# Publications

2014
Urs Gasser, Jonathan Zittrain, Robert Faris, and Rebekah Heacock Jones. 2014. “Internet Monitor 2014: Reflections on the Digital World: Platforms, Policy, Privacy, and Public Discourse.” Social Science Research Network. SSRN VersionAbstract

This publication is the second annual report of the Internet Monitor project at the Berkman Centerfor Internet & Society at Harvard University. As with the inaugural report, this year’s edition is a collaborative effort of the extended Berkman community. Internet Monitor 2014: Reflections on the Digital World includes nearly three dozen contributions from friends and colleagues around the world that highlight and discuss some of the most compelling events and trends in the digitally networked environment over the past year.

The result, intended for a general interest audience, brings together reflection and analysis on a broad range of issues and regions — from an examination of Europe’s “right to be forgotten” to a review of the current state of mobile security to an exploration of a new wave of movements attempting to counter hate speech online — and offers it up for debate and discussion. Our goal remains not to provide a definitive assessment of the “state of the Internet” but rather to provide a rich compendium of commentary on the year’s developments with respect to the online space.

Last year’s report examined the dynamics of Internet controls and online activity through the actions of government, corporations, and civil society. We focus this year on the interplay between technological platforms and policy; growing tensions between protecting personal privacy and using big data for social good; the implications of digital communications tools for public discourse and collective action; and current debates around the future of Internet governance.

The report reflects the diversity of ideas and input the Internet Monitor project seeks to invite. Some of the contributions are descriptive; others prescriptive. Some contain purely factual observations; others offer personal opinion. In addition to those in traditional essay format, contributions this year include a speculative fiction story exploring what our increasingly data-driven world might bring, a selection of “visual thinking” illustrations that accompany a number of essays, a “Year in Review” timeline that highlights many of the year’s most fascinating Internet-related news stories (and an interactive version of which is available at the netmonitor.org), and a slightly tongue-in-cheek “By the Numbers” section that offers a look at the year’s important digital statistics. We believe that each contribution offers insights, and hope they provoke further reflection, conversation, and debate in both offline and online settings around the globe.

Michael Kearns, Mallesh Pai, Aaron Roth, and Jonathan Ullman. 2014. “Mechanism Design in Large Games: Incentives and Privacy.” In Proceedings of the 5th Conference on Innovations in Theoretical Computer Science, Pp. 403–410. New York, NY, USA: ACM. Publisher's Version
Mallesh M Pai, Aaron Roth, and Jonathan Ullman. 2014. “An Anti-Folk Theorem for Large Repeated Games with Imperfect Monitoring.” CoRR, abs/1402.2801.
Yiling Chen, Or Sheffet, and Salil Vadhan. 2014. “Privacy Games.” In 10th Conference on Web and Internet Economics (WINE). Beijing, China.
Lucas Waye. 2014. “Privacy Integrated Data Stream Queries.” In Proceedings of the 2014 International Workshop on Privacy & Security in Programming (PSP '14). New York, NY: ACM. ACM Digital Library Version
Raef Bassily, Adam Smith, and Abhradeep Thakurta. 2014. “Private Empirical Risk Minimization, Revisited.” In ICML 2014 Workshop on Learning, Security and Privacy. Beijing, China. Publisher's VersionAbstract

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point's contribution to the loss function is Lipschitz bounded and that the domain of optimization is bounded. We provide a separate set of algorithms and matching lower bounds for the setting in which the loss functions are known to also be strongly convex.

Our algorithms run in polynomial time, and in some cases even match the optimal non-private running time (as measured by oracle complexity). We give separate algorithms (and lower bounds) for (ϵ,0)- and (ϵ,δ)-differential privacy; perhaps surprisingly, the techniques used for designing optimal algorithms in the two cases are completely different.

Our lower bounds apply even to very simple, smooth function families, such as linear and quadratic functions. This implies that algorithms from previous work can be used to obtain optimal error rates, under the additional assumption that the contributions of each data point to the loss function is smooth. We show that simple approaches to smoothing arbitrary loss functions (in order to apply previous techniques) do not yield optimal error rates. In particular, optimal algorithms were not previously known for problems such as training support vector machines and the high-dimensional median.

Justin Hsu, Aaron Roth, Tim Roughgarden, Jonathan Ullman, Javier Esparza, Pierre Fraigniaud, Thore Husfeldt, and Elias Koutsoupias. 2014. “Privately Solving Linear Programs.” In Automata, Languages, and Programming, 8572: Pp. 612-624. Springer Berlin Heidelberg. Publisher's Version
Kobbi Nissim, Salil Vadhan, and David Xiao. 2014. “Redrawing the Boundaries on Purchasing Data from Privacy-sensitive Individuals.” In Proceedings of the 5th Conference on Innovations in Theoretical Computer Science, Pp. 411–422. New York, NY, USA: ACM. Publisher's Version
Vitaly Feldman and David Xiao. 2014. “Sample Complexity Bounds on Differentially Private Learning via Communication Complexity.” Proceedings of The 27th Conference on Learning Theory (COLT 2014) 35, Pp. 1-20. Barcelona, Spain: JMLR Workshop and Conference Proceedings. Publisher's VersionAbstract

In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private PAC and agnostic learning was studied in a number of prior works starting with (Kasiviswanathan et al., 2008) but a number of basic questions still remain open (Beimel et al. 2010; Chaudhuri and Hsu, 2011; Beimel et al., 2013ab).

