Private Center Points and Learning of Halfspaces

Amos Beimel, Shay Moran, Kobbi Nissim, Uri Stemmer

Research output: Contribution to journalConference articlepeer-review

19 Scopus citations

Abstract

We present a private agnostic learner for halfspaces over an arbitrary finite domain X ⊂ Rd with sample complexity poly(d, 2log∗ |X|). The building block for this learner is a differentially private algorithm for locating an approximate center point of m > poly(d, 2log∗ |X|) points – a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al. FOCS’15]. This relationship suggests that the problem of privately locating a center point may have further applications in the design of differentially private algorithms. We also provide a lower bound on the sample complexity for privately finding a point in the convex hull. For approximate differential privacy, we show a lower bound of m = Ω(d+ log |X|), whereas for pure differential privacy m = Ω(d log |X|).

Original languageEnglish
Pages (from-to)269-282
Number of pages14
JournalProceedings of Machine Learning Research
Volume99
StatePublished - 2019
Externally publishedYes
Event32nd Conference on Learning Theory, COLT 2019 - Phoenix, United States
Duration: 25 Jun 201928 Jun 2019

Funding

FundersFunder number
National Science FoundationCCF-1412958, 1565387
Simons Foundation
Israel Science Foundation152/17

    Keywords

    • Differential privacy
    • Halfspaces
    • Private PAC learning
    • Quasi-concave functions

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