In response to calls for open data and growing privacy threats, organizations are increasingly adopting privacy-preserving techniques that add noise to published datasets. These techniques seek to protect privacy of data subjects while enabling useful analyses. With expert feedback, we developed empirically-driven documentation explaining the noise characteristics of two Wikipedia pageview datasets: one using rounding (heuristic privacy) and another using differential privacy (DP, formal privacy). We then used these documents to conduct a task-based contextual inquiry (n=15) exploring how data users—largely unfamiliar with these methods—perceive, interact with, and interpret privacy-preserving noise during data analysis.

We study a \emph{max-risk} objective for active learning in $d$-armed bandits: a learner adaptively allocates a budget of $T$ samples across $d$ groups to minimize the worst-case per-group uncertainty index $\max_{k\in[d]}\sigma_k^2/n_k$. We develop a local minimax framework and prove the first general lower bound for this objective, valid for any finite-variance hypothesis class $\mathcal H$. The bound separates difficulty into three orthogonal factors: a \emph{budget} term, a \emph{heteroscedasticity} index measuring how unevenly the uncertainty is spread across arms, and a model-dependent curvature functional, the \emph{Variance Local Curvature} ($\mathrm{VLC}$), which captures how much information a local change of variance creates inside $\mathcal H$. For smooth classes, the $\mathrm{VLC}$ is a reparametrization of a variance–Fisher information, with closed-form values for common families. Benchmarking against the strongest available upper bound shows near-optimality up to logarithmic factors in broad regimes, and pinpoints a systematic gap in highly heterogeneous instances. Our proof introduces two key ingredients: a loss-induced $\ell_1$ geometry on the decision space, and a representation-based instance generator that reduces hard-instance construction to an explicit random matrix calculation.

In causal inference with observational studies, synthetic control (SC) has emerged as a prominent tool. SC has traditionally been applied to aggregate-level datasets, but more recent work has extended its use to individual-level data. As they contain a greater number of observed units, this shift introduces the curse of dimensionality to SC. To address this, we propose Cluster Synthetic Control (ClusterSC), based on the idea that groups of individuals may exist where behavior aligns internally but diverges between groups. ClusterSC incorporates a clustering step to select only the relevant donors for the target. We provide theoretical guarantees on the improvements induced by ClusterSC, supported by empirical demonstrations on synthetic and real-world datasets. The results indicate that ClusterSC consistently outperforms classical SC approaches.

The *turnstile* continual release model of differential privacy captures scenarios where a privacy-preserving real-time analysis is sought for a dataset evolving through additions and deletions. In typical applications of real-time data analysis, both the length of the stream $T$ and the size of the universe $|\mathcal{U}|$ from which data come can be extremely large. This motivates the study of private algorithms in the turnstile setting using space sublinear in both $T$ and $|\mathcal{U}|$. In this paper, we give the first sublinear space differentially private algorithms for the fundamental problems of counting distinct elements in the turnstile streaming model. Our algorithm achieves, on arbitrary streams, $O_{\eta}(T^{1/3})$ space and additive error, and a $(1+\eta)$-relative approximation for all $\eta \in (0,1)$. Our result significantly improves upon the space requirements of the state-of-the-art algorithms for this problem, which is linear, approaching the known $\Omega(T^{1/4})$ additive error lower bound for arbitrary streams. Moreover, when a bound $W$ on the number of times an item appears in the stream is known, our algorithm provides $O_{\eta}(\sqrt{W})$ additive error, using $O_{\eta}(\sqrt{W})$ space. This additive error asymptotically matches that of prior work which required instead linear space. Our results address an open question posed by Jain et al. about designing low-memory mechanisms for this problem. We complement this results with a space lower bound for this problem, which shows that any algorithm that uses similar techniques must use space $\Omega(T^{1/3})$.