Our main contribution is an equivalence between the sample complexity of differentially-private learning of a concept class C (or SCDP(C)) and the randomized one-way communication complexity of the evaluation problem for concepts from C. Using this equivalence we prove the following bounds:

• SCDP(C)=Ω(LDim(C)), where LDim(C) is the Littlestone's (1987) dimension characterizing the number of mistakes in the online-mistake-bound learning model. This result implies that SCDP(C) is different from the VC-dimension of C, resolving one of the main open questions from prior work.
• For any t, there exists a class C such that LDim(C)=2 but SCDP(C)t.
• For any t, there exists a class C such that the sample complexity of (pure) α-differentially private PAC learning is Ω(t/α) but the sample complexity of the relaxed (α,β)-differentially private PAC learning is O(log(1/β)/α). This resolves an open problem from (Beimel et al., 2013b).

We also obtain simpler proofs for a number of known related results. Our equivalence builds on a characterization of sample complexity by Beimel et al., (2013a) and our bounds rely on a number of known results from communication complexity.

Adam Tanner. 2014. What Stays in Vegas: The World of Personal Data -- Lifeblood of Big Business -- and the End of Privacy as We Know It., Pp. 336. New York, NY: Public Affairs. Available on AmazonAbstract

The greatest threat to privacy today is not the NSA, but good-old American companies. Internet giants, leading retailers, and other firms are voraciously gathering data with little oversight from anyone.

In Las Vegas, no company knows the value of data better than Caesars Entertainment. Many thousands of enthusiastic clients pour through the ever-open doors of their casinos. The secret to the company’s success lies in their one unrivaled asset: they know their clients intimately by tracking the activities of the overwhelming majority of gamblers. They know exactly what games they like to play, what foods they enjoy for breakfast, when they prefer to visit, who their favorite hostess might be, and exactly how to keep them coming back for more.

Caesars’ dogged data-gathering methods have been so successful that they have grown to become the world’s largest casino operator, and have inspired companies of all kinds to ramp up their own data mining in the hopes of boosting their targeted marketing efforts. Some do this themselves. Some rely on data brokers. Others clearly enter a moral gray zone that should make American consumers deeply uncomfortable.

We live in an age when our personal information is harvested and aggregated whether we like it or not. And it is growing ever more difficult for those businesses that choose not to engage in more intrusive data gathering to compete with those that do. Tanner’s timely warning resounds: Yes, there are many benefits to the free flow of all this data, but there is a dark, unregulated, and destructive netherworld as well.

