K. Nissim, U. Stemmer, and S. Vadhan, “Locating a Small Cluster Privately,” in PODS 2016, ACM SIGMOD/PODS Conference, San Francisco, USA, 2016, 2016.Abstract

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.

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E. Vayena, U. Gasser, A. Wood, D. R. O'Brien, and M. Altman, “Elements of a New Ethical Framework for Big Data Research,” Washington and Lee Law Review, vol. 72, no. 3, 2016. WLULR VersionAbstract

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.

M. Bun and M. Zhandry, “Order revealing encryption and the hardness of private learning,” in Proceedings of the 12th Theory of Cryptography Conference (TCC 2016), Tel-Aviv, Israel, 2016. ArXiv VersionAbstract

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.

PDF icon BunZhandry.pdf
K. Nissim, U. Stemmer, and S. Vadhan, “Locating a Small Cluster Privately,” 2016. ArXiv VersionAbstract

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.

J. Murtagh and S. Vadhan, “The Complexity of Computing the Optimal Composition of Differential Privacy,” in Theory of Cryptography Conference (TCC 2016), 2016. ArXiv VersionAbstract

In the study of differential privacy, composition theorems (starting with the original paper of Dwork, McSherry, Nissim, and Smith (TCC'06)) bound the degradation of privacy when composing several differentially private algorithms. Kairouz, Oh, and Viswanath (ICML'15) showed how to compute the optimal bound for composing k arbitrary (ϵ,δ)-differentially private algorithms. We characterize the optimal composition for the more general case of k arbitrary (ϵ1,δ1),,(ϵk,δk)-differentially private algorithms where the privacy parameters may differ for each algorithm in the composition. We show that computing the optimal composition in general is #P-complete. Since computing optimal composition exactly is infeasible (unless FP=#P), we give an approximation algorithm that computes the composition to arbitrary accuracy in polynomial time. The algorithm is a modification of Dyer's dynamic programming approach to approximately counting solutions to knapsack problems (STOC'03).

PDF icon MurtaghVadhan.pdf
M. Altman, A. Wood, D. O'Brien, S. Vadhan, and U. Gasser, “Towards a Modern Approach to Privacy-Aware Government Data Releases,” Berkeley Technology Law Journal, vol. 30, no. 3, 2016. BTLJ VersionAbstract

Transparency is a fundamental principle of democratic governance. Making government data more widely available promises to enhance organizational transparency, improve government functions, encourage civic engagement, support the evaluation of government decisions, and ensure accountability for public institutions. Furthermore, releases of government data promote growth in the private sector, guiding investment and other commercial decisions, supporting innovation in the technology sectors, and promoting economic development and competition generally. Improving access to government data also advances the state of research and scientific knowledge, changing how researchers approach their fields of study and enabling them to ask new questions and gain better insights into human behaviors. For instance, the increased availability of large-scale datasets is advancing developments in computational social science, a field that is rapidly changing the study of humans, human behavior, and human institutions, and effectively shifting the evidence base of social science. Scientists are also developing methods to mine and model new data sources and big data, and data collected from people and institutions have proven useful in unexpected ways. In the area of public health, Google Flu Trends, which provides a useful and timely supplement to conventional flu tracking methods by analyzing routine Google queries, is a widely publicized example of the unexpected uses of data. These are, of course, just a few examples of the many benefits of open data.

PDF icon modernopendataprivacy.pdf
E. Vayena and U. Gasser, “Between Openness and Privacy in Genomics.,” PLoS Med , vol. 13, no. 1, 2016. PLoS VersionAbstract

Summary Points

  • Advancing genomic research depends on the accessing and sharing of genomic data. However, the increasing need for sharing escalates the tension between genomic privacy and openness.
  • Promoting openness while protecting privacy is a challenge that cannot be overcome only with technical solutions such as encryption and differential privacy. Although such solutions are crucial, we still need to confront some fundamental normative tensions that are intensified in the era of genomics and big data. Here are at least three:
  • The right to genomic privacy is not an absolute right. If privacy is understood as control over information or data, privacy is not about maximal levels of control, but rather about reasonable measures of control.
  • Although individual control is necessary, it is not a sufficient safeguard of privacy. Individuals’ willingness to be open about their data does not obviate responsibility for reducing privacy risks on the part of the data users.
  • Data governance models, such as data cooperatives, that enable meaningful and continuous roles of the individuals whose data are at stake hold promise for reconciling privacy and openness.
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M. Gaboardi, H. woo Lim, R. Rogers, and S. Vadhan, “Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing,” 2016. ArXiv VersionAbstract

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.

V. Karwa and A. Slavković, “Inference using noisy degrees: Differentially private $\beta$-model and synthetic graphs,” Annals of Statistics , vol. 44, no. 1, pp. 87-112, 2016. ArXiv's VersionAbstract

The β-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the β-model, and show that the MLE never exists for the degree partition β-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of β-model, and show it is consistent and asymptotically normally distributed - it achieves the same rate of convergence as the nonprivate estimator. We present an efficient algorithm for the private estimator that can be used to release synthetic graphs. Our techniques can also be used to release degree distributions and degree partitions accurately and privately, and to perform inference from noisy degrees arising from contexts other than privacy. We evaluate the proposed estimator on real graphs and compare it with a current algorithm for releasing degree distributions and find that it does significantly better. Finally, our paper addresses shortcomings of current approaches to a fundamental problem of how to perform valid statistical inference from data released by privacy mechanisms, and lays a foundational groundwork on how to achieve optimal and private statistical inference in a principled manner by modeling the privacy mechanism; these principles should be applicable to a class of models beyond the β-model.

