We consider the problem of designing and analyzing differentially private algorithms that can be implemented on discrete models of computation in strict polynomial time, motivated by known attacks on floating point implementations of real-arithmetic differentially private algorithms (Mironov, CCS 2012) and the potential for timing attacks on expected polynomialtime algorithms. We use a case study the basic problem of approximating the histogram of a categorical dataset over a possibly large data universe X . The classic Laplace Mechanism (Dwork, McSherry, Nissim, Smith, TCC 2006 and J. Privacy & Confidentiality 2017) does not satisfy our requirements, as it is based on real arithmetic, and natural discrete analogues, such as the Geometric Mechanism (Ghosh, Roughgarden, Sundarajan, STOC 2009 and SICOMP 2012), take time at least linear in |X |, which can be exponential in the bit length of the input.
In this paper, we provide strict polynomial-time discrete algorithms for approximate histograms whose simultaneous accuracy (the maximum error over all bins) matches that of the Laplace Mechanism up to constant factors, while retaining the same (pure) differential privacy guarantee. One of our algorithms produces a sparse histogram as output. Its “per-bin accuracy” (the error on individual bins) is worse than that of the Laplace Mechanism by a factor of log |X |, but we prove a lower bound showing that this is necessary for any algorithm that produces a sparse histogram. A second algorithm avoids this lower bound, and matches the per-bin accuracy of the Laplace Mechanism, by producing a compact and efficiently computable representation of a dense histogram; it is based on an (n + 1)-wise independent implementation of an appropriately clamped version of the Discrete Geometric Mechanism.
A new line of work [6, 9, 15, 2] demonstrates how differential privacy  can be used as a mathematical tool for guaranteeing generalization in adaptive data analysis. Specifically, if a differentially private analysis is applied on a sample S of i.i.d. examples to select a lowsensitivity function f , then w.h.p. f (S) is close to its expectation, although f is being chosen based on the data. Very recently, Steinke and Ullman  observed that these generalization guarantees can be used for proving concentration bounds in the non-adaptive setting, where the low-sensitivity function is fixed beforehand. In particular, they obtain alternative proofs for classical concentration bounds for low-sensitivity functions, such as the Chernoff bound and McDiarmid’s Inequality. In this work, we set out to examine the situation for functions with high-sensitivity, for which differential privacy does not imply generalization guarantees under adaptive analysis. We show that differential privacy can be used to prove concentration bounds for such functions in the non-adaptive setting.
This document is a primer on differential privacy, which is a formal mathematical framework for guaranteeing privacy protection when analyzing or releasing statistical data. Recently emerging from the theoretical computer science literature, differential privacy is now in initial stages of implementation and use in various academic, industry, and government settings. Using intuitive illustrations and limited mathematical formalism, this document provides an introduction to differential privacy for non-technical practitioners, who are increasingly tasked with making decisions with respect to differential privacy as it grows more widespread in use. In particular, the examples in this document illustrate ways in which social scientists can conceptualize the guarantees provided by differential privacy with respect to the decisions they make when managing personal data about research subjects and informing them about the privacy protection they will be afforded.
Ezgi Cicek, Gilles Barthe, Marco Gaboardi, Deepak Garg, and Jan Hoffmann. 1/2017. “Relational Cost Analysis.” Symposium on the Principle of Programming Languages, ACM.Abstract
Establishing quantitative bounds on the execution cost of programs is essential in many areas of computer science such as complexity analysis, compiler optimizations, security and privacy. Techniques based on program analysis, type systems and abstract interpretation are well-studied, but methods for analyzing how the execution costs of two programs compare to each other have not received attention. Naively combining the worst and best case execution costs of the two programs does not work well in many cases because such analysis forgets the similarities between the programs or the inputs. In this work, we propose a relational cost analysis technique that is capable of establishing precise bounds on the difference in the execution cost of two programs by making use of relational properties of programs and inputs. We develop RelCost, a refinement type and effect system for a higher-order functional language with recursion and subtyping. The key novelty of our technique is the combination of relational refinements with two modes of typing—relational typing for reasoning about similar computations/inputs and unary typing for reasoning about unrelated computations/inputs. This combination allows us to analyze the execution cost difference of two programs more precisely than a naive non-relational approach. We prove our type system sound using a semantic model based on step-indexed unary and binary logical relations accounting for non-relational and relational reasoning principles with their respective costs. We demonstrate the precision and generality of our technique through examples.