Imbalanced learning occurs in classification settings where the distribution of class-labels is highly skewed in the training data, such as when predicting rare diseases or in fraud detection. This class imbalance presents a significant algorithmic challenge, which can be further exacerbated when privacy-preserving techniques such as differential privacy are applied to protect sensitive training data. Our work formalizes these challenges and provides a number of algorithmic solutions. We consider DP variants of pre-processing methods that privately augment the original dataset to reduce the class imbalance, alongside DP variants of in-processing techniques, which adjust the learning algorithm to account for the imbalance. For each method, we either adapt an existing imbalanced learning technique to the private setting or demonstrate its incompatibility with differential privacy. Finally, we empirically evaluate these privacy-preserving imbalanced learning methods under various data and distributional settings. We find that private synthetic data methods perform well as a data pre-processing step, while class-weighted ERMs are an alternative in higher-dimensional settings where private synthetic data suffers from the curse of dimensionality.

Differential privacy is a popular privacy-enhancing technology that has been deployed both by industry and government agencies. Unfortunately, existing explanations of differential privacy fail to set accurate privacy expectations for data subjects, which depend on the choice of deployment model. We design and evaluate new explanations of differential privacy for the local and central models, drawing inspiration from prior work explaining other privacy-enhancing technologies such as encryption. We reflect on the challenges in evaluating explanations and on the tradeoffs between qualitative and quantitative evaluation strategies. These reflections offer guidance for other researchers seeking to design and evaluate explanations of privacy-enhancing technologies.

In this work we first show that the classical Thompson sampling algorithm for multi-arm bandits is differentially private as-is, without any modification. We provide per-round privacy guarantees as a function of problem parameters and show composition over $T$ rounds; since the algorithm is unchanged, existing $O(\sqrt{NT\log N})$ regret bounds still hold and there is no loss in performance due to privacy. We then show that simple modifications – such as pre-pulling all arms a fixed number of times, increasing the sampling variance – can provide tighter privacy guarantees. We again provide privacy guarantees that now depend on the new parameters introduced in the modification, which allows the analyst to tune the privacy guarantee as desired. We also provide a novel regret analysis for this new algorithm, and show how the new parameters also impact expected regret. Finally, we empirically validate and illustrate our theoretical findings in two parameter regimes and demonstrate that tuning the new parameters substantially improve the privacy-regret tradeoff.

Synthetic control is a causal inference tool used to estimate the treatment effects of an intervention by creating synthetic counterfactual data. This approach combines measurements from other similar observations (i.e., donor pool) to predict a counterfactual time series of interest (i.e., target unit) by analyzing the relationship between the target and the donor pool before the intervention. As synthetic control tools are increasingly applied to sensitive or proprietary data, formal privacy protections are often required. In this work, we suggest the first algorithms for differentially private synthetic control with explicit error bounds based on the analysis of the sensitivity of the synthetic control query. Our approach builds upon tools from non-private synthetic control and differentially private empirical risk minimization. We empirically evaluate the performance of our algorithms and show favorable results in a variety of parameter regimes.

We consider a fundamental problem where there are multiple groups whose data distributions are unknown, and an analyst would like to learn the mean of each group. We consider an active learning framework to sequentially collect $T$ samples with bandit, each period observing a sample from a chosen group. After observing a sample, the analyst may update their estimate of the mean and variance of that group and choose the next group accordingly. The objective is to dynamically collect samples to minimize the $p$-norm of the vector of variances of our mean estimators after $T$ rounds. We propose an algorithm, Variance-UCB, that selects groups according to a an upper bound on the variance estimate adjusted to the $p$-norm chosen. We show that the regret of Variance-UCB is $O(T^{-2})$ for finite $p$, and prove that no algorithm can do better. When $p$ is infinite, we recover the $O(T^{-1.5})$ obtained in \cite{activelearning, carpentier2011upper} and provide a new lower bound showing that no algorithm can do better.

We propose and initiate the study of privacy elasticity---the responsiveness of economic variables to small changes in the level of privacy given to participants in an economic system. Individuals rarely experience either full privacy or a complete lack of privacy; we propose to use differential privacy---a computer-science theory increasingly adopted by industry and government---as a standardized means of quantifying continuous privacy changes. The resulting privacy measure implies a privacy-elasticity notion that is portable and comparable across contexts. We demonstrate the feasibility of this approach by estimating the privacy elasticity of public-good contributions in a lab experiment.

