Differentially Private E-Values

TL;DR

This paper introduces a framework for converting e-values into differentially private versions, ensuring data privacy without sacrificing statistical power, demonstrated through experiments in various sensitive applications.

Contribution

The paper presents a novel biased multiplicative noise mechanism that guarantees differential privacy for e-values while maintaining their statistical validity and power.

Findings

Differentially private e-values retain strong statistical power.

The proposed method is effective across multiple real-world applications.

Asymptotic power matches that of non-private e-values.

Abstract

E-values have gained prominence as flexible tools for statistical inference and risk control, enabling anytime- and post-hoc-valid procedures under minimal assumptions. However, many real-world applications fundamentally rely on sensitive data, which can be leaked through e-values. To ensure their safe release, we propose a general framework to transform non-private e-values into differentially private ones. Towards this end, we develop a novel biased multiplicative noise mechanism that ensures our e-values remain statistically valid. We show that our differentially private e-values attain strong statistical power, and are asymptotically as powerful as their non-private counterparts. Experiments across online risk monitoring, private healthcare, and conformal e-prediction demonstrate our approach's effectiveness and illustrate its broad applicability.