Bounds on the Sample Complexity for Private Learning and Private Data Release

Learning is a task that generalizes many of the analyses that are applied to collections of data, and in particular, collections of sensitive individual information. Hence, it is natural to ask what can be learned while preserving individual privacy. [Kasiviswanathan, Lee, Nissim, Raskhodnikova, and Smith; FOCS 2008] initiated such a discussion. They formalized the notion of private learning, as a combination of PAC learning and differential privacy, and investigated what concept classes can be learned privately. Somewhat surprisingly, they showed that, ignoring time complexity, every PAC learning task could be performed privately with polynomially many samples, and in many natural cases this could even be done in polynomial time. While these results seem to equate non-private and private learning, there is still a significant gap: the sample complexity of (non-private) PAC learning is crisply characterized in terms of the VC-dimension of the concept class, whereas this relationship ...

• Type: Conference
• Year: 2010
• Where: TCC
• Authors: Amos Beimel, Shiva Prasad Kasiviswanathan, Kobbi Nissim
• Keywords: Cryptography, Proper Private Learners, Proper Private Learning, Sample Complexity, TCC 2010