Functional Rényi Differential Privacy for Generative Modeling

Differential privacy (DP) has emerged as a rigorous notion to quantify data privacy. Subsequently, Rényi differential privacy (RDP) has become an alternative to the ordinary DP notion in both theoretical and empirical studies, because of its convenient compositional rules and flexibility. However, most mechanisms with DP (RDP) guarantees are essentially based on randomizing a fixed, finite-dimensional vector output. In this work, following Hall et al. [12] we further extend RDP to functional outputs, where the output space can be infinite-dimensional, and develop all necessary tools, e.g.