Variational Bayes In Private Settings (VIPS)

TL;DR

This paper presents a privacy-preserving framework for Variational Bayes that ensures differential privacy across a broad class of models, using advanced techniques to minimize noise and maintain inference accuracy.

Contribution

It introduces a general differential privacy framework for Variational Bayes applicable to many models, including non-CE models, with novel methods to reduce noise through advanced composition and subsampling.

Findings

Effective privacy-preserving variational inference demonstrated on real datasets.

Reduced noise and improved privacy guarantees using moments accountant and subsampling.

Applicable to models like LDA, logistic regression, and sigmoid belief networks.

Abstract

Many applications of Bayesian data analysis involve sensitive information, motivating methods which ensure that privacy is protected. We introduce a general privacy-preserving framework for Variational Bayes (VB), a widely used optimization-based Bayesian inference method. Our framework respects differential privacy, the gold-standard privacy criterion, and encompasses a large class of probabilistic models, called the Conjugate Exponential (CE) family. We observe that we can straightforwardly privatise VB's approximate posterior distributions for models in the CE family, by perturbing the expected sufficient statistics of the complete-data likelihood. For a broadly-used class of non-CE models, those with binomial likelihoods, we show how to bring such models into the CE family, such that inferences in the modified model resemble the private variational Bayes algorithm as closely as possible, using the Polya-Gamma data augmentation scheme. The iterative nature of variational Bayes presents a further challenge since iterations increase the amount of noise needed. We overcome this by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple VB iterations and thus significantly decreases the amount of additive noise; and (2) the privacy amplification effect of subsampling mini-batches from large-scale data in stochastic learning. We empirically demonstrate the effectiveness of our method in CE and non-CE models including latent Dirichlet allocation, Bayesian logistic regression, and sigmoid belief networks, evaluated on real-world datasets.