Learning Privately with Labeled and Unlabeled Examples

Amos Beimel, Kobbi Nissim, Uri Stemmer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A private learner is an algorithm that given a sample of labeled individual examples outputs a generalizing hypothesis while preserving the privacy of each individual. In 2008, Kasiviswanathan et al. (FOCS 2008) gave a generic construction of private learners, in which the sample complexity is (generally) higher than what is needed for non-private learners. This gap in the sample complexity was then further studied in several followup papers, showing that (at least in some cases) this gap is unavoidable. Moreover, those papers considered ways to overcome the gap, by relaxing either the privacy or the learning guarantees of the learner. We suggest an alternative approach, inspired by the (non-private) models of semi-supervised learning and active-learning, where the focus is on the sample complexity of labeled examples whereas unlabeled examples are of a significantly lower cost. We consider private semi-supervised learners that operate on a random sample, where only a (hopefully small) portion of this sample is labeled. The learners have no control over which of the sample elements are labeled. Our main result is that the labeled sample complexity of private learners is characterized by the VC dimension. We present two generic constructions of private semi-supervised learners. The first construction is of learners where the labeled sample complexity is proportional to the VC dimension of the concept class, however, the unlabeled sample complexity of the algorithm is as big as the representation length of domain elements. Our second construction presents a new technique for decreasing the labeled sample complexity of a given private learner, while roughly maintaining its unlabeled sample complexity. In addition, we show that in some settings the labeled sample complexity does not depend on the privacy parameters of the learner.

Original languageEnglish
Pages (from-to)177-215
Number of pages39
JournalAlgorithmica
Volume83
Issue number1
DOIs
StatePublished - Jan 2021
Externally publishedYes

Funding

FundersFunder number
Check Point Institute for Information Security
Center for Research on Computation and Society
Ministry of Science and Technology, Israel
Frankel Center for Computer Science
European Research Council
National Science Foundation1237235, 1565387
Israel Science Foundation152/17, 544/13
Horizon 2020 Framework Programme742754
International Business Machines Corporation1871/19
Harvard UniversityCNS-1237235, 276/12

    Keywords

    • Active learning
    • Differential privacy
    • PAC learning
    • Semi-supervised learning

    Fingerprint

    Dive into the research topics of 'Learning Privately with Labeled and Unlabeled Examples'. Together they form a unique fingerprint.

    Cite this