Biopharming

Abstract

The exponential mechanism is a general method to construct a randomized estima-tor that satisfies (ε, 0)-differential privacy. Recently, Wang et al. showed that the Gibbs posterior, which is a data-dependent probability distribution that contains the Bayesian posterior, is essentially equivalent to the exponential mechanism un-der certain boundedness conditions on the loss function. While the exponential mechanism provides a way to build an (ε, 0)-differential private algorithm, it re-quires boundedness of the loss function, which is quite stringent for some learning problems. In this paper, we focus on (ε, δ)-differential privacy of Gibbs posteriors with convex and Lipschitz loss functions. Our result extends the classical expo-nential mechanism, allowing the loss functions to have an unbounded sensitivity.