A. Wood, et al., “Comments on the Proposed Rules to Revise the Federal Policy for the Protection of Human Subjects”. 2016. Regulations.govAbstract

Alexandra Wood, Edo Airoldi, Micah Altman, Yves-Alexandre de Montjoye, Urs Gasser, David O'Brien, and Salil Vadhan submitted comments in response to the September 2015 notice of proposed rulemaking to revise the Federal Policy for the Protection of Human Subjects. With the ability to collect and analyze massive quantities of data related to human characteristics, behaviors, and interactions, researchers are increasingly able to explore phenomena in finer detail and with greater confidence. A major challenge for realizing the full potential of these recent advances will be protecting the privacy of human subjects. Drawing from their research findings and a forthcoming article articulating a modern approach to privacy analysis, the authors offer recommendations for updating the Common Rule to reflect recent developments in the scientific understanding of privacy. The suggested revisions ultimately aim to enable wider collection, use, and sharing of research data while providing stronger privacy protection for human subjects.


Specific recommendations include:


  • Incorporating clear and consistent definitions for privacy, confidentiality, and security.

  • Providing similar levels of protection to research activities that pose similar risks.

  • Relying on standards and requirements that recognize the limitations of traditional de-identification techniques, the inadequacy of binary conceptions of “identifiable” and “publicly-available” information, and the significance of inference risks to privacy.

  • Creating a new privacy standard based not on a binary identifiability standard, but on the extent to which attributes that may be revealed or inferred depend on an individual’s data and the potential harm that may result.

  • Requiring investigators to conduct systematic privacy analyses and calibrate their use of privacy and security controls to the specific intended uses and privacy risks at every stage of the information lifecycle.

  • Addressing informational risks using a combination of privacy and security controls rather than relying on a single control such as consent or de-­identification and adopting tiered access models where appropriate.

  • Forming an advisory committee of data privacy experts to help the Secretary of Health and Human Services develop guidance on applying privacy and security controls that are closely matched to the intended uses and privacy risks in specific research activities.


The authors argue that addressing these issues will help lead researchers towards state-of-the-art privacy practices and advance the exciting research opportunities enabled by new data sources and technologies for collecting, analyzing, and sharing data about individuals.

The full comments are also available through
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Y. Chen, K. Nissim, and B. Waggoner, “Fair Information Sharing for Treasure Hunting.,” in AAI Conference on Artificial Intelligence, North America, 2015. PDF Abstract

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.

C. Dwork, A. Smith, T. Steinke, J. Ullman, and S. Vadhan, “Robust Traceability from Trace Amounts,” in IEEE Symposium on Foundations of Computer Science (FOCS 2015), Berkeley, California, 2015.PDF icon robust.pdf
M. Bun, K. Nissim, and U. Stemmer, “Simultaneous private learning of multiple concepts,” 2015.
S. Zheng, The Differential Privacy of Bayesian Inference. Bachelor's thesis, Harvard College, 2015. DASH Version
M. Bun, K. Nissim, U. Stemmer, and S. Vadhan, “Differentially Private Release and Learning of Threshold Functions,” in 56th Annual IEEE Symposium on Foundations of Computer Science (FOCS 15), Berkeley, California, 2015. ArXiv VersionAbstract

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 yx, 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 nΩ(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 n2(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 dimensions, this lower bound extends to nΩ(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.

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D. Abrams, “What Stays in Vegas: The Road to “Zero Privacy",” New England Law Review, vol. 49, no. 4, 2015. Publisher's Version
L. Sweeney, M. Crosas, and M. Bar-Sinai, “Sharing Sensitive Data with Confidence: The Datatags System,” Technology Science , 2015. Technology ScienceAbstract

Society generates data on a scale previously unimagined. Wide sharing of these data promises to improve personal health, lower healthcare costs, and provide a better quality of life. There is a tendency to want to share data freely. However, these same data often include sensitive information about people that could cause serious harms if shared widely. A multitude of regulations, laws and best practices protect data that contain sensitive personal information. Government agencies, research labs, and corporations that share data, as well as review boards and privacy officers making data sharing decisions, are vigilant but uncertain. This uncertainty creates a tendency not to share data at all. Some data are more harmful than other data; sharing should not be an all-or-nothing choice. How do we share data in ways that ensure access is commensurate with risks of harm?

O. Sheffet, “Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression,” 2015. ArXiv VersionAbstract

We introduce three differentially-private algorithms that approximates the 2nd-moment matrix of the data. These algorithm, which in contrast to existing algorithms output positive-definite matrices, correspond to existing techniques in linear regression literature. Specifically, we discuss the following three techniques. (i) For Ridge Regression, we propose setting the regularization coefficient so that by approximating the solution using Johnson-Lindenstrauss transform we preserve privacy. (ii) We show that adding a small batch of random samples to our data preserves differential privacy. (iii) We show that sampling the 2nd-moment matrix from a Bayesian posterior inverse-Wishart distribution is differentially private provided the prior is set correctly. We also evaluate our techniques experimentally and compare them to the existing "Analyze Gauss" algorithm of Dwork et al.

M. Bun and J. Thaler, “Hardness Amplification and the Approximate Degree of Constant-Depth Circuits,” International Colloquium on Automata, Languages, and Programming (ICALP 2015) BG, 2015. ArXiv VersionPDF icon hardnessamplification.pdf
A. Askarov, S. Moore, C. Dimoulas, and S. Chong, “Cryptographic Enforcement of Language-Based Erasure,” Proceedings of the 28th IEEE Computer Security Foundations Symposium (CSF), 2015.