Differentially Private Bayesian Programming

TL;DR

PrivInfer is a new framework that enables writing and verifying differentially private Bayesian algorithms using a probabilistic programming language with a relational type system, combining recent advances in Bayesian inference and privacy verification.

Contribution

It introduces PrivInfer, a novel expressive framework that verifies differential privacy of Bayesian programs via a relational refinement type system.

Findings

Successfully verifies privacy for multiple Bayesian inference examples

Integrates probabilistic programming with differential privacy verification

Leverages recent advances in Bayesian inference and type systems

Abstract

We present PrivInfer, an expressive framework for writing and verifying differentially private Bayesian machine learning algorithms. Programs in PrivInfer are written in a rich functional probabilistic programming language with constructs for performing Bayesian inference. Then, differential privacy of programs is established using a relational refinement type system, in which refinements on probability types are indexed by a metric on distributions. Our framework leverages recent developments in Bayesian inference, probabilistic programming languages, and in relational refinement types. We demonstrate the expressiveness of PrivInfer by verifying privacy for several examples of private Bayesian inference.