Differentially Private Log-Location-Scale Regression Using Functional
  Mechanism
Jiewen Sheng Xiaolei Fang
This article introduces differentially private log-location-scale (DP-LLS)
regression models, which incorporate differential privacy into LLS regression
through the functional mechanism. The proposed models are established by
injecting noise into the log-likelihood function of LLS regression for
perturbed parameter estimation. We will derive the sensitivities utilized to
determine the magnitude of the injected noise and prove that the proposed
DP-LLS models satisfy $\epsilon$-differential privacy. In addition, we will
conduct simulations and case studies to evaluate the performance of the
proposed models. The findings suggest that predictor dimension, training sample
size, and privacy budget are three key factors impacting the performance of the
proposed DP-LLS regression models. Moreover, the results indicate that a
sufficiently large training dataset is needed to simultaneously ensure decent
performance of the proposed models and achieve a satisfactory level of privacy
protection.