Personal data is now collected at larger scales than ever before. Growing concerns of data subjects and regulatory demands, however, have raised issues of protecting the privacy of individuals whose data are collected and analysed. In this talk I will discuss recent work in the field of differential privacy, specifically local differential privacy (LDP), which aims to formalise the notion of privacy and data security. I will present work on the connections between this modern field and the more classical topic of robust statistics. Then, motivated by the difficulty of high-dimensional problems under LDP constraints, I will present results on the new user-level variant concerned with the common setting in which each individual holds multiple data points. Material will be taken from recent work with with Alexander Kent, Mengchu Li and Yi Yu.
