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The sparse vector technique is a powerful differentially private primitivethat allows an analyst to check whether queries in a stream are greater orlesser than a threshold. This technique has a unique property -- the algorithmworks by adding noise with a finite variance to the queries and the threshold,and guarantees privacy that only degrades with (a) the maximum sensitivity ofany one query in stream, and (b) the number of positive answers output by thealgorithm. Recent work has developed variants of this algorithm, which we call{\em generalized private threshold testing}, and are claimed to have privacyguarantees that do not depend on the number of positive or negative answersoutput by the algorithm. These algorithms result in a significant improvementin utility over the sparse vector technique for a given privacy budget, andhave found applications in frequent itemset mining, feature selection inmachine learning and generating synthetic data.  In this paper we critically analyze the privacy properties of generalizedprivate threshold testing. We show that generalized private threshold testingdoes not satisfy \epsilon-differential privacy for any finite \epsilon. Weidentify a subtle error in the privacy analysis of this technique in priorwork. Moreover, we show an adversary can use generalized private thresholdtesting to recover counts from the datasets (especially small counts) exactlywith high accuracy, and thus can result in individuals being reidentified. Wedemonstrate our attacks empirically on real datasets.

On the Privacy Properties of Variants on the Sparse Vector Technique