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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(More)
We compare the sample complexity of private learning [Kasiviswanathan et al. 2008] and sanitization [Blum et al. 2008] under pure ǫ-differential privacy [Dwork et al. TCC 2006] and approximate (ǫ, δ)-differential privacy [Dwork et al. Eurocrypt 2006]. We show that the sample complexity of these tasks under approximate differential privacy can be(More)
We prove new upper and lower bounds on the sample complexity of (&#x03B5;, &#x03B4;) differentially private algorithms for releasing approximate answers to threshold functions. A threshold function c over a totally ordered domain X evaluates to c<sub>z</sub>(y) = 1 if y &#x2264; x, and evaluates to 0 otherwise. We give the first nontrivial lower bound for(More)
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(More)
We investigate the {\em direct-sum} problem in the context of differentially private PAC learning: What is the sample complexity of solving <i>k</i> learning tasks <i>simultaneously</i> under differential privacy, and how does this cost compare to that of solving <i>k</i> learning tasks without privacy? In our setting, an individual example consists of a(More)
We present new practical local differentially private heavy hitters algorithms achieving optimal or near-optimal worst-case error and running time – TreeHist and Bitstogram. In both algorithms, server running time is Õ(n) and user running time is Õ(1), hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring O(n)(More)
A new line of work [6, 9, 15, 2] demonstrates how differential privacy [8] 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(More)