’s computer is impractical, leading to analyses taking place in the cloud, and requiring unusual expertise, collaboration, and tool development. The increased amount of information in these large datasets is an advantage, but at the same time it poses an increased risk of revealing personally identifiable sensitive information. In this article, we discuss solutions to these new challenges so that the social sciences can realize the potential of big data.
We prove new upper and lower bounds on the sample complexity of (ϵ,δ) differentially private algorithms for releasing approximate answers to threshold functions. A threshold function cx over a totally ordered domain X evaluates to cx(y)=1 if y≤x, and evaluates to 0 otherwise. We give the first nontrivial lower bound for releasing thresholds with (ϵ,δ) differential privacy, showing that the task is impossible over an infinite domain X, and moreover requires sample complexity n≥Ω(log∗|X|), which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with n≤2(1+o(1))log∗|X| samples. This improves the previous best upper bound of 8(1+o(1))log∗|X| (Beimel et al., RANDOM '13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with (ϵ,δ) differential privacy and learning without privacy. For properly learning thresholds in ℓ dimensions, this lower bound extends to n≥Ω(ℓ⋅log∗|X|). To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database D of elements from X, the interior point problem asks for an element between the smallest and largest elements in D. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy.
Emerging large-scale data sources hold tremendous potential for new scientific research into human biology, behaviors, and relationships. At the same time, big data research presents privacy and ethical challenges that the current regulatory framework is ill-suited to address. In light of the immense value of large-scale research data, the central question moving forward is not whether such data should be made available for research, but rather how the benefits can be captured in a way that respects fundamental principles of ethics and privacy.
In a search task, a group of agents compete to be the first to find the solution. Each agent has different private information to incorporate into its search. This problem is inspired by settings such as scientific research, Bitcoin hash inversion, or hunting for some buried treasure. A social planner such as a funding agency, mining pool, or pirate captain might like to convince the agents to collaborate, share their information, and greatly reduce the cost of searching. However, this cooperation is in tension with the individuals' competitive desire to each be the first to win the search. The planner's proposal should incentivize truthful information sharing, reduce the total cost of searching, and satisfy fairness properties that preserve the spirit of the competition. We design contract-based mechanisms for information sharing without money. The planner solicits the agents' information and assigns search locations to the agents, who may then search only within their assignments. Truthful reporting of information to the mechanism maximizes an agent's chance to win the search. Epsilon-voluntary participation is satisfied for large search spaces. In order to formalize the planner's goals of fairness and reduced search cost, we propose a simplified, simulated game as a benchmark and quantify fairness and search cost relative to this benchmark scenario. The game is also used to implement our mechanisms. Finally, we extend to the case where coalitions of agents may participate in the mechanism, forming larger coalitions recursively.
We propose graph encryption schemes that efficiently support approximate shortest distance queries on large-scale encrypted graphs. Shortest distance queries are one of the most fundamental graph operations and have a wide range of applications. Using such graph encryption schemes, a client can outsource large-scale privacy-sensitive graphs to an untrusted server without losing the ability to query it. Other applications include encrypted graph databases and controlled disclosure systems. We propose GRECS (stands for GRaph EnCryption for approximate Shortest distance queries) which includes three schemes that are provably secure against any semi-honest server. Our first construction makes use of only symmetric-key operations, resulting in a computationally-efficient construction. Our second scheme, makes use of somewhat-homomorphic encryption and is less computationally-efficient but achieves optimal communication complexity (i.e., uses a minimal amount of bandwidth). Finally, our third scheme is both computationally-efficient and achieves optimal communication complexity at the cost of a small amount of additional leakage. We implemented and evaluated the efficiency of our constructions experimentally. The experiments demonstrate that our schemes are efficient and can be applied to graphs that scale up to 1.6 million nodes and 11 million edges.
On September 24-25, 2013, the Privacy Tools for Sharing Research Data project at Harvard University held a workshop titled "Integrating Approaches to Privacy across the Research Data Lifecycle." Over forty leading experts in computer science, statistics, law, policy, and social science research convened to discuss the state of the art in data privacy research. The resulting conversations centered on the emerging tools and approaches from the participants’ various disciplines and how they should be integrated in the context of real-world use cases that involve the management of confidential research data.
Researchers are increasingly obtaining data from social networking websites, publicly-placed sensors, government records and other public sources. Much of this information appears public, at least to first impressions, and it is capable of being used in research for a wide variety of purposes with seemingly minimal legal restrictions. The insights about human behaviors we may gain from research that uses this data are promising. However, members of the research community are questioning the ethics of these practices, and at the heart of the matter are some difficult questions about the boundaries between public and private information. This workshop report, the second in a series, identifies selected questions and explores issues around the meaning of “public” in the context of using data about individuals for research purposes.
We show an essentially tight bound on the number of adaptively chosen statistical queries that a computationally efficient algorithm can answer accurately given n samples from an unknown distribution. A statistical query asks for the expectation of a predicate over the underlying distribution, and an answer to a statistical query is accurate if it is “close” to the correct expectation over the distribution. This question was recently studied by Dwork et al. (2015), who showed how to answer Ω( ˜ n 2 ) queries efficiently, and also by Hardt and Ullman (2014), who showed that answering O˜(n 3 ) queries is hard. We close the gap between the two bounds and show that, under a standard hardness assumption, there is no computationally efficient algorithm that, given n samples from an unknown distribution, can give valid answers to O(n 2 ) adaptively chosen statistical queries. An implication of our results is that computationally efficient algorithms for answering arbitrary, adaptively chosen statistical queries may as well be differentially private. We obtain our results using a new connection between the problem of answering adaptively chosen statistical queries and a combinatorial object called an interactive fingerprinting code Fiat and Tassa (2001). In order to optimize our hardness result, we give a new Fourier-analytic approach to analyzing fingerprinting codes that is simpler, more flexible, and yields better parameters than previous constructions.