First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The set in question in this paper is the set of function with bounded partial derivatives up to order K. The authors' technique mimics the work of Thaler et al (ICALP 2012) only the authors decompose the queries not into regular polynomials (Chebyshev polynomials in the case of Thaler et al), but rather to trigonometric polynomial in this case. The bulk of the work is indeed to show that the abovementioned set of queries can be well-approximated by trigonometric polynomials. Having established that, adding Laplace noise to each monomial suffices to guarantee differential privacy.

Machine learning is often conducted on datasets containing sensitive information, such as medical records, commercial data, etc. The benefit of learning from such data is tremendous. But when releasing sensitive data, one must take privacy into consideration, and has to tradeoff between the accuracy and the amount of privacy loss of the individuals in the database. In this paper we study differential privacy [11], which has become a standard concept of privacy. Differential privacy guarantees that almost nothing new can be learned from the database that contains one specific individual's information compared with that from the database without that individual's information. More concretely, a mechanism which releases information about the database is said to preserve differential privacy, if the change of a single database element does not affect the probability distribution of the output significantly. Therefore differential privacy provides strong guarantees against attacks; the risk of any individual to submit her information to the database is very small.