2013
ShivaPrasad Kasiviswanathan, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith. 2013. “Analyzing Graphs with Node Differential Privacy.” In Theory of Cryptography, 7785: Pp. 457-476. Springer Berlin Heidelberg. Springer LinkAbstract
We develop algorithms for the private analysis of network data that provide accurate analysis of realistic networks while satisfying stronger privacy guarantees than those of previous work. We present several techniques for designing node differentially private algorithms, that is, algorithms whose output distribution does not change significantly when a node and all its adjacent edges are added to a graph. We also develop methodology for analyzing the accuracy of such algorithms on realistic networks. The main idea behind our techniques is to “project” (in one of several senses) the input graph onto the set of graphs with maximum degree below a certain threshold. We design projection operators, tailored to specific statistics that have low sensitivity and preserve information about the original statistic. These operators can be viewed as giving a fractional (low-degree) graph that is a solution to an optimization problem described as a maximum flow instance, linear program, or convex program. In addition, we derive a generic, efficient reduction that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph. This reduction is based on analyzing the smooth sensitivity of the “naive” truncation that simply discards nodes of high degree.
ShivaPrasad Kasiviswanathan, Kobbi Nissim, Sofya Raskhodnikova, and Adam Smith. 2013. “Analyzing Graphs with Node Differential Privacy.” In Proceedings of the 10th Theory of Cryptography Conference on Theory of Cryptography, Pp. 457–476. Berlin, Heidelberg: Springer-Verlag. Publisher's Version
Jonathan Ullman. 2013. “Answering n{2+o(1)} counting queries with differential privacy is hard.” In Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, Pp. 361-370. Palo Alto, California, USA: ACM. DOIAbstract
A central problem in differentially private data analysis is how to design efficient algorithms capable of answering large numbers of counting queries on a sensitive database. Counting queries are of the form "What fraction of individual records in the database satisfy the property q?" We prove that if one-way functions exist, then there is no algorithm that takes as input a database db ∈ dbset, and k = ~Θ(n2) arbitrary efficiently computable counting queries, runs in time poly(d, n), and returns an approximate answer to each query, while satisfying differential privacy. We also consider the complexity of answering "simple" counting queries, and make some progress in this direction by showing that the above result holds even when we require that the queries are computable by constant-depth (AC0) circuits. Our result is almost tight because it is known that ~Ω(n2) counting queries can be answered efficiently while satisfying differential privacy. Moreover, many more than n2 queries (even exponential in n) can be answered in exponential time. We prove our results by extending the connection between differentially private query release and cryptographic traitor-tracing schemes to the setting where the queries are given to the sanitizer as input, and by constructing a traitor-tracing scheme that is secure in this setting.
Amos Beimel, Kobbi Nissim, and Uri Stemmer. 2013. “Characterizing the Sample Complexity of Private Learners.” In Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, Pp. 97–110. New York, NY, USA: ACM. Publisher's Version
Amos Beimel, Kobbi Nissim, and Uri Stemmer. 2013. “Characterizing the sample complexity of private learners.” In Proceedings of the 4th conference on Innovations in Theoretical Computer Science, Pp. 97-110. Berkeley, California, USA: ACM. DOIAbstract
In 2008, Kasiviswanathan el al. defined private learning as a combination of PAC learning and differential privacy [16]. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while preserving the privacy of each individual. Kasiviswanathan et al. gave a generic construction of private learners for (finite) concept classes, with sample complexity logarithmic in the size of the concept class. This sample complexity is higher than what is needed for non-private learners, hence leaving open the possibility that the sample complexity of private learning may be sometimes significantly higher than that of non-private learning. We give a combinatorial characterization of the sample size sufficient and necessary to privately learn a class of concepts. This characterization is analogous to the well known characterization of the sample complexity of non-private learning in terms of the VC dimension of the concept class. We introduce the notion of probabilistic representation of a concept class, and our new complexity measure RepDim corresponds to the size of the smallest probabilistic representation of the concept class. We show that any private learning algorithm for a concept class C with sample complexity m implies RepDim(C) = O(m), and that there exists a private learning algorithm with sample complexity m = O(RepDim(C)). We further demonstrate that a similar characterization holds for the database size needed for privately computing a large class of optimization problems and also for the well studied problem of private data release.
Justin Hsu, Aaron Roth, and Jonathan Ullman. 2013. “Differential privacy for the analyst via private equilibrium computation.” In Proceedings of the 45th annual ACM symposium on Symposium on theory of computing, Pp. 341-350. Palo Alto, California, USA: ACM. DOIAbstract
We give new mechanisms for answering exponentially many queries from multiple analysts on a private database, while protecting dif- ferential privacy both for the individuals in the database and for the analysts. That is, our mechanism's answer to each query is nearly insensitive to changes in the queries asked by other analysts. Our mechanism is the first to offer differential privacy on the joint distribution over analysts' answers, providing privacy for data an- alysts even if the other data analysts collude or register multiple accounts. In some settings, we are able to achieve nearly optimal error rates (even compared to mechanisms which do not offer an- alyst privacy), and we are able to extend our techniques to handle non-linear queries. Our analysis is based on a novel view of the pri- vate query-release problem as a two-player zero-sum game, which may be of independent interest.
Latanya Sweeney. 2013. “Discrimination in online ad delivery.” Commun. ACM, 56, 5, Pp. 44–54. DOIAbstract
We study the problem of answering \emph{$k$-way marginal} queries on a database $D \in (\{0,1\}^d)^n$, while preserving differential privacy. The answer to a $k$-way marginal query is the fraction of the database's records $x \in \{0,1\}^d$ with a given value in each of a given set of up to $k$ columns. Marginal queries enable a rich class of statistical analyses on a dataset, and designing efficient algorithms for privately answering marginal queries has been identified as an important open problem in private data analysis. For any $k$, we give a differentially private online algorithm that runs in time $$\min{\exp(d^{1-\Omega(1/\sqrt{k})}), \exp(d / \log^{.99} d)\}$$ per query and answers any (possibly superpolynomially long and adaptively chosen) sequence of $k$-way marginal queries up to error at most $\pm .01$ on every query, provided $n \gtrsim d^{.51}$. To the best of our knowledge, this is the first algorithm capable of privately answering marginal queries with a non-trivial worst-case accuracy guarantee on a database of size $\poly(d, k)$ in time $\exp(o(d))$. Our algorithms are a variant of the private multiplicative weights algorithm (Hardt and Rothblum, FOCS '10), but using a different low-weight representation of the database. We derive our low-weight representation using approximations to the OR function by low-degree polynomials with coefficients of bounded $L_1$-norm. We also prove a strong limitation on our approach that is of independent approximation-theoretic interest. Specifically, we show that for any $k = o(\log d)$, any polynomial with coefficients of $L_1$-norm $poly(d)$ that pointwise approximates the $d$-variate OR function on all inputs of Hamming weight at most $k$ must have degree $d^{1-O(1/\sqrt{k})}$.