---

Differentially Private Empirical Cumulative Distribution Functions

---

Abstract

Empirical cumulative distribution functions are a fundamental tool in machine learning, with applications to various domains. Making them differentially private is essential to protect individuals' confidentiality. This paper proposes strategies for computing differentially private empirical distribution functions. Although releasing complete functions incurs a higher privacy cost, it provides significantly richer information to the learner. We establish privacy guarantees using a novel privacy accounting observation that reduces the required noise variance by half compared to prior results in differential privacy under continual observation. Furthermore, we detail methods for reconstructing exploitable cumulative distribution functions from their privatized versions via monotonization techniques. Finally, we survey relevant applications and present experimental results validating our approach.