Differentially Private E-Values

Daniel Csillag, Diego Mesquita

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 applications fundamentally rely on sensitive data, which can be leaked through e-values. To ensure their safe release, we propose a general framework for differentially private e-values that transforms any non-private e-value into a differentially private one. Towards this end, we develop a novel biased multiplicative noise mechanism that ensures our differentially private 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 broad applicability.

Submission Number: 863