Local differential privacy (LDP) can provide each user with strong privacy guarantees under untrusted data curators while ensuring accurate statistics derived from privatized data. Due to its powerfulness, LDP has been widely adopted to protect privacy in various tasks (e.g., heavy hitters discovery, probability estimation) and systems (e.g., Google Chrome, Apple iOS). Although @math -LDP has been proposed for many years, the more general notion of @math -LDP has only been studied in very few papers, which mainly consider mean estimation for numeric data. Besides, prior solutions achieve @math -LDP by leveraging Gaussian mechanism, which leads to low accuracy of the aggregated results. In this paper, we propose novel mechanisms that achieve @math -LDP with high utility in data analytics and machine learning. Specifically, we first design @math -LDP algorithms for collecting multi-dimensional numeric data, which can ensure higher accuracy than the optimal Gaussian mechanism while guaranteeing strong privacy for each user. Then, we investigate different local protocols for categorical attributes under @math -LDP. Furthermore, we conduct theoretical analysis on the error bound and variance of the proposed algorithms. Experimental results on real and synthetic datasets demonstrate the high data utility of our proposed algorithms on both simple data statistics and complex machine learning models.
Therefore, local differential privacy (LDP) @cite_56 @cite_11 has received considerable attention recently since it no longer assumes a trusted data curator. Specifically, each user applies LDP to protect her his local information and reports only the noisy data to an aggregator. This is in the same spirit as the classical randomized response technique @cite_46 . LDP not only provides strong privacy guarantees for each user, but also protects the aggregator from data breaches since the aggregator does not collect users' true data in the first place. Kasiviswanathan @cite_56 have precisely addressed the powerful characterization of the local private learning algorithms. Google has developed RAPPOR @cite_3 to collect user statistics for Chrome under @math -LDP with strong privacy protections and high analysis accuracy on the collected data. Afterward, Fanti @cite_7 extended RAPPOR to conduct complex joint distribution estimations.
@cite_7 @cite_3 @cite_56 @cite_46 @cite_11
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Randomized Aggregatable Privacy-Preserving Ordinal Response, or RAPPOR, is a technology for crowdsourcing statistics from end-user client software, anonymously, with strong privacy guarantees. In short, RAPPORs allow the forest of client data to be studied, without permitting the possibility of looking at individual trees. By applying randomized response in a novel manner, RAPPOR provides the mechanisms for such collection as well as for efficient, high-utility analysis of the collected data. In particular, RAPPOR permits statistics to be collected on the population of client-side strings with strong privacy guarantees for each client, and without linkability of their reports. This paper describes and motivates RAPPOR, details its differential-privacy and utility guarantees, discusses its practical deployment and properties in the face of different attack models, and, finally, gives results of its application to both synthetic and real-world data. Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask, What concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in contexts where aggregate information is released about a database containing sensitive information about individuals. Our goal is a broad understanding of the resources required for private learning in terms of samples, computation time, and interaction. We demonstrate that, ignoring computational constraints, it is possible to privately agnostically learn any concept class using a sample size approximately logarithmic in the cardinality of the concept class. Therefore, almost anything learnable is learnable privately: specifically, if a concept class is learnable by a (nonprivate) algorithm with polynomial sample complexity and output size, then it can be learned privately using a polynomial number of samples. We also present a computationally efficient private probabilistically approximately correct learner for the class of parity functions. This result dispels the similarity between learning with noise and private learning (both must be robust to small changes in inputs), since parity is thought to be very hard to learn given random classification noise. Local (or randomized response) algorithms are a practical class of private algorithms that have received extensive investigation. We provide a precise characterization of local private learning algorithms. We show that a concept class is learnable by a local algorithm if and only if it is learnable in the statistical query (SQ) model. Therefore, for local private learning algorithms, the similarity to learning with noise is stronger: local learning is equivalent to SQ learning, and SQ algorithms include most known noise-tolerant learning algorithms. Finally, we present a separation between the power of interactive and noninteractive local learning algorithms. Because of the equivalence to SQ learning, this result also separates adaptive and nonadaptive SQ learning. Abstract For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain questions. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. In this paper it is argued that such bias is potentially removable through allowing the interviewee to maintain privacy through the device of randomizing his response. A randomized response method for estimating a population proportion is presented as an example. Unbiased maximum likelihood estimates are obtained and their mean square errors are compared with the mean square errors of conventional estimates under various assumptions about the underlying population. Working under local differential privacy-a model of privacy in which data remains private even from the statistician or learner-we study the tradeoff between privacy guarantees and the utility of the resulting statistical estimators. We prove bounds on information-theoretic quantities, including mutual information and Kullback-Leibler divergence, that influence estimation rates as a function of the amount of privacy preserved. When combined with minimax techniques such as Le Cam's and Fano's methods, these inequalities allow for a precise characterization of statistical rates under local privacy constraints. In this paper, we provide a treatment of two canonical problem families: mean estimation in location family models and convex risk minimization. For these families, we provide lower and upper bounds for estimation of population quantities that match up to constant factors, giving privacy-preserving mechanisms and computationally efficient estimators that achieve the bounds.