  The collection of individuals' data has become commonplace in many
industries. Local differential privacy (LDP) offers a rigorous approach to
preserving privacy whereby the individual privatises their data locally,
allowing only their perturbed datum to leave their possession. LDP thus
provides a provable privacy guarantee to the individual against both
adversaries and database administrators. Existing LDP mechanisms have
successfully been applied to low-dimensional data, but in high dimensions the
privacy-inducing noise largely destroys the utility of the data. In this work,
our contributions are two-fold: first, by adapting state-of-the-art techniques
from representation learning, we introduce a novel approach to learning LDP
mechanisms. These mechanisms add noise to powerful representations on the
low-dimensional manifold underlying the data, thereby overcoming the
prohibitive noise requirements of LDP in high dimensions. Second, we introduce
a novel denoising approach for downstream model learning. The training of
performant machine learning models using collected LDP data is a common goal
for data collectors, and downstream model performance forms a proxy for the LDP
data utility. Our approach significantly outperforms current state-of-the-art
LDP mechanisms.
