The offline query release mechanism given in this section is from Blum et al. , which gave bounds in terms of the VC-Dimension of the query class (Theorem 4.9). The generalization to fat shattering dimension is given in .
The online query release mechanism given in this section is from Hardt and Rothblum . This mechanism uses the classic multiplica- tive weights update method, for which Arora, Hazan and Kale give an excellent survey . Slightly improved bounds for the private multi- plicative weights mechanism were given by Gupta et al. , and the analysis here follows the presentation from .