@article{e7180ccbef3b4ee4b46f2730c591df96,

title = "Characterizing the sample complexity of pure private learners",

abstract = "Kasiviswanathan et al. (FOCS 2008) defined private learning as a combination of PAC learning and differential privacy. Informally, a private learner is applied to a collection of labeled individual information and outputs a hypothesis while preserving the privacy of each individual. Kasiviswanathan et al. left open the question of characterizing the sample complexity of private learners. We give a combinatorial characterization of the sample size sufficient and necessary to learn a class of concepts under pure differential privacy. This characterization is analogous to the well known characterization of the sample complexity of non-private learning in terms of the VC dimension of the concept class. We introduce the notion of probabilistic representation of a concept class, and our new complexity measure RepDim corresponds to the size of the smallest probabilistic representation of the concept class. We show that any private learning algorithm for a concept class C with sample complexity m implies RepDim(C) = O(m), and that there exists a private learning algorithm with sample complexity m = O(RepDim(C)). We further demonstrate that a similar characterization holds for the database size needed for computing a large class of optimization problems under pure differential privacy, and also for the well studied problem of private data release.",

keywords = "Differential privacy, PAC learning, Sample complexity",

author = "Amos Beimel and Kobbi Nissim and Uri Stemmer",

note = "Publisher Copyright: {\textcopyright} 2019 Amos Beimel and Kobbi Nissim and Uri Stemmer.",

year = "2019",

month = sep,

day = "1",

language = "אנגלית",

volume = "20",

journal = "Journal of Machine Learning Research",

issn = "1532-4435",

publisher = "Microtome Publishing",

}