  The objective of differential privacy (DP) is to protect privacy by producing
an output distribution that is indistinguishable between any two neighboring
databases. However, traditional differentially private mechanisms tend to
produce unbounded outputs in order to achieve maximum disturbance range, which
is not always in line with real-world applications. Existing solutions attempt
to address this issue by employing post-processing or truncation techniques to
restrict the output results, but at the cost of introducing bias issues. In
this paper, we propose a novel differentially private mechanism which uses a
composite probability density function to generate bounded and unbiased outputs
for any numerical input data. The composition consists of an activation
function and a base function, providing users with the flexibility to define
the functions according to the DP constraints. We also develop an optimization
algorithm that enables the iterative search for the optimal hyper-parameter
setting without the need for repeated experiments, which prevents additional
privacy overhead. Furthermore, we evaluate the utility of the proposed
mechanism by assessing the variance of the composite probability density
function and introducing two alternative metrics that are simpler to compute
than variance estimation. Our extensive evaluation on three benchmark datasets
demonstrates consistent and significant improvement over the traditional
Laplace and Gaussian mechanisms. The proposed bounded and unbiased composite
differentially private mechanism will underpin the broader DP arsenal and
foster future privacy-preserving studies.
