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arXiv 2602.05219cs.LG

通过收缩实现隐私预测

Private Prediction via Shrinkage

Department of Computer Science, Georgetown University(计算机科学系,乔治城大学)

Chao Yan

AI总结:

该研究提出了一种在流式设置中通过收缩方法实现差分隐私预测的算法,针对不同的对手类型和概念类,给出了不同数量的带标签样本需求。

摘要:

我们研究了Dwork和Feldman(COLT 2018)引入的差分隐私预测:一个算法接收一个带标签的样本集S,然后在回答一系列无标签查询时,输出记录必须相对于S保持(ε,δ)-差分隐私。标准组合方法导致T次查询的依赖关系为√T。我们证明在流式设置中,这种依赖关系可以降低到T的对数多项式。对于一个无意识的在线对手和任何概念类C,我们给出一个私有预测器,能够用|S|=~O(VC(C)^{3.5}log^{3.5}T)个带标签的示例回答T次查询。对于一个适应性的在线对手和R^d上的半空间,我们得到|S|=~O(d^{5.5}logT)。

英文摘要:

We study differentially private prediction introduced by Dwork and Feldman (COLT 2018): an algorithm receives one labeled sample set $S$ and then answers a stream of unlabeled queries while the output transcript remains $(\varepsilon,δ)$-differentially private with respect to $S$. Standard composition yields a $\sqrt{T}$ dependence for $T$ queries. We show that this dependence can be reduced to polylogarithmic in $T$ in streaming settings. For an oblivious online adversary and any concept class $\mathcal{C}$, we give a private predictor that answers $T$ queries with $|S|= \tilde{O}(VC(\mathcal{C})^{3.5}\log^{3.5}T)$ labeled examples. For an adaptive online adversary and halfspaces over $\mathbb{R}^d$, we obtain $|S|=\tilde{O}\left(d^{5.5}\log T\right)$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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