Minimax optimal goodness-of-fit testing for densities and multinomials under a local differential privacy constraint

Understand

Finding anonymization mechanisms to protect personal data is at the heart of recent machine learning research.

• Here, we consider the consequences of local differential privacy constraints on goodness-of-fit testing, i.e.
• the statistical problem assessing whether sample points are generated from a fixed density $f_0$, or not.
• The observations are kept hidden and replaced by a stochastic transformation satisfying the local differential privacy constraint.