Program sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in terms of metrics on the input and output spaces, requiring that an r-sensitive function map inputs that are at distance d to outputs that are at distance at most r⋅d. Program sensitivity is thus an analogue of Lipschitz continuity for programs. Reed and Pierce introduced Fuzz, a functional language with a linear type system that can express program sensitivity. They show soundness operationally, in the form of a metric preservation property. Inspired by their work, we study program sensitivity and metric preservation from a denotational point of view. In particular, we introduce metric CPOs, a novel semantic structure for reasoning about computation on metric spaces, by endowing CPOs with a compatible notion of distance. This structure is useful for reasoning about metric properties of programs, and specifically about program sensitivity. We demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.
We show a new lower bound on the sample complexity of (ε, δ)-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally on the parameter δ, which loosely corresponds to the probability that the algorithm fails to be private, and is the first to smoothly interpolate between approximate differential privacy (δ > 0) and pure differential privacy (δ = 0).
When it is ethical and legal to use a sensitive attribute (such as gender or race) in machine learning systems, the question remains how to do so. We show that the naive application of machine learning algorithms using sensitive features leads to an inherent tradeoff in accuracy between groups. We provide a simple and efficient decoupling technique, that can be added on top of any black-box machine learning algorithm, to learn different classifiers for different groups. Transfer learning is used to mitigate the problem of having too little data on any one group.
The method can apply to a range of fairness criteria. In particular, we require the application designer to specify as joint loss function that makes explicit the trade-off between fairness and accuracy. Our reduction is shown to efficiently find the minimum loss as long as the objective has a certain natural monotonicity property which may be of independent interest in the study of fairness in algorithms.
Many data summarization applications are captured by the general framework of submodular maximization. As a consequence, a wide range of efficient approximation algorithms have been developed. However, when such applications involve sensitive data about individuals, their privacy concerns are not automatically addressed. To remedy this problem, we propose a general and systematic study of differentially private submodular maximization. We present privacy-preserving algorithms for both monotone and non-monotone submodular maximization under cardinality, matroid, and p-extendible system constraints, with guarantees that are competitive with optimal. Along the way, we analyze a new algorithm for non-monotone submodular maximization, which is the first (even non-privately) to achieve a constant approximation ratio while running in linear time. We additionally provide two concrete experiments to validate the efficacy of these algorithms.
Privacy-preserving statistical data analysis addresses the general question of protecting privacy when publicly releasing information about a sensitive dataset. A privacy attack takes seemingly innocuous released information and uses it to discern the private details of individuals, thus demonstrating that such information compromises privacy. For example, re-identification attacks have shown that it is easy to link supposedly de-identified records to the identity of the individual concerned. This survey focuses on attacking aggregate data, such as statistics about how many individuals have a certain disease, genetic trait, or combination thereof. We consider two types of attacks: reconstruction attacks, which approximately determine a sensitive feature of all the individuals covered by the dataset, and tracing attacks, which determine whether or not a target individual's data are included in the dataset.Wealso discuss techniques from the differential privacy literature for releasing approximate aggregate statistics while provably thwarting any privacy attack.
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showing that our the parameters are optimal up to polylogarithmic factors.
Federal government statistics provide critical information to the country and serve a key role in a democracy. For decades, sample surveys with instruments carefully designed for particular data needs have been one of the primary methods for collecting data for federal statistics. However, the costs of conducting such surveys have been increasing while response rates have been declining, and many surveys are not able to fulfill growing demands for more timely information and for more detailed information at state and local levels.
We consider the problem of answering queries about a sensitive dataset subject to differential privacy. The queries may be chosen adversarially from a larger set Q of allowable queries in one of three ways, which we list in order from easiest to hardest to answer:
• Offline: The queries are chosen all at once and the differentially private mechanism answers the queries in a single batch.
• Online: The queries are chosen all at once, but the mechanism only receives the queries in a streaming fashion and must answer each query before seeing the next query.
• Adaptive: The queries are chosen one at a time and the mechanism must answer each query before the next query is chosen. In particular, each query may depend on the answers given to previous queries.
Many differentially private mechanisms are just as efficient in the adaptive model as they are in the offline model. Meanwhile, most lower bounds for differential privacy hold in the offline setting. This suggests that the three models may be equivalent. We prove that these models are all, in fact, distinct. Specifically, we show that there is a family of statistical queries such that exponentially more queries from this family can be answered in the offline model than in the online model. We also exhibit a family of search queries such that exponentially more queries from this family can be answered in the online model than in the adaptive model. We also investigate whether such separations might hold for simple queries like threshold queries over the real line.
We apply Tags, a framework for modeling data handling policies, to a welfare policy. The generated model is useful for assessing entitlements of specific cases, and for gaining insights into the modeled policy as a whole.