  There is an increasing demand to make data "open" to third parties, as data
sharing has great benefits in data-driven decision making. However, with a wide
variety of sensitive data collected, protecting privacy of individuals,
communities and organizations, is an essential factor in making data "open".
The approaches currently adopted by industry in releasing private data are
often ad hoc and prone to a number of attacks, including re-identification
attacks, as they do not provide adequate privacy guarantees. While differential
privacy has attracted significant interest from academia and industry by
providing rigorous and reliable privacy guarantees, the reduced utility and
inflexibility of current differentially private algorithms for data release is
a barrier to their use in real-life. This paper aims to address these two
challenges. First, we propose a novel mechanism to augment the conventional
utility of differential privacy by fusing two Laplace or geometric
distributions together. We derive closed form expressions for entropy, variance
of added noise, and absolute expectation of noise for the proposed piecewise
mixtures. Then the relevant distributions are utilised to theoretically prove
the privacy and accuracy guarantees of the proposed mechanisms. Second, we show
that our proposed mechanisms have greater flexibility, with three parameters to
adjust, giving better utility in bounding noise, and mitigating larger
inaccuracy, in comparison to typical one-parameter differentially private
mechanisms. We then empirically evaluate the performance of piecewise mixture
distributions with extensive simulations and with a real-world dataset for both
linear count queries and histogram queries. The empirical results show an
increase in all utility measures considered, while maintaining privacy, for the
piecewise mixture mechanisms compared to standard Laplace or geometric
mechanisms.