A key challenge for decision makers when incorporating black box machine learned models into practice is being able to understand the predictions provided by these models. One set of methods proposed to address this challenge is that of training surrogate explainer models which approximate how the more complex model is computing its predictions. Explainer methods are generally classified as either local or global explainers depending on what portion of the data space they are purported to explain. The improved coverage of global explainers usually comes at the expense of explainer fidelity (i.e., how well the explainer's predictions match that of the black box model). One way of trading off the advantages of both approaches is to aggregate several local explainers into a single explainer model with improved coverage. However, the problem of aggregating these local explainers is computationally challenging, and existing methods only use heuristics to form these aggregations. In this paper, we propose a local explainer aggregation method which selects local explainers using non-convex optimization. In contrast to other heuristic methods, we use an integer optimization framework to combine local explainers into a near-global aggregate explainer. Our framework allows a decision-maker to directly tradeoff coverage and fidelity of the resulting aggregation through the parameters of the optimization problem. We also propose a novel local explainer algorithm based on information filtering. We evaluate our algorithmic framework on two healthcare datasets: the Parkinson's Progression Marker Initiative (PPMI) data set and a geriatric mobility dataset from the UCI machine learning repository. Our choice of these healthcare-related datasets is motivated by the anticipated need for explainable precision medicine. We find that our method outperforms existing local explainer aggregation methods in terms of both fidelity and coverage of classification. It also improves on fidelity over existing global explainer methods, particularly in multi-class settings, where state-of-the-art methods achieve 70% and ours achieves 90%.

The sequential hypothesis testing problem is a class of statistical analyses where the sample size is not fixed in advance. Instead, the decision-process takes in new observations sequentially to make real-time decisions for testing an alternative hypothesis against a null hypothesis until some stopping criterion is satisfied. In many common applications of sequential hypothesis testing, the data can be highly sensitive and may require privacy protection; for example, sequential hypothesis testing is used in clinical trials, where doctors sequentially collect data from patients and must determine when to stop recruiting patients and whether the treatment is effective. The field of differential privacy has been developed to offer data analysis tools with strong privacy guarantees, and has been commonly applied to machine learning and statistical tasks. In this work, we study the sequential hypothesis testing problem under a slight variant of differential privacy, known as Renyi differential privacy. We present a new private algorithm based on Wald’s Sequential Probability Ratio Test (SPRT) that also gives strong theoretical privacy guarantees. We provide theoretical analysis on statistical performance measured by Type I and Type II error as well as the expected sample size. We also empirically validate our theoretical results on several synthetic databases, showing that our algorithms also perform well in practice. Unlike previous work in private hypothesis testing that focused only on the classical fixed sample setting, our results in the sequential setting allow a conclusion to be reached much earlier, and thus saving the cost of collecting additional samples.

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and demonstrated utility, Wasserstein distances are sensitive to outliers in the considered distributions, which hinders applicability in practice. We propose a new outlier-robust Wasserstein distance $\mathsf{W}_p^\varepsilon$ which allows for $\varepsilon$ outlier mass to be removed from each contaminated distribution. Under standard moment assumptions, $\mathsf{W}_p^\varepsilon$ is shown to be minimax optimal for robust estimation under the Huber $\varepsilon$-contamination model. Our formulation of this robust distance amounts to a highly regular optimization problem that lends itself better for analysis compared to previously considered frameworks. Leveraging this, we conduct a thorough theoretical study of $\mathsf{W}_p^\varepsilon$, encompassing robustness guarantees, characterization of optimal perturbations, regularity, duality, and statistical estimation. In particular, by decoupling the optimization variables, we arrive at a simple dual form for $\mathsf{W}_p^\varepsilon$ that can be implemented via an elementary modification to standard, duality-based OT solvers. We illustrate the virtues of our framework via applications to generative modeling with contaminated datasets.

A key challenge in many modern data analysis tasks is that user data is heterogeneous. Different users may possess vastly different numbers of data points. More importantly, it cannot be assumed that all users sample from the same underlying distribution. This is true, for example in language data, where different speech styles result in data heterogeneity. In this work we propose a simple model of heterogeneous user data that differs in both distribution and quantity of data, and we provide a method for estimating the population-level mean while preserving user-level differential privacy. We demonstrate asymptotic optimality of our estimator and also prove general lower bounds on the error achievable in our problem.

