Carlos Soto: Functional Gaussian Differential Privacy for Private 3D Human Faces

The problem of releasing a Gaussian Differentially Private (GDP) 3D human face is considered. The human face is a complex structure with many features and is inherently tied to one's identity. Protecting this data in a formally private way is important yet challenging, given the dimensionality of the problem. Approximate DP techniques for functional data is extended to the GDP framework. A novel representation, face radial curves, of a 3D face is further proposed as a set of functions, and then the proposed GDP functional data mechanism is utilized. To preserve the shape of the face while injecting noise, tools from shape analysis for the novel representation of the face are relied on. It is shown that the method preserves the shape of the average face and injects less noise than traditional methods for the same privacy budget. The mechanism consists of two primary components; the first is generally applicable to function value summaries (as are commonly found in nonparametric statistics or functional data analysis), while the second is general to disk-like surfaces and hence more applicable than just to human faces.