Location-dependent privacy

We study the problem of releasing private data where the severity of the privacy concerns depends on the data itself. As a working example, we focus on the problem where a user shares an approximation of her private GPS location with a location-based service under privacy constraints that depend on the population density at user's current location itself; in densely populated areas, less noise is required to preserve privacy. We formalize this notion by extending the definition of differential privacy to locally Lipschitz privacy, we establish a connection between differential privacy and the eikonal equation, and we propose a method for computing such privacy-preserving mechanisms. Specifically, this connection allows existing optimized solvers to be used for numerically building private mechanisms and provides a different view of differential privacy. Our approach is illustrated in the scenario where a user within the greater Philadelphia area privately reports her location, where the privacy concerns depend on the population density.