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Faster private release of marginals on small databases

Content Provider	ACM Digital Library
Author	Thaler, Justin Wan, Andrew Chandrasekaran, Karthekeyan Ullman, Jonathan
Abstract	We study the problem of answering k-way marginal queries on a database D ϵ $(\{0,1\}^{d})^{n},$ while preserving differential privacy. The answer to a k-way marginal query is the fraction of the database's records x in $\{0,1\}^{d}$ with a given value in each of a given set of up to k columns. Marginal queries enable a rich class of statistical analyses on a dataset, and designing efficient algorithms for privately answering marginal queries has been identified as an important open problem in private data analysis. For any k, we give a differentially private online algorithm that runs in time poly (n, $2^{o(d)})$ per query and answers any sequence of poly(n) many k-way marginal queries with error at most ±0.01 on every query, provided n ≥ $d^{0.51}.$ To the best of our knowledge, this is the first algorithm capable of privately answering marginal queries with a non-trivial worst-case accuracy guarantee for databases containing poly(d, k) records in time exp(o(d)). Our algorithm runs the private multiplicative weights algorithm (Hardt and Rothblum, FOCS '10) on a new approximate polynomial representation of the database. We derive our representation for the database by approximating the OR function restricted to low Hamming weight inputs using low-degree polynomials with coefficients of bounded $L_{1-norm}.$ In doing so, we show new upper and lower bounds on the degree of such polynomials, which may be of independent approximation-theoretic interest.
Starting Page	387
Ending Page	402
Page Count	16
File Format	PDF
ISBN	9781450326988
DOI	10.1145/2554797.2554833
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-01-12
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Differential privacy Approximation theory Marginal queries
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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