Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Private Discrete Noise Adding Mechanism: Conditions,
  Properties and Optimization   Differential privacy is a standard framework to quantify the privacy loss in
the data anonymization process. To preserve differential privacy, a random
noise adding mechanism is widely adopted, where the trade-off between data
privacy level and data utility is of great concern. The privacy and utility
properties for the continuous noise adding mechanism have been well studied.
However, the related works are insufficient for the discrete random mechanism
on discretely distributed data, e.g., traffic data, health records. This paper
focuses on the discrete random noise adding mechanisms. We study the basic
differential privacy conditions and properties for the general discrete random
mechanisms, as well as the trade-off between data privacy and data utility.
Specifically, we derive a sufficient and necessary condition for discrete
epsilon-differential privacy and a sufficient condition for discrete (epsilon,
delta)-differential privacy, with the numerical estimation of differential
privacy parameters. These conditions can be applied to analyze the differential
privacy properties for the discrete noise adding mechanisms with various kinds
of noises. Then, with the differential privacy guarantees, we propose an
optimal discrete epsilon-differential private noise adding mechanism under the
utility-maximization framework, where the utility is characterized by the
similarity of the statistical properties between the mechanism's input and
output. For this setup, we find that the class of the discrete noise
probability distributions in the optimal mechanism is Staircase-shaped.

37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat