Conformal prediction (CP) has attracted broad attention as a simple and flexible framework for uncertainty quantification through prediction sets. In this work, we study how to deploy CP under differential privacy (DP) in a statistically efficient manner. We first introduce differential CP, a non-splitting conformal procedure that avoids the efficiency loss caused by data splitting and serves as a bridge between oracle CP and private conformal inference. By exploiting the stability properties of DP mechanisms, differential CP establishes a direct connection to oracle CP and inherits corresponding validity behavior. Building on this idea, we develop Differentially Private Conformal Prediction (DPCP), a fully private procedure that combines DP model training with a private quantile mechanism for calibration. We establish the end-to-end privacy guarantee of DPCP and investigate its coverage properties under additional regularity conditions. We further study the efficiency of both differential CP and DPCP under empirical risk minimization and general regression models, showing that DPCP can produce tighter prediction sets than existing private split conformal approaches under the same privacy budget. Numerical experiments on synthetic and real datasets demonstrate the practical effectiveness of the proposed methods.

翻译：保形预测（CP）作为一种通过预测集进行不确定性量化的简单灵活框架，已获得广泛关注。本文研究如何在满足差分隐私（DP）约束下以统计高效的方式部署保形预测。我们首先引入差分保形预测——一种无需数据分割的保形方法，该方法避免了数据分割导致的效率损失，并充当了理想保形预测与私有保形推断之间的桥梁。通过利用差分隐私机制的稳定性特性，差分保形预测建立了与理想保形预测的直接关联，并继承了相应的有效性行为。基于这一思想，我们开发了差分隐私保形预测（DPCP），这是一种完全私有的方法，它将差分隐私模型训练与用于校准的私有分位数机制相结合。我们建立了DPCP的端到端隐私保证，并在附加正则性条件下研究了其覆盖性质。我们进一步研究了经验风险最小化和一般回归模型下差分保形预测与DPCP的效率，表明在相同隐私预算下，DPCP能比现有私有分割保形方法产生更紧致的预测集。在合成数据集与真实数据集上的数值实验验证了所提方法的实际有效性。