We consider accurately answering smooth queries while preserving differential
privacy. A query is said to be K-smooth if it is specified by a function
defined on [−1,1]d whose partial derivatives up to order K are all
bounded. We develop an ϵ-differentially private mechanism for the
class of K-smooth queries. The major advantage of the algorithm is that it
outputs a synthetic database. In real applications, a synthetic database output
is appealing. Our mechanism achieves an accuracy of O(n−2d+KK​/ϵ), and runs in polynomial time. We also
generalize the mechanism to preserve (ϵ,δ)-differential privacy
with slightly improved accuracy. Extensive experiments on benchmark datasets
demonstrate that the mechanisms have good accuracy and are efficient