标题： 用于隐私保护机器学习的共形预测 显示英文标题

标题： Conformal Prediction for Privacy-Preserving Machine Learning

摘要： 我们研究将共形预测（CP）与确定性加密数据上的监督学习相结合，旨在弥合严格的不确定性量化与隐私保护机器学习之间的差距。 使用MNIST数据集的AES加密变体，我们证明了即使直接在加密域中应用，CP方法仍然有效，这是由于固定密钥加密下数据交换性的保持。 我们测试了基于$p$值的传统与基于$e$值的共形预测器。 我们的实证评估表明，训练于确定性加密数据上的模型仍能提取有意义的结构，达到36.88%的测试准确率——明显高于每个实例加密时观察到的随机猜测（9.56%）。 此外， 基于$e$值的CP在4.3损失阈值校准下实现了超过60%的预测集覆盖，正确捕捉到了5000个测试案例中的4888个真实标签。 相比之下，基于$p$值的CP产生了更小的预测集，但覆盖准确性有所降低。 这些发现突显了在加密数据环境下CP的潜力和局限性，并强调了预测集紧凑性与可靠性之间的关键权衡。 %我们的工作为安全、隐私感知学习系统中的原则性不确定性量化奠定了基础。 显示英文摘要

摘要： We investigate the integration of Conformal Prediction (CP) with supervised learning on deterministically encrypted data, aiming to bridge the gap between rigorous uncertainty quantification and privacy-preserving machine learning. Using AES-encrypted variants of the MNIST dataset, we demonstrate that CP methods remain effective even when applied directly in the encrypted domain, owing to the preservation of data exchangeability under fixed-key encryption. We test traditional $p$-value-based against $e$-value-based conformal predictors. Our empirical evaluation reveals that models trained on deterministically encrypted data retain the ability to extract meaningful structure, achieving 36.88\% test accuracy -- significantly above random guessing (9.56\%) observed with per-instance encryption. Moreover, $e$-value-based CP achieves predictive set coverage of over 60\% with 4.3 loss-threshold calibration, correctly capturing the true label in 4888 out of 5000 test cases. In contrast, the $p$-value-based CP yields smaller predictive sets but with reduced coverage accuracy. These findings highlight both the promise and limitations of CP in encrypted data settings and underscore critical trade-offs between prediction set compactness and reliability. %Our work sets a foundation for principled uncertainty quantification in secure, privacy-aware learning systems.