Differentially Private Release and Learning of Threshold Functions

DSpace/Manakin Repository

Differentially Private Release and Learning of Threshold Functions

Citable link to this page


Title: Differentially Private Release and Learning of Threshold Functions
Author: Bun, Mark; Nissim, Kobbi; Stemmer, Uri; Vadhan, Salil P.

Note: Order does not necessarily reflect citation order of authors.

Citation: Bun, Mark, Kobbi Nissim, Uri Stemmer, Salil Vadhan. 2015. Differentially private release and learning of threshold functions. IEEE 56th Annual Symposium on Foundations of Computer Science: 634-649. doi:10.1109/FOCS.2015.45.
Full Text & Related Files:
Abstract: We prove new upper and lower bounds on the sample complexity of (ε, δ) differentially private algorithms for releasing approximate answers to threshold functions. A threshold function cx over a totally ordered domain X evaluates to cx(y)=1 if y ≤ x, and evaluates to 0 otherwise. We give the first nontrivial lower bound for releasing thresholds with (ε, δ) differential privacy, showing that the task is impossible over an infinite domain X, and moreover requires sample complexity n ≥ Ω(log∗ |X|), which grows with the size of the domain. Inspired by the techniques used to prove this lower bound, we give an algorithm for releasing thresholds with n ≤ 2(1+o(1)) log∗ |X| samples. This improves the previous best upper bound of 8(1+o(1)) log∗ |X| (Beimel et al., RANDOM ’13). Our sample complexity upper and lower bounds also apply to the tasks of learning distributions with respect to Kolmogorov distance and of properly PAC learning thresholds with differential privacy. The lower bound gives the first separation between the sample complexity of properly learning a concept class with (ε, δ) differential privacy and learning without privacy. For properly learning thresholds in dimensions, this lower bound extends to n ≥ Ω( · log∗ |X|). To obtain our results, we give reductions in both directions from releasing and properly learning thresholds and the simpler interior point problem. Given a database D of elements from X, the interior point problem asks for an element between the smallest and largest elements in D. We introduce new recursive constructions for bounding the sample complexity of the interior point problem, as well as further reductions and techniques for proving impossibility results for other basic problems in differential privacy.
Published Version: doi:10.1109/FOCS.2015.45
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:34614372
Downloads of this work:

Show full Dublin Core record

This item appears in the following Collection(s)


Search DASH

Advanced Search