TY - JOUR

T1 - The Sparse Vector Technique, Revisited

AU - Kaplan, Haim

AU - Mansour, Yishay

AU - Stemmer, Uri

N1 - Publisher Copyright:
© 2021 H. Kaplan, Y. Mansour & U. Stemmer.

PY - 2021

Y1 - 2021

N2 - We revisit one of the most basic and widely applicable techniques in the literature of differential privacy – the sparse vector technique [Dwork et al., STOC 2009]. This simple algorithm privately tests whether the value of a given query on a database is close to what we expect it to be. It allows to ask an unbounded number of queries as long as the answer is close to what we expect, and halts following the first query for which this is not the case. We suggest an alternative, equally simple, algorithm that can continue testing queries as long as any single individual does not contribute to the answer of too many queries whose answer deviates substantially form what we expect. Our analysis is subtle and some of its ingredients may be more widely applicable. In some cases our new algorithm allows to privately extract much more information from the database than the original. We demonstrate this by applying our algorithm to the shifting heavy-hitters problem: On every time step, each of n users gets a new input, and the task is to privately identify all the current heavy-hitters. That is, on time step i, the goal is to identify all data elements x such that many of the users have x as their current input. We present an algorithm for this problem with improved error guarantees over what can be obtained using existing techniques. Specifically, the error of our algorithm depends on the maximal number of times that a single user holds a heavy-hitter as input, rather than the total number of times in which a heavy-hitter exists.

AB - We revisit one of the most basic and widely applicable techniques in the literature of differential privacy – the sparse vector technique [Dwork et al., STOC 2009]. This simple algorithm privately tests whether the value of a given query on a database is close to what we expect it to be. It allows to ask an unbounded number of queries as long as the answer is close to what we expect, and halts following the first query for which this is not the case. We suggest an alternative, equally simple, algorithm that can continue testing queries as long as any single individual does not contribute to the answer of too many queries whose answer deviates substantially form what we expect. Our analysis is subtle and some of its ingredients may be more widely applicable. In some cases our new algorithm allows to privately extract much more information from the database than the original. We demonstrate this by applying our algorithm to the shifting heavy-hitters problem: On every time step, each of n users gets a new input, and the task is to privately identify all the current heavy-hitters. That is, on time step i, the goal is to identify all data elements x such that many of the users have x as their current input. We present an algorithm for this problem with improved error guarantees over what can be obtained using existing techniques. Specifically, the error of our algorithm depends on the maximal number of times that a single user holds a heavy-hitter as input, rather than the total number of times in which a heavy-hitter exists.

KW - Differential privacy

KW - heavy hitters

KW - sparse vector

UR - http://www.scopus.com/inward/record.url?scp=85162673976&partnerID=8YFLogxK

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AN - SCOPUS:85162673976

SN - 2640-3498

VL - 134

SP - 2747

EP - 2776

JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 34th Conference on Learning Theory, COLT 2021

Y2 - 15 August 2021 through 19 August 2021

ER -