Date of Award
2020
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Applied Mathematics
First Advisor
Aaron L. Roth
Abstract
Differential privacy has seen remarkable success as a rigorous and practical for-
malization of data privacy in the past decade. But it also has some well known
weaknesses, lacking comprehensible interpretation and an accessible and precise
toolkit. This is due to the inappropriate (ε, δ) parametrization and the frequent
approximation in the analysis. We overcome the difficulties by
1. relaxing the traditional (ε, δ) notion to the so-called f -differential privacy
from a decision theoretic viewpoint, hencing giving it strong interpretation,
and
2. with the relaxed notion, perform exact analysis without unnecessary approx-
imation.
Miraculously, with the relaxation and exact analysis, the theory is endowed with
various algebraic structures, and enjoys a central limit theorem. The central limit
theorem highlights the role of a specific family of DP notion called Gaussian Dif-
ferential Privacy. We demonstrate the use of the tools we develop by giving an
improved analysis of the privacy guarantees of noisy stochastic gradient descent.
Recommended Citation
Dong, Jinshuo, "Gaussian Differential Privacy And Related Techniques" (2020). Publicly Accessible Penn Dissertations. 3866.
https://repository.upenn.edu/edissertations/3866