Normalizing flow models have risen as a popular solution to the problem of density estimation, enabling high-quality synthetic data generation as well as exact probability density evaluation. However, in contexts where individuals are directly associated with the training data, releasing such a model raises privacy concerns. In this work, we propose the use of normalizing flow models that provide explicit differential privacy guarantees as a novel approach to the problem of privacy-preserving density estimation. We evaluate the efficacy of our approach empirically using benchmark datasets, and we demonstrate that our method substantially outperforms previous state-of-the-art approaches. We additionally show how our algorithm can be applied to the task of differentially private anomaly detection.

In this work we consider the problem of online submodular maximization under a cardinality constraint with differential privacy (DP). A stream of T submodular functions over a common finite ground set U arrives online, and at each time-step the decision maker must choose at most k elements of U before observing the function. The decision maker obtains a profit equal to the function evaluated on the chosen set and aims to learn a sequence of sets that achieves low expected regret. In the full-information setting, we develop an $(\varepsilon,\delta)$-DP algorithm with expected (1-1/e)-regret bound of $O( \frac{k^2\log |U|\sqrt{T \log k/\delta}}{\varepsilon} )$. This algorithm contains k ordered experts that learn the best marginal increments for each item over the whole time horizon while maintaining privacy of the functions. In the bandit setting, we provide an $(\varepsilon,\delta+ O(e^{-T^{1/3}}))$-DP algorithm with expected (1-1/e)-regret bound of $O( \frac{\sqrt{\log k/\delta}}{\varepsilon} (k (|U| \log |U|)^{1/3})^2 T^{2/3} )$. One challenge for privacy in this setting is that the payoff and feedback of expert i depends on the actions taken by her i-1 predecessors. This particular type of information leakage is not covered by post-processing, and new analysis is required. Our techniques for maintaining privacy with feedforward may be of independent interest.

Despite recent widespread deployment of differential privacy, relatively little is known about what users think of differential privacy. In this work, we seek to explore users' privacy expectations related to differential privacy. Specifically, we investigate (1) whether users care about the protections afforded by differential privacy, and (2) whether they are therefore more willing to share their data with differentially private systems. Further, we attempt to understand (3) users' privacy expectations of the differentially private systems they may encounter in practice and (4) their willingness to share data in such systems. To answer these questions, we use a series of rigorously conducted surveys (n=2424).

In hypothesis testing, a \emph{false discovery} occurs when a hypothesis is incorrectly rejected due to noise in the sample. When adaptively testing multiple hypotheses, the probability of a false discovery increases as more tests are performed. Thus the problem of \emph{False Discovery Rate (FDR) control} is to find a procedure for testing multiple hypotheses that accounts for this effect in determining the set of hypotheses to reject. The goal is to minimize the number (or fraction) of false discoveries, while maintaining a high true positive rate (i.e., correct discoveries). In this work, we study False Discovery Rate (FDR) control in multiple hypothesis testing under the constraint of differential privacy for the sample. Unlike previous work in this direction, we focus on the \emph{online setting}, meaning that a decision about each hypothesis must be made immediately after the test is performed, rather than waiting for the output of all tests as in the offline setting. We provide new private algorithms based on state-of-the-art results in non-private online FDR control. Our algorithms have strong provable guarantees for privacy and statistical performance as measured by FDR and power. We also provide experimental results to demonstrate the efficacy of our algorithms in a variety of data environments.

The change-point detection problem seeks to identify distributional changes at an unknown change-point $k^*$ in a stream of data. This problem appears in many important practical settings involving personal data, including biosurveillance, fault detection, finance, signal detection, and security systems. The field of differential privacy offers data analysis tools that provide powerful worst-case privacy guarantees. We study the statistical problem of change-point detection through the lens of differential privacy. We give private algorithms for both online and offline change-point detection, analyze these algorithms theoretically, and provide empirical validation of our results.

