arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.06404cs.CRcs.PL
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差分隐私方案的判定准确性

Deciding Accuracy of Differential Privacy Schemes

Gilles Barthe, Rohit Chadha, Paul Krogmeier, A. Prasad Sistla, Mahesh Viswanathan

摘要:

差分隐私是一个数学框架,用于开发具有可证明的隐私和准确性保证的统计计算。与差分隐私的隐私组件(具有明确的数学和直观含义)相反,差分隐私的准确性组件没有普遍接受的定义;差分隐私算法的准确性声明因算法而异,并且不是一般定义的实例。我们将程序不连续性确定为现有\emph{ad hoc}定义中的一个共同主题,并引入另一种精度概念,该精度由我们称为{ \distance}的参数化-输入$x$的{ \distance} w.r.t.,确定性计算$f$和距离$d$,是所有$y$上的最小距离$d(x,y)$,使得$f(y)\neq f(x)$。我们表明,我们的准确性的概念包含在理论计算机科学中使用的定义,并捕捉已知的准确性索赔差分隐私算法。事实上,我们对准确性的一般概念有助于我们在某些情况下证明更好的主张。接下来,我们研究了准确性的可判定性。我们首先表明,准确性一般是不可判定的。然后,我们定义了一个非平凡类的概率计算的准确性是可判定的(无条件地,或假设Schanuel猜想)。我们实现我们的决策过程和实验评估我们的方法的有效性,从文献中常见的算法的准确性生成证明或反例。

英文摘要:

Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing \emph{ad hoc} definitions and introduce an alternative notion of accuracy parametrized by, what we call, {\distance} -- the {\distance} of an input $x$ w.r.t., a deterministic computation $f$ and a distance $d$, is the minimal distance $d(x,y)$ over all $y$ such that $f(y)\neq f(x)$. We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuel's conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature.

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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