G. Barthe, G. P. Farina, M. Gaboardi, E. J. Gallego Arias, A. D. Gordon, J. Hsu, and P.-Y. Strub. 10/2016. “Differentially Private Bayesian Programming .” 23rd ACM Conference on Computer and Communications Security, CCS.
Recently, various protocols have been proposed for securely outsourcing database storage to a third party server, ranging from systems with “full-fledged” security based on strong cryptographic primitives such as fully homomorphic encryption or oblivious RAM, to more practical implementations based on searchable symmetric encryption or even on deterministic and order-preserving encryption. On the flip side, various attacks have emerged that show that for some of these protocols confidentiality of the data can be compromised, usually given certain auxiliary information. We take a step back and identify a need for a formal understanding of the inherent efficiency/privacy trade-off in outsourced database systems, independent of the details of the system. We propose abstract models that capture secure outsourced storage systems in sufficient generality, and identify two basic sources of leakage, namely access pattern and communication volume. We use our models to distinguish certain classes of outsourced database systems that have been proposed, and deduce that all of them exhibit at least one of these leakage sources. We then develop generic reconstruction attacks on any system supporting range queries where either access pattern or communication volume is leaked. These attacks are in a rather weak passive adversarial model, where the untrusted server knows only the underlying query distribution. In particular, to perform our attack the server need not have any prior knowledge about the data, and need not know any of the issued queries nor their results. Yet, the server can reconstruct the secret attribute of every record in the database after about N 4 queries, where N is the domain size. We provide a matching lower bound showing that our attacks are essentially optimal. Our reconstruction attacks using communication volume apply even to systems based on homomorphic encryption or oblivious RAM in the natural way. Finally, we provide experimental results demonstrating the efficacy of our attacks on real datasets with a variety of different features. On all these datasets, after the required number of queries our attacks successfully recovered the secret attributes of every record in at most a few seconds.
Widespread sharing of scientific datasets holds great promise for new scientific discoveries and great risks for personal privacy. Dataset handling policies play the critical role of balancing privacy risks and scientific value. We propose an extensible, formal, theoretical model for dataset handling policies. We define binary operators for policy composition and for comparing policy strictness, such that propositions like "this policy is stricter than that policy" can be formally phrased. Using this model, The policies are described in a machine-executable and human-readable way. We further present the Tags programming language and toolset, created especially for working with the proposed model. Tags allows composing interactive, friendly questionnaires which, when given a dataset, can suggest a data handling policy that follows legal and technical guidelines. Currently, creating such a policy is a manual process requiring access to legal and technical experts, which are not always available. We present some of Tags' tools, such as interview systems, visualizers, development environment, and questionnaire inspectors. Finally, we discuss methodologies for questionnaire development. Data for this paper include a questionnaire for suggesting a HIPAA compliant data handling policy, and formal description of the set of data tags proposed by the authors in a recent paper.
Differential Privacy is a theoretical framework for ensuring the privacy of individual-level data when performing statistical analysis of privacy-sensitive datasets. The goal of this tutorial is to convey the deep connections between differential privacy and a variety of other topics in computational complexity, cryptography, and theoretical computer science at large. This tutorial was written starting from notes taken during a minicourse given by the author and Kunal Talwar at the 26th McGill Invitational Workshop on Computational Complexity in February 2014, at the Bellairs Institute in Holetown, Barbados.
We provide an overview of PSI (“a Private data Sharing Interface”), a system we are devel- oping to enable researchers in the social sciences and other fields to share and explore privacy- sensitive datasets with the strong privacy protections of differential privacy.
Poster presented at Theory and Practice of Differential Privacy (TPDP 2016).
Recent work has constructed economic mechanisms that are both truthful and differentially private. In these mechanisms, privacy is treated separately from truthfulness; it is not incorporated in players’ utility functions (and doing so has been shown to lead to nontruthfulness in some cases). In this work, we propose a new, general way of modeling privacy in players’ utility functions. Specifically, we only assume that if an outcome o has the property that any report of player i would have led to o with approximately the same probability, then o has a small privacy cost to player i. We give three mechanisms that are truthful with respect to our modeling of privacy: for an election between two candidates, for a discrete version of the facility location problem, and for a general social choice problem with discrete utilities (via a VCG-like mechanism). As the number n of players increases, the social welfare achieved by our mechanisms approaches optimal (as a fraction of n).
The traditional notion of generalization---i.e., learning a hypothesis whose empirical error is close to its true error---is surprisingly brittle. As has recently been noted in [DFH+15b], even if several algorithms have this guarantee in isolation, the guarantee need not hold if the algorithms are composed adaptively. In this paper, we study three notions of generalization---increasing in strength---that are robust to postprocessing and amenable to adaptive composition, and examine the relationships between them. We call the weakest such notion Robust Generalization. A second, intermediate, notion is the stability guarantee known as differential privacy. The strongest guarantee we consider we call Perfect Generalization. We prove that every hypothesis class that is PAC learnable is also PAC learnable in a robustly generalizing fashion, with almost the same sample complexity. It was previously known that differentially private algorithms satisfy robust generalization. In this paper, we show that robust generalization is a strictly weaker concept, and that there is a learning task that can be carried out subject to robust generalization guarantees, yet cannot be carried out subject to differential privacy. We also show that perfect generalization is a strictly stronger guarantee than differential privacy, but that, nevertheless, many learning tasks can be carried out subject to the guarantees of perfect generalization.
Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly defined. Intuitively, implicit updates shrink standard stochastic gradient descent updates. The amount of shrinkage depends on the observed Fisher information matrix, which does not need to be explicitly computed; thus, implicit procedures increase stability without increasing the computational burden. Our theoretical analysis provides the first full characterization of the asymptotic behavior of both standard and implicit stochastic gradient descent-based estimators, including finite-sample error bounds. Importantly, analytical expressions for the variances of these stochastic gradient-based estimators reveal their exact loss of efficiency. We also develop new algorithms to compute implicit stochastic gradient descent-based estimators for generalized linear models, Cox proportional hazards, M-estimators, in practice, and perform extensive experiments. Our results suggest that implicit stochastic gradient descent procedures are poised to become a workhorse for approximate inference from large data sets.
"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."
Privacy preserving mechanisms such as differential privacy inject additional randomness in the form of noise in the data, beyond the sampling mechanism. Ignoring this additional noise can lead to inaccurate and invalid inferences. In this paper, we incorporate the privacy mechanism explicitly into the likelihood function by treating the original data as missing, with an end goal of estimating posterior distributions over model parameters. This leads to a principled way of performing valid statistical inference using private data, however, the corresponding likelihoods are intractable. In this paper, we derive fast and accurate variational approximations to tackle such intractable likelihoods that arise due to privacy. We focus on estimating posterior distributions of parameters of the naive Bayes log-linear model, where the sufficient statistics of this model are shared using a differentially private interface. Using a simulation study, we show that the posterior approximations outperform the naive method of ignoring the noise addition mechanism.
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.
In today’s ever evolving data ecosystem it is evident that data generated for a wide range of purposes unrelated to biomedicine possess tremendous potential value for biomedical research. Analyses of our Google searches, social media content, loyalty card points and the like are used to draw a fairly accurate picture of our health, our future health, our attitudes towards vaccination, disease outbreaks within a county and epidemic trajectories in other continents. These data sets are different from traditional biomedical data, if a biomedical purpose is the categorical variable. Yet the results their analyses yield are of serious biomedical relevance. This paper discusses important but unresolved challenges within typical biomedical data, and it explores examples of non-biomedical Big Data with high biomedical value, including the specific conundrums these engender, especially when we apply biomedical data concepts to them. It also highlights the “digital phenotype” project, illustrating the Big Data ecosystem in action and an approach believed as likely to yield biomedical and health knowledge. We argue that to address the challenges and make full use of the opportunities that Big Data offers to biomedicine, a new ethical framework taking a data ecosystem approach is urgently needed. We conclude by discussing key components, design requirements and substantive normative elements of such a framework.
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.
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.
The fields of law and computer science incorporate contrasting notions of the privacy risks associated with the analysis and release of statistical data about individuals and groups of individuals. Emerging concepts from the theoretical computer science literature provide formal mathematical models for quantifying and mitigating privacy risks, where the set of risks they take into account is much broader than the privacy risks contemplated by many privacy laws. An example of such a model is differential privacy, which provides a provable guarantee of privacy against a wide range of potential attacks, including types of attacks currently unknown or unforeseen. The subject of much theoretical investigation, new privacy technologies based on formal models have recently been making significant strides towards practical implementation. For these tools to be used with sensitive personal information, it is important to demonstrate that they satisfy relevant legal requirements for privacy protection. However, making such an argument is challenging due to the conceptual gaps between the legal and technical approaches to defining privacy. Notably, information privacy laws are generally subject to interpretation and some degree of flexibility, which creates uncertainty for the implementation of more formal approaches. This Article articulates the gaps between legal and technical approaches to privacy and presents a methodology for rigorously arguing that a technological method for privacy protection satisfies the requirements of a particular law. The proposed methodology has two main components: (i) extraction of a formal mathematical requirement of privacy based on a legal standard found in an information privacy law, and (ii) construction of a rigorous mathematical proof for establishing that a technological privacy solution satisfies the mathematical requirement derived from the law. To handle ambiguities that can lead to different interpretations of a legal standard, the methodology takes a conservative “worst-case” approach and attempts to extract a mathematical requirement that is robust to potential ambiguities. Under this approach, the mathematical proof demonstrates that a technological method satisfies a broad range of reasonable interpretations of a legal standard. The Article demonstrates the application of the proposed methodology with an example bridging between the requirements of the Family Educational Rights and Privacy Act of 1974 and differential privacy.
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.
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).