Differential privacy is a rigorous mathematical model of privacy protection that has been the subject of deep theoretical research and also been deployed in real-world systems. This workshop aims to bring together a diverse array of researchers and practitioners to provoke stimulating discussion about the current state of differential privacy, in theory and practice. TPDP aims to be an inclusive forum that seeks to grow and diversify the differential privacy community.

The change-point detection problem seeks to identify distributional changes in streams of data. Increasingly, tools for change-point detection are applied in settings where data may be highly sensitive and formal privacy guarantees are required, such as identifying disease outbreaks based on hospital records, or IoT devices detecting activity within a home. Differential privacy has emerged as a powerful technique for enabling data analysis while preventing information leakage about individuals. Much of the prior work on change-point detection{—}including the only private algorithms for this problem{—}requires complete knowledge of the pre-change and post-change distributions, which is an unrealistic assumption for many practical applications of interest. This work develops differentially private algorithms for solving the change-point detection problem when the data distributions are unknown. Additionally, the data may be sampled from distributions that change smoothly over time, rather than fixed pre-change and post-change distributions. We apply our algorithms to detect changes in the linear trends of such data streams. Finally, we also provide experimental results to empirically validate the performance of our algorithms.

We consider a generalization of the third degree price discrimination problem studied in [4](Bergemann et al., 2015), where an intermediary between the buyer and the seller can design market segments to maximize any linear combination of consumer surplus and seller revenue. Unlike in [4], we assume that the intermediary only has partial information about the buyer's value. We consider three different models of information, with increasing order of difficulty. In the first model, we assume that the intermediary's information allows him to construct a probability distribution of the buyer's value. Next we consider the sample complexity model, where we assume that the intermediary only sees samples from this distribution. Finally, we consider a bandit online learning model, where the intermediary can only observe past purchasing decisions of the buyer, rather than her exact value. For each of these models, we present algorithms to compute optimal or near optimal market segmentation.

The sensitivity metric in differential privacy, which is informally defined as the largest marginal change in output between neighboring databases, is of substantial significance in determining the accuracy of private data analyses. Techniques for improving accuracy when the average sensitivity is much smaller than the worst-case sensitivity have been developed within the differential privacy literature, including tools such as smooth sensitivity, Sample-and-Aggregate, Propose-Test-Release, and Lipschitz extensions. In this work, we provide a new and general Sensitivity-Preprocessing framework for reducing sensitivity, where efficient application gives state-of-the-art accuracy for privately outputting the important statistical metrics median and mean when no underlying assumptions are made about the database. In particular, our framework compares favorably to smooth sensitivity for privately outputting median, in terms of both running time and accuracy. Furthermore, because our framework is a preprocessing step, it can also be complementary to smooth sensitivity and any other private mechanism, where applying both can achieve further gains in accuracy. We additionally introduce a new notion of individual sensitivity and show that it is an important metric in the variant definition of personalized differential privacy. We show that our algorithm can extend to this context and serve as a useful tool for this variant definition and its applications in markets for privacy. Given the effectiveness of our framework in these important statistical metrics, we further investigate its properties and show that: (1) Our construction is conducive to efficient implementation with strong accuracy guarantees, evidenced by an O(n) implementation for median (with presorted data), and O(n2) implementation for more complicated functions such as mean, α-trimmed mean, and variance. (2) Our construction is both NP-hard and also optimal in the general setting (3) Our construction can be extended to higher dimensions, although it incurs accuracy loss that is linear in the dimension.

In this paper we develop the first algorithms for online submodular minimization that preserve differential privacy under full information feedback and bandit feedback. Our first result is in the full information setting, where the algorithm can observe the entire function after making its decision at each time step. We give an algorithm in this setting that is $\eps$-differentially private and achieves expected regret $\tilde{O}\left(\frac{n\sqrt{T}}{\eps}\right)$ over $T$ rounds for a collection of $n$ elements. Our second result is in the bandit setting, where the algorithm can only observe the cost incurred by its chosen set, and does not have access to the entire function. This setting is significantly more challenging due to the limited information. Our algorithm using bandit feedback is $\eps$-differentially private and achieves expected regret $\tilde{O}\left(\frac{n^{3/2}T^{2/3}}{\eps}\right)$.

We study the problem of learning Bayesian-optimal revenue-maximizing auctions. The classical approach to maximizing revenue requires a known prior distribution on the demand of the bidders, although recent work has shown how to replace the knowledge of a prior distribution with a polynomial sample. However, in an online setting, when buyers can participate in multiple rounds, standard learning techniques are susceptible to \emph{strategic overfitting}: bidders can improve their long-term wellbeing by manipulating the trajectory of the learning algorithm in earlier rounds. For example, they may be able to strategically adjust their behavior in earlier rounds to achieve lower, more favorable future prices. Such non-truthful behavior can hinder learning and harm revenue. In this paper, we combine tools from differential privacy, mechanism design, and sample complexity to give a repeated auction that (1) learns bidder demand from past data, (2) is approximately revenue-optimal, and (3) strategically robust, as it incentivizes bidders to behave truthfully.

The large majority of differentially private algorithms focus on the static setting, where queries are made on an unchanging database. This is unsuitable for the myriad applications involving databases that grow over time. To address this gap in the literature, we consider the dynamic setting, in which new data arrive over time. Previous results in this setting have been limited to answering a single non-adaptive query repeatedly as the database grows. In contrast, we provide tools for richer and more adaptive analysis of growing databases. Our first contribution is a novel modification of the private multiplicative weights algorithm, which provides accurate analysis of exponentially many adaptive linear queries (an expressive query class including all counting queries) for a static database. Our modification maintains the accuracy guarantee of the static setting even as the database grows without bound. Our second contribution is a set of general results which show that many other private and accurate algorithms can be immediately extended to the dynamic setting by rerunning them at appropriate points of data growth with minimal loss of accuracy, even when data growth is unbounded.

The change-point detection problem seeks to identify distributional changes at an unknown change-point k* in a stream of data. This problem appears in many important practical settings involving personal data, including biosurveillance, fault detection, finance, signal detection, and security systems. The field of differential privacy offers data analysis tools that provide powerful worst-case privacy guarantees. We study the statistical problem of change-point problem through the lens of differential privacy. We give private algorithms for both online and offline change-point detection, analyze these algorithms theoretically, and then provide empirical validation of these results.

The traditional notion of \emphgeneralization—i.e., learning a hypothesis whose empirical error is close to its true error—is surprisingly brittle. As has recently been noted [Dwork et al. 2015], 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 \emphrobust to postprocessing and amenable to adaptive composition, and examine the relationships between them. We call the weakest such notion \emphRobust Generalization. A second, intermediate, notion is the stability guarantee known as \emphdifferential privacy. The strongest guarantee we consider we call \emphPerfect 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.

We initiate the study of a quantity that we call coordination complexity. In a distributed optimization problem, the information defining a problem instance is distributed among n parties, who need to each choose an action, which jointly will form a solution to the optimization problem. The coordination complexity represents the minimal amount of information that a centralized coordinator, who has full knowledge of the problem instance, needs to broadcast in order to coordinate the n parties to play a nearly optimal solution.

We study how privacy technologies affect user and advertiser behavior in a simple economic model of targeted advertising. In our model, a consumer first decides whether or not to buy a good, and then an advertiser chooses an advertisement to show the consumer. The consumer's value for the good is correlated with her type, which determines which ad the advertiser would prefer to show to her---and hence, the advertiser would like to use information about the consumer's purchase decision to target the ad that he shows.

