Approximate Span Liftings
arXiv:1710.09010 · doi:10.1109/LICS.2019.8785668
Abstract
We develop new abstractions for reasoning about relaxations of differential privacy: Rényi differential privacy, zero-concentrated differential privacy, and truncated concentrated differential privacy, which express different bounds on statistical divergences between two output probability distributions. In order to reason about such properties compositionally, we introduce approximate span-lifting, a novel construction extending the approximate relational lifting approaches previously developed for standard differential privacy to a more general class of divergences, and also to continuous distributions. As an application, we develop a program logic based on approximate span-liftings capable of proving relaxations of differential privacy and other statistical divergence properties.
References in corpus (8)
- Deep Learning with Differential Privacy
- Renyi Differential Privacy
- LightDP: Towards Automating Differential Privacy Proofs
- Advanced Probabilistic Couplings for Differential Privacy
- Synthesizing Coupling Proofs of Differential Privacy
- Approximate Relational Hoare Logic for Continuous Random Samplings
- Differentially Private Bayesian Programming
- Stochastic k-Server: How Should Uber Work?
Cited by in corpus (7)
- Chorus: a Programming Framework for Building Scalable Differential Privacy Mechanisms
- Duet: An Expressive Higher-order Language and Linear Type System for Statically Enforcing Differential Privacy
- Injective Objects and Fibered Codensity Liftings
- Probabilistic Relational Reasoning via Metrics
- Divergences on Monads for Relational Program Logics
- Testing Differential Privacy with Dual Interpreters
- GradInf: Gradient Estimation as Probabilistic Inference