- Thesis:
*Master in Mathematics*- Author:
**Moritz Holzmann**- Title:
*Minimax optimal goodness-of-fit testing for densities under a local differential privacy constraint*- Supervisors:
- Sandra Schluttenhofer and Jan JOHANNES
- Abstract:
- The protection of data privacy is a major problem aspect in machine learning research, therefore anonymization mechanisms become a widely researched field. In this document we work with local differential privacy as anonymization mechanisms. We replace the hidden real valued observations with a stochastic transformations that satisfy the local differential privacy constraint. More precise for a given density f0 we test if the variables are distributed with a given density f0 or not. The difference to normal goodness-of-fit testing is that we only have the given privacy view and the real values are hidden. In this setting we use a new testing method which estimates the quadratic distance between the densities f and f0. As results we provide a upper bound on the minimax separation rate over Besov balls. We also provide a suitable lower bound which shows the optimality of our result. In addition we quantify the cost we have to pay for the use of data privacy.
- Reference:
- J. Lam-Weil, B. Laurent and J.-M. Loubes.
*Minimax optimal goodness-of-fit testing for densities under a local differential privacy constraint.*Technical report, arXiv:2002.04254, 2020.