提出隐私保护下的紧致预测集方法，提升数据隐私与预测精度的平衡。
Differentially Private Conformal Prediction
- 基于差分隐私机制设计非拆分校准流程，避免数据分割损失效率。
- 在相同隐私预算下，预测集比现有方法更紧凑，覆盖概率仍可靠。
- 适合注重隐私且需高精度不确定性量化的研究者使用。
共形预测（CP）作为一种灵活的不确定性量化框架，通过预测集形式获得广泛关注。本文研究如何在差分隐私（DP）约束下高效部署共形预测。首先提出差分共形预测（Differential CP），一种无需数据分割的共形推断方法，克服了数据分割带来的效率损失，并建立与理想共形预测之间的桥梁。利用差分隐私机制的稳定性特性，该方法直接连接到理想共形预测，继承其有效性。在此基础上，构建完全私有的差分私有共形预测（DPCP）方法，结合差分私有模型训练与私有分位数校准机制。本文建立了DPCP的端到端隐私保证，并在额外正则条件下分析其覆盖率性质。进一步在经验风险最小化与一般回归模型下评估Differential CP与DPCP的效率，结果表明，在相同隐私预算下，DPCP生成的预测集比现有私有分段共形方法更紧致。在合成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。
原文摘要 · Abstract (English)
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.
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