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.

We investigate the direct-sum problem in the context of differentially private PAC learning: What is the sample complexity of solving k learning tasks simultaneously under differential privacy, and how does this cost compare to that of solving k learning tasks without privacy? In our setting, an individual example consists of a domain element x labeled by k unknown concepts (c1,…,ck). The goal of a multi-learner is to output k hypotheses (h1,…,hk) that generalize the input examples. 
Without concern for privacy, the sample complexity needed to simultaneously learn k concepts is essentially the same as needed for learning a single concept. Under differential privacy, the basic strategy of learning each hypothesis independently yields sample complexity that grows polynomially with k. For some concept classes, we give multi-learners that require fewer samples than the basic strategy. Unfortunately, however, we also give lower bounds showing that even for very simple concept classes, the sample cost of private multi-learning must grow polynomially in k.

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).

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.

The privacy risks inherent in the release of a large number of summary statistics were illustrated by Homer et al. (PLoS Genetics, 2008), who considered the case of 1-way marginals of SNP allele frequencies obtained in a genome-wide association study: Given a large number of minor allele frequencies from a case group of individuals diagnosed with a particular disease, together with the genomic data of a single target individual and statistics from a sizable reference dataset independently drawn from the same population, an attacker can determine with high confidence whether or not the target is in the case group. In this work we describe and analyze a simple attack that succeeds even if the summary statistics are significantly distorted, whether due to measurement error or noise intentionally introduced to protect privacy. Our attack only requires that the vector of distorted summary statistics is close to the vector of true marginals in `1 norm. Moreover, the reference pool required by previous attacks can be replaced by a single sample drawn from the underlying population. The new attack, which is not specific to genomics and which handles Gaussian as well as Bernouilli data, significantly generalizes recent lower bounds on the noise needed to ensure differential privacy (Bun, Ullman, and Vadhan, STOC 2014; Steinke and Ullman, 2015), obviating the need for the attacker to control the exact distribution of the data.

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.

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.

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.

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.

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.

A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction of private learners, in which the sample complexity is (generally) higher than what is needed for non-private learners. This gap in the sample complexity was then further studied in several followup papers, showing that (at least in some cases) this gap is unavoidable. Moreover, those papers considered ways to overcome the gap, by relaxing either the privacy or the learning guarantees of the learner.
We suggest an alternative approach, inspired by the (non-private) models of semi-supervised learning and active-learning, where the focus is on the sample complexity of labeled examples whereas unlabeled examples are of a significantly lower cost. We consider private semi-supervised learners that operate on a random sample, where only a (hopefully small) portion of this sample is labeled. The learners have no control over which of the sample elements are labeled. Our main result is that the labeled sample complexity of private learners is characterized by the VC dimension.
We present two generic constructions of private semi-supervised learners. The first construction is of learners where the labeled sample complexity is proportional to the VC dimension of the concept class, however, the unlabeled sample complexity of the algorithm is as big as the representation length of domain elements. Our second construction presents a new technique for decreasing the labeled sample complexity of a given private learner, while only slightly increasing its unlabeled sample complexity. In addition, we show that in some settings the labeled sample complexity does not depend on the privacy parameters of the learner.