Differentially Private E-Values

2025-10-21

AI Summary

This work addresses privacy leakage when using e-values for statistical inference and risk control under sensitive data scenarios. We propose the first general framework to transform any non-private e-value into a differentially private (DP) e-value, supporting arbitrary stopping times and post-hoc valid inference. Our core innovation is a bias-corrected multiplicative noise mechanism that preserves the strong statistical power of e-values under strict ε-DP guarantees, achieving asymptotic performance approaching that of the non-private counterpart. The method integrates DP mechanisms, online monitoring, conformal prediction, and hypothesis testing. Experiments on online risk monitoring, healthcare analytics, and conformal e-prediction demonstrate that our approach significantly outperforms existing DP-e-value methods—delivering both high statistical efficacy and rigorous privacy protection.

Technology Category

• Machine Learning: Privacy
• Natural Language Processing: Ethics — Bias, Fairness, Transparency & Privacy
• Computer Vision: Bias, Fairness & Privacy

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Preventing sensitive data leakage through e-values in statistical inference
• Developing differentially private e-values using biased multiplicative noise
• Maintaining statistical power while ensuring privacy across various applications

Innovation

• Novel biased multiplicative noise mechanism for privacy
• Transforms non-private e-values into differentially private
• Ensures statistical validity while maintaining strong power