arXiv:2602.10228cs.LG2026-02

根据任务需求智能分配隐私预算,生成更准确的合成数据。

PRISM: Differentially Private Synthetic Data with Structure-Aware Budget Allocation for Prediction

  • 按预测任务结构分三类:因果、图模型、无结构,针对性选特征。
  • 在分布偏移下,因果特征选择使AUC达0.73,远超随机水平0.49。
  • 适合需高精度预测且关注隐私保护的数据发布场景。

差分隐私(DP)为数据发布提供数学保障,限制攻击者对个体信息的推断。然而,实现该保护通常需加噪,且当测量大量统计量时噪声会累积。现有差分隐私合成数据方法对所有特征一视同仁,均匀分配噪声,忽视了具体预测任务的需求。本文提出以预测为中心的方法——PRISM,依据结构知识分三种情形:在因果情形下,若已知目标变量Y的因果父节点且存在分布偏移,则聚焦于这些父节点以增强鲁棒性;在图模型情形下,若已知贝叶斯网络结构且分布稳定,目标变量的马尔可夫毯即为最优预测特征集;在预测情形下,当无结构知识时,通过差分隐私方法筛选特征,不声称恢复因果或图结构。PRISM机制包括:(i) 根据相应情形识别预测特征子集;(ii) 构建针对性摘要统计量;(iii) 分配预算以最小化预测误差上界;(iv) 基于图模型推断生成合成数据。理论证明了端到端隐私保证与风险边界。实验表明,任务感知预算分配显著提升预测精度,在分布偏移下,针对因果父节点的策略达到AUC≈0.73,而基于相关性的选择退化至随机水平≈0.49。

原文摘要 · Abstract (English)

Differential privacy (DP) provides a mathematical guarantee limiting what an adversary can learn about any individual from released data. However, achieving this protection typically requires adding noise, and noise can accumulate when many statistics are measured. Existing DP synthetic data methods treat all features symmetrically, spreading noise uniformly even when the data will serve a specific prediction task. We develop a prediction-centric approach operating in three regimes depending on available structural knowledge. In the causal regime, when the causal parents of $Y$ are known and distribution shift is expected, we target the parents for robustness. In the graphical regime, when a Bayesian network structure is available and the distribution is stable, the Markov blanket of $Y$ provides a sufficient feature set for optimal prediction. In the predictive regime, when no structural knowledge exists, we select features via differentially private methods without claiming to recover causal or graphical structure. We formalize this as PRISM, a mechanism that (i) identifies a predictive feature subset according to the appropriate regime, (ii) constructs targeted summary statistics, (iii) allocates budget to minimize an upper bound on prediction error, and (iv) synthesizes data via graphical-model inference. We prove end-to-end privacy guarantees and risk bounds. Empirically, task-aware allocation improves prediction accuracy compared to generic synthesizers. Under distribution shift, targeting causal parents achieves AUC $\approx 0.73$ while correlation-based selection collapses to chance ($\approx 0.49$).

差分隐私合成数据预测优化

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