On Differentially Private Subspace Estimation Without Distributional Assumptions

Private data analysis faces a significant challenge known as the curse of dimensionality, leading to increased costs. However, many datasets possess an inherent low-dimensional structure. For instance, during optimization via gradient descent, the gradients frequently reside near a low-dimensional subspace. If the low-dimensional structure could be privately identified using a small amount of points, we could avoid paying (in terms of privacy and accuracy) for the high ambient dimension.
On the negative side, Dwork, Talwar, Thakurta, and Zhang (STOC 2014) …

analysis assumptions challenge costs cs.cr cs.ds cs.lg data data analysis datasets dimensionality gradient instance low near optimization private data small the curse of dimensionality via