We consider the design of private prediction markets, financial markets designed to elicit predictions about uncertain events without revealing too much information about market participants' actions or beliefs. Our goal is to design market mechanisms in which participants' trades or wagers influence the market's behavior in a way that leads to accurate predictions, yet no single participant has too much influence over what others are able to observe. We study the possibilities and limitations of such mechanisms using tools from differential privacy. We begin by designing a private one-shot wagering mechanism in which bettors specify a belief about the likelihood of a future event and a corresponding monetary wager. Wagers are redistributed among bettors in a way that more highly rewards those with accurate predictions. We provide a class of wagering mechanisms that are guaranteed to satisfy truthfulness, budget balance on expectation, and other desirable properties while additionally guaranteeing epsilon-joint differential privacy in the bettors' reported beliefs, and analyze the trade-off between the achievable level of privacy and the sensitivity of a bettor's payment to her own report. We then ask whether it is possible to obtain privacy in dynamic prediction markets, focusing our attention on the popular cost-function framework in which securities with payments linked to future events are bought and sold by an automated market maker. We show that under general conditions, it is impossible for such a market maker to simultaneously achieve bounded worst-case loss and epsilon-differential privacy without allowing the privacy guarantee to degrade extremely quickly as the number of trades grows, making such markets impractical in settings in which privacy is valued. We conclude by suggesting several avenues for potentially circumventing this lower bound.

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also give an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer, for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings.

We consider the problem of fitting a linear model to data held by individuals who are concerned about their privacy. Incentivizing most players to truthfully report their data to the analyst constrains our design to mechanisms that provide a privacy guarantee to the participants; we use differential privacy to model individuals’ privacy losses. This immediately poses a problem, as differentially private computation of a linear model necessarily produces a biased estimation, and existing approaches to design mechanisms to elicit data from privacy-sensitive individuals do not generalize well to biased estimators. We overcome this challenge through an appropriate design of the computation and payment scheme.

We consider the problem of a data analyst who may purchase an unbiased estimate of some statistic from multiple data providers. From each provider i, the analyst has a choice: she may purchase an estimate from that provider that has variance chosen from a finite menu of options. Each level of variance has a cost associated with it, reported (possibly strategically) by the data provider. The analyst wants to choose the minimum cost set of variance levels, one from each provider, that will let her combine her purchased estimators into an aggregate estimator that has variance at most some fixed desired level. Moreover, she wants to do so in such a way that incentivizes the data providers to truthfully report their costs to the mechanism. We give a dominant strategy truthful solution to this problem that yields an estimator that has optimal expected cost, and violates the variance constraint by at most an additive term that tends to zero as the number of data providers grows large.

We study a very general class of games — multi-dimensional aggregative games — which in particular generalize both anonymous games and weighted congestion games. For any such game that is also large , we solve the equilibrium selection problem in a strong sense. In particular, we give an efficient weak mediator : a mechanism which has only the power to listen to reported types and provide non-binding suggested actions, such that (a) it is an asymptotic Nash equilibrium for every player to truthfully report their type to the mediator, and then follow its suggested action; and (b) that when players do so, they end up coordinating on a particular asymptotic pure strategy Nash equilibrium of the induced complete information game. In fact, truthful reporting is an ex-post Nash equilibrium of the mediated game, so our solution applies even in settings of incomplete information, and even when player types are arbitrary or worst-case (i.e. not drawn from a common prior). We achieve this by giving an efficient differentially private algorithm for computing a Nash equilibrium in such games. The rates of convergence to equilibrium in all of our results are inverse polynomial in the number of players n . We also apply our main results to a multi-dimensional market game. Our results can be viewed as giving, for a rich class of games, a more robust version of the Revelation Principle, in that we work with weaker informational assumptions (no common prior), yet provide a stronger solution concept (ex-post Nash versus Bayes Nash equilibrium). In comparison to previous work, our main conceptual contribution is showing that weak mediators are a game theoretic object that exist in a wide variety of games – previously, they were only known to exist in traffic routing games. We also give the first weak mediator that can implement an equilibrium optimizing a linear objective function, rather than implementing a possibly worst-case Nash equilibrium.

This paper initiates the study of the testable implications of choice data in settings where agents have privacy preferences. We adapt the standard conceptualization of consumer choice theory to a situation where the consumer is aware of, and has preferences over, the information revealed by her choices. The main message of the paper is that little can be inferred about consumers' preferences once we introduce the possibility that the consumer has concerns about privacy. This holds even when consumers' privacy preferences are assumed to be monotonic and separable. This motivates the consideration of stronger assumptions and, to that end, we introduce an additive model for privacy preferences that does have testable implications.

Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 – 